Split (1)

train · ~1.24B rows (showing the first 1.67M)

text stringlengths 8 1.01M
Designed to meet the Common Core requirements of the University of London Syllabus B, and other similar schemes offered by the major boards, this book incorporates both modern and effective traditional approaches to mathematical understanding. Worked examples and exercises support the text. An ELBS/LPBB edition is AS and A Level Modular Mathematics Core Motivating readers by making maths easier to learn, this work includes complete past exam papers and student friendly worked solutions which build up to practice questions, for all round exam preparation. It also includes a Live Text CDROM which ... Edexcel AS and A Level Modular Mathematics: Core Presenting worked examples and solutions leading to practice questions, this helps students to learn maths. It features sample past exam papers for exam preparation, and includes regular review sections. It includes a CD ROM which contains what students need ... Revise Edexcel AS and A Level Modular Mathematics Help your students push for the top grades with these focused Revision Guides! Ideal for use alongside the Student Books, they provide worked exam questions, and and hints and tips for focussed revision. .
Product Description Saxon Math 7/6 will help middle-school students gain a solid foundation of algebraic reasoning and geometric skills as they prepare to move on to higher-level math. Rigorous and methodologically proven, math is taught through incremental development of new material and continual review of the old, along with in-depth "investigations." Following Saxon Math 6/5, concepts such as functions and coordinate graphing, integers, exponential expressions, and prime factorization are introduced. Lessons contain a warm-up, introduction to new concepts, lesson practice where the new skill is practiced, and mixed practice, which is comprised of old and new problems. Designed for students in Grade 6, or Grade 7Saxon Math 76 Home Study Kit Fourth Edition 4.9 5 43 43 Excellent! Love this curriculum! I discovered in when I was working in Juvenile Detention Center and was amazed at the results I saw with teens that had significant learning disabilities, hated school, and of course math! After couple of weeks on this curriculum, most were making A's and the confidence they were getting, reflected on their behavior. Now I use it on my kids and they love it, although my daughter is disappointed that I am making her start at a lower level, but public school math left so many holes, that we are doing alot of back work before we can successfully move forward. Thank you Saxon! November 12, 2013 Love It!! There is no better Math text than the Saxon series. I introduced it in the 1980's in the Christian high school were our two older daughters were in my class. I have never seen anything to rival the approach Saxon takes. I have a Masters Degree in Teaching Math and enough years of teaching all levels and courses from K-12 and tutoring teens and adults through college and graduate school. The Saxon approach is where the rubber meets the road for giving a student the best foundation and tools for success in any field of study and just plain old everyday life. You will not find a Saxon student who grows up to hate Math. They will be the parents who love to help their kids with homework problems, too. September 12, 2013 Do you want your child overly prepared? The Saxon Curriculum prepares your child years above their public school counterparts. After Algebra II in this program for my daughter I put her in public school for Advanced Math. She was so far ahead of where they were and where they were going that I pulled her out and ordered Saxon Advanced Math for her to complete at home. The curriculum prepares our children far ahead of the same curriculum taught elsewhere. You will not be disappointed. I will never stray again. My daughter is now in Calculus in the College and my son will be following in her footsteps because of Saxon. April 24, 2013
Mathematical Applications for the ManagementATHEMATICAL APPLICATIONS FOR THE MANAGEMENT, LIFE, AND SOCIAL SCIENCES, 9th EDITION is intended for a two-semester applied calculus or combined finite mathematics and applied calculus course. The book's concept-based approach, multiple presentation methods, and interesting and relevant applications keep students who typically take the course—business, economics, life sciences, and social sciences majors— Ninth Edition is a brief review of algebra to prepare students with different backgrounds for the material in later chapters.
I have found that while student graphing calculators have become powerful tools not only for advanced math, but for determining derivatives (and integrals!), having those tools available where the results can be put up on a larger screen, or where multiple lines can be displayed in color. I recently came across where there is a collection of such calculators. While neither WyzAnt or I can guarantee all the calculators will (or will continue to) work as the site describes, I have recently been using the definite integral and graphing calculator, which produced nice, clear & colorful results, which helped clarify a problem we were having with an otherwise very functional black-and-white graphing calculator. A word to the wise, the online calculators typically require very specific methods of entering functions. For example these calculators often require extra parentheses () or symbols. For example, if I wrote 5 cos 4x, you would assume... read more It is often examples that make ideas understandable to students and current events can be a good source of examples. Case in point. Today in Wisconsin, the issue of the day is the outcome of the recall elections and problems with the exit polling. As a tutor, the outcome isn't interesting, but exit polling like all surveys is key to the usefulness of statistics! In fact, it gives a great opportunity to illustrate some of the basic (and non-mathematical) ideas and concepts of statistics — usually the ideas presented at the beginning of most introduction-to-statistics courses. Statistical inferences are grounded in some basic definitions and assumptions (in bold). A population is a defined collection of individuals that we want to know some data about and a sample is a group taken from the population that we are going to actually collect data from (Sullivan, 2010, p. 5; Triola, 2010, p. 4). If we wanted to know the actual data about a population, which is called a parameter,... read more I've been working recently with a student who "presented" as a student struggling with physics. But in many ways, the physics is less of an issue than applying mathematics to the physics concepts. Their text is Glencoe's Physics Principles and Problems, which some reviewers describe as much as a math text as a science text. After helping with several chapters of homework, I would say that the problems at the end of each section or chapter tend to focus on those where mathematics can be applied to the physics, and that as a result if the tests are based upon those questions, the test will be as much a test of the student's understanding of the mathematics as their knowledge of the science. In many ways, it was the time consuming nature of the mathematics that was creating problems for the student. This is not an uncommon phenomenon in that the development of math allows for new models of science, or that scientific theories require mathematical descriptions of the phenomenon... read more Mark Twain is often credited as saying that there are "lies, damn lies, and statistics" but as someone who tutors in statistics, I see it more as there are people who tell lies and lies with statistics. Statistics themselves are only numbers, and while calculations can be mistaken, the wrong formulas can be used and yes numbers can be used to mislead people; the numbers themselves do not lie. The problem for most people with statistics is that it is an unusual way to think about and manipulate numbers. This week, I have been helping a student better understand the implications of an average of a sample, also referred to as the mean in order to prepare for an upcoming standardized test. Generally, a sample consists of individuals 1, 2, 3, …, n, who each have some numerical characteristic x1, x2, x3, …, xn. For example, a sample of individual's resting heart rate (measured in beats per minute, bpm) could be as follows: Individual 1 has a rate of 43 bpm, 2 has 47,... read more Particularly with regards to standardized tests, the test makers are not only testing for competency, which could be tested with straightforward questions, but are also testing for excellence, to separate out each test taker by their percentile rank, and to sort among percentiles the difference between Top 20%, Top 10%, Top 5%, Top 1%, and even to smaller units. Thus, test makers often use not only the problem, but they often use a non-standard or non-intuitive presentation of the information and often deliberately pick potential answers that either mislead the test taker or that confirm a common mistake that test takers might make. But this effort is also a test taker's biggest advantage and opportunity. An ambush is not an ambush if the person being ambushed knows about it ahead of time. Thus, when preparing for and taking standardized tests, the test taker should be on the lookout for non-standard presentations of questions, and be weary of selecting an obvious or... read more For most people, solving a problem or a question is not difficult if they have a model to follow and the correct data to plug into the model. Take one of the most basic functions, paying for something at a cash register. If the cashier tells you the Happy Meal costs (with tax) $4.23, and you hand the cashier a $10.00 bill, I suspect that most cashiers will give and most people will expect their $5.77 in change. Oh, you can confuse people and make the problem more difficult (7 dimes, a nickel and two pennies, rather than 3 quarters and two pennies), but these are just "tricks." This works, because for the vast majority of people, this is an "ordinary" occurrence something we've either done or witnessed hundreds of times, and we can intuitively extend our addition and subtraction rules to a new problem. Unfortunately, most classroom topics are taught like the math example above using clear, intuitive, and easily understood examples, but tested using confusing tricks to... read more A growing area of educational thought is reconsidering the pros and cons of single-sex education, i.e. all-male or all-female schools. In Madison this week, the president and CEO of the Madison Urban League proposed opening an all-male school for grades 6-9 aimed at African-American students (Troller, 2010). The hope is that such a school can take advantage of the ways that young men learn differently from young women and provide dedicated adult-male support that young men who often lack such support need (Troller, 2010). Obviously, this idea raises issues about the history of racial segregation, the fight for integrated schools, and the challenge of civil rights for people of all races in the United States. But single-sex education is not solely a desire for more all-male schools, rather there is a movement towards creating more all-female schools as well (Meehan, 2007). As Meehan (2007) observes, girls behave and learn differently in the classroom, and as a result... read more Often students are confused with variables: those x's, y's, z's and other letters that begin to replace numbers beginning in algebra and continuing on into geometry, algebra II, Trigonometry, Precalculus, and Calculus. While there are several aspects to variables, one of the best ways to start is to understand a variable as a placeholder for a number. Take the equation: 7 + 3 = 10. Inserting x into this equation for the number 3 produces the "same" equation 7 + x = 10. Yet this equation also shows how a variable is "defined" in that x must equal 3 for the equation to work. More often variables are defined, however, not by a specific number, but with an idea that covers either a to-be-determined range of numbers or an as yet unknown number. Try this example. Suppose I go to the store planning to put a cheese and cracker tray together for an upcoming football game. I have 24oz. of cheese and 28oz. of crackers and I expect each person to eat 4 oz. of cheese and they need... read more
Mathematics Faculty Student projects In the Department of Mathematics, we seek to engage students in activities and projects that they find of particular interest. This gives students the opportunity to delve more deeply into mathematical ideas. The simple answer is: you like mathematics and/or you are good at it. However, you may have other more practical concerns such as: "what can I do with a math major?" or "will I be able to make a living?"
where your votes shape what the world is talking about. Not from personal experience. Tao's notes are my first exposure to analysis, and I'm not even quite finished with analysis I. I've also used Abbott's Understanding Analysis as supplementary reading, but that book is more expensive than Dover's offerings. Shilov's Elementary Real and Complex Analysis looks like it might be good (although the Kindle version in the book preview is pretty hideous). Actually, now I'm considering replacing Abbott with Shilov, which would make this the second Shilov text I'm using as a supplement (the other being his Linear Algebra book). It does appear to follow the definition-proof-theorem format pretty consistently; whether that's a good thing is largely a matter of personal taste. I like using this sort of book as a supplement rather than a primary text (at least at this stage). I think it's worth noting that I've looked at several open and/or free texts, and, for the most part, their quality hasn't caught up with the best print texts. That said, there are a few free resources out there that I quite like. MIT OCW's Mathematics for Computer Science is basically a discrete math course and is quite good (there are a few other offerings of this course available here; the course number is 18.062J). I'm also fond of Terence Tao's undergraduate real analysis notes (and Real Analysis II). But these are essentially a first draft, and there are quite a few errors present. Since he published a cleaned-up version in (not free) book form, it's unlikely they will ever be corrected. If you want to purchase the book, I'd either wait for the third edition or print a copy of this errata page for the first volume and this one for the second. Note that Tao's approach in the first course is quite idiosyncratic; he starts from the Peano axioms and spends quite a bit of time (the first two weeks) working up to a construction of a real number system. Personally, I found it to be good practice with induction, and it helped me more confidently apply algebraic knowledge from school appropriately. But these topics are not real analysis proper. He also doesn't shy away from atypical definitions (some of which are not equivalent to standard definitions), but after working through the course, you should have attained sufficient mathematical maturity to adjust as is necessary. It's also worth mentioning that, even though they're not free or open source, Dover has published quite a few excellent texts which are about $4-12 on Amazon. The best way to prepare for university math is to start doing it. With math the bulk of learning occurs by doing problems; proceeding in this way should quickly eliminate any qualms about large workloads. - This is an excellent starting point; Carnegie-Mellon has done an excellent job here eliminating the tedium of carrying out a detailed propositional proof while still requiring the relevant thought processes. Many math students never take a course in logic proper (although undergraduate textbooks tend to include material regarding logic and set theory in the first chapter, so that students see it several times by the time they graduate), but the natural deduction approach used here is quite intuitive and mirrors the proof structure of basic mathematical arguments. - This is a transition course. If a university offers such a course, students typically take a course like this before moving on to courses which consist mostly of math majors and for which the bulk of the assignments involve proving some assertion. Personally, I don't see the point of delaying this material; even though elementary calculus courses tend to de-emphasize theory in favor of techniques for solving "real-world" problems, facility with basic proof techniques can make the subject more rewarding for a student of mathematics. Some well-reviewed alternatives (which I have either read only in part or not at all) include: Finally, here's an extremely accessible introduction to abstract algebra which could reasonably be read alongside a transition course. Pinter does an excellent job carefully guiding students through problems. Once you have one or two theory driven courses under your belt, you could probably handle a more advanced text, but this is a lovely little book in any case. When I'm using electronic materials, I tend to extract and print the core material (mostly just definitions and theorems) using a snipping tool and word processor; then, I annotate that while reading and keep it in a folder. I find that the brevity often makes for more efficient reference than the text itself. Of course, there's no one right way to self-study, but this works pretty well for me. But without defining "rule," the second definition is too imprecise to really determine equivalence (although it's not particularly uncommon). Munkres essentially defines a 'rule of assignment' as a subset of a Cartesian product AxB like that of the first definition; then, he defines a function as a rule of assignment paired with a codomain containing B. This definition is similar to the first, except we formally distinguish functions with different codomains defined by the same subset of a Cartesian product AxB. But it certainly doesn't correspond with the way that I would be inclined think of a rule when the term is presented without definition. A proof really depends on your starting point. Most real analysis texts (at least the ones I've seen so far) start with the assumption that the real numbers are a complete ordered field. In this case, as other posters have mentioned, a field is by definition closed under addition, multiplication, and negation, and so it follows immediately that we can define a function f(x)=4-x2 on the whole set of real numbers. It turns out to be possible to start with axioms for set theory and to (slowly) show that the existence of a complete ordered field (which we identify as the real numbers) is a consequence. In this case, we work up to the rationals and show that they form an ordered field; then, we construct the real numbers as equivalence classes of either Cauchy sequences of rationals or Dedekind cuts. Then, we have to define what it means to add, multiply, and negate real numbers and show that these operations are well-defined (they never take us out of the reals). As for your question, as simplectic mentioned, the typical definition of a function really allows us to choose any domain we want, provided the function is well-defined on its entire domain. In this terminology, the question is really asking for the maximum possible domain for a function f defined by the rule f(x)=4-x2, and, from the above discussion, you are correct that this function can be defined on all of R. But asserting that it is true by definition might not be very convincing, and starting from the ZF axioms would certainly be overkill. You might be better off asking what values the function might take outside of the teacher's suggested domain (for example, f(5)=-21). Actually, it just dawned on me that the image set of this function (i.e., the range, although range is sometimes defined to mean something slightly different) is the interval (-∞,4]. Is it possible the teacher meant to ask for the range? The page for the GRE math subject test provides a pretty good listing of the core areas that most math undergraduates study. Here's a basic listing of the courses associated with this material, starting with those most likely to be required by a university: single- and multivariable calculus, differential equations, linear algebra, real analysis, abstract algebra, discrete mathematics, complex analysis, topology. This list is far from exhaustive, but I think it captures most of the basics. Textbooks will be difficult to avoid. There are a lot of free materials out there, but the best materials are still largely in print. Amazon reviews and reference requests from Math Stack Exchange are good resources for narrowing down a textbook search. The best (legal) place to finalize your search is a university library. As others have mentioned, working through a math text is quite time-consuming, and you'll likely find the experience more pleasant if you choose materials which you enjoy reading. One issue you may encounter is that textbook problem sets tend to be massive (although there are exceptions); this is so that professors have a lot of choices when assigning problems from the text. But for a student learning the material for the first time, it's difficult to choose a decent sample of problems. Instead of trying to work them all, search for course pages from courses which used your selected text and do any problems which were assigned or recommended. One very important thing to remember is that human memory is fragile; keep well-organized notebooks for review. Some good notebook fodder includes definitions and theorems, copies of problem sets, and well-written solutions (think of scratch work as a rough draft). Finally, transition courses can be quite helpful when starting with proof-based math. I quite like Carnegie-Mellon OLI's Logic and Proofs for a relatively gentle introduction to propositional logic followed by the Saylor Foundation's Introduction to Mathematical Reasoning. There's no reason to wait until you start a degree program to start studying math if you think you might be interested. The Internet era has made education extremely accessible, and math as a field has adapted to this shift more than almost any other (with the possible exceptions of computer science and software engineering). Of course, you won't get a degree self-studying. But the ability to choose your own pedagogical approach is quite powerful (although it does require considerable effort), and if you do end up pursuing a degree, it certainly doesn't hurt to have seen some of the material beforehand. Here are a few things that I've found helpful over the past few months: Use course prerequisites as general guidelines for determining what order to study things (although often course requirements are simply there to ensure that students have the appropriate level of "mathematical maturity" before registering for a particular course and are not strictly necessary). Many mathematics educators seem to be of the opinion that a course in mathematical logic in particular is unimportant and that students can pick it up as they work through standard course material. Although I do agree that an axiomatic treatment of logic is not particularly enlightening for someone studying math, I found Carnegie-Mellon OLI's Logic & Proofs course (which uses the 'natural deduction' approach) to be extremely helpful. Although the free material only covers propositional logic, transitioning to predicate logic is not particularly difficult. A transition course is very helpful making the move into more theoretical coursework. I used this one, but I've heard good things about Keith Devlin's Coursera course and about this book. I like to find a textbook that I like, then find a course page from a university with a well-regarded math program which uses that book as a guide for problem selection. Amazon reviews as well as the advice of people on Math StackExchange are my favored resources for finding good books. You also may find it helpful to read a few texts/lecture notes on the same topic, but I prefer to choose one primary resource and to use the others for concurrent review. After covering foundations at an introductory level, try to work through a few different subjects simultaneously. When I'm stuck on a particular problem, sometimes it's helpful to just set it aside and work on something else for a bit. Often, when I turn back to the problem, I find that I have some insight into how to approach it that actively working on it did not produce. From what I've read, Euclid's actual proof structure is slightly different. The difference is pretty subtle, but this is the way I've seen it a few times: Consider be any finite collection of primes; we will call this collection S. Label the primes in S as above (in your post) and define pp similarly. Consider the (exhaustive) cases wherein pp + 1 either is or is not prime. If it is prime, obviously it is a prime which is not in S. If it is not prime, then it is a product of primes. Since none of the primes in the collection can be factors of pp + 1 (as you have shown), it must have some prime factors not in the collection. In either case, the (arbitrary) finite collection of primes does not contain every prime. Thus, we have shown that no finite collection of primes can contain all of the primes, and it follows that the set of all primes cannot be finite. The main difference is that Euclid does not argue (directly) by contradiction[1] . But although the absence of argument by contradiction might be easier to digest, I think need to understand the idea of reasoning about arbitrary mathematical objects may be the reason I more commonly see it presented via the contradiction route. [1] Let P be the set of primes, and let S be a subset of P. "If S is finite, then S does not equal P" is the contrapositive of "If S equals P, then S is infinite," so these statements are logically equivalent. ∧ (which is what is meant by ^ here) actually generally stands for 'and' (i.e., logical conjunction). If we're allowing ourselves to use the shorthand wherein we attach set existence to a variable following 'there exists' or 'for all', we can write more briefly ∃x∈Z . ∀y∈Z. (y>0 => x≤y). Hereafter, I will write 'and' for conjunction, 'or' for disjunction, and 'not' for negation. If we translate back into the long way of writing it, the typical way of doing so gives ∃x. (x∈Z and ∀y. (y∈Z => (y>0 => x≤y)). But A => (B => C) is propositionally equivalent to (A and B) => C[1] , so this is the same as saying ∃x. (x∈Z and ∀y. ((y∈Z and y>0) => x≤y)) or ∃x∈Z. ∀y. ((y∈Z and y>0) => x≤y), as above. [1] I use ~ to mean 'is equivalent to'. A => (B => C) ~ (not A) or (B => C) ~ (not A) or (not B or C) ~ (not A or not B) or C ~ (not (A and B)) or C ~ (A and B) => C. =v= The below is not standard (as far as I know). =v= As an aside, we could allow ourselves to write ∀y. (P(y) => Q(y)) as ∀P(y). Q(y) and we could write ∃y. (P(y) and Q(y)) as ∃P(y). Q(y) for any statements P(a) and Q(a); this is consistent with the manner in which we often attach set membership to quantified variables. Then we could rewrite the assertion as ∃x∈Z . ∀(y∈Z and y>0). x≤y. This sort of notation has the advantage that it suggests that we can ignore the stuff next to the quantifier when we're determining the negation through the mechanical process of flipping quantifiers and negating the inner expression (I find that sometimes writing a pseudo-formal expression makes it easier to carry out the process of negation in practice). And indeed we can. Consider the negation of ∀P(y). Q(y). The proof is actually showing that every function from the natural numbers to the real open interval (0,1) fails to map to every element of (0,1). I wouldn't worry too much about it right now; Cantor's diagonalization proof is a common example when introducing things because it has a nice intuitive interpretation, but any proof you see at this stage will necessarily be sketchy or will use ideas you have yet to encounter. In the post I'm replying to, T is not R. Consider the function g:N->T defined by g(1) = y and g(n) = f(n-1) if n > 1. If f maps to every element of S, then g maps to every element of T = S U {y}. The point is that since f is arbitrary, every function from N to R fails to map to at least one element, so no such function can be a one-to-one correspondence. It actually turns out that there are uncountably many elements that any function from N to R fails to map to, but that isn't necessary to obtain the desired result here. We can, however, find sets larger than the natural numbers that are the same size as the real numbers. The power set of the natural numbers is one, but a proof isn't easy. For ratios, you are comparing relative values. Imagine you have three rulers of the following lengths: ruler 1 is one foot long, ruler 2 is two feet long, and ruler 3 is three feet long. Then we might express the ratio of ruler 1:ruler 2:ruler 3 as 1:2:3. Or we could measure them in inches and express the ratio as 12:24:36. Or in yards as (1/3):(2/3):1. Notice that in each case, all of the numbers are being scaled by the same value. Your given example 2:3:x = 1:4:6 doesn't actually work because 1=2(1/2) while 4=3(4/3). You can find a scaling factor for converting the first ratio into the second by comparing terms in the same location. For example, consider 2:3:x=x:5:y from your original post. 3 and 5 are given second terms in each, so we need to find some number that we multiply by 3 to get 5. If 3a=5, then a=5/3. Then we must multiply every term in the first ratio by 5/3 to determine the second, so that x=2(5/3)=10/3 and y=x(5/3)=(10/3)(5/3)=50/9. For anyone else reading, about 15% of the population is black, and about 16% of homicides against white people are committed by non-whites. The reason I didn't address Blawraw so explicitly is because he/she is clearly just trying to justify being racist, and engaging in the first place was a mistake. It's irrelevant. Applying the same sort of reasoning to a myriad of other individual statistics leads to all sorts of wacky conclusions. But even in this case, all you have shown is that it's approximately proportional. In any case, I'm not interested in getting somewhere; debating the statistical merits of racism is astoundingly dumb (as was reading the front page of reddit without first logging in). If you push the statistical line of reasoning far enough, it becomes clear that you should be more afraid of your friends and family members than anyone else, and the argument for so-called "statistical stereotyping" kind of falls apart. Okay, what the fuck. There's an article on the Daily Mail's website that (rightfully) calls the creepshots subreddit "disgusting" and "vile"...but then they illustrate with a fucking creepshot right in the middle of the article. I won't link to the article, but here's twoblog posts on some blog called Tabloid Watch about a possibly different article with pictures removed. =( Don't give up. Your algebra needs some work, and I would recommend putting off university maths until later. But it's never too late to learn. Studying maths outside of the context of a formal education institution can be much more rewarding, and the quality and quantity of freely available resources are constantly improving. [Note: I use letter superscripts such as[X] below to indicate a footnote. I recommend not reading them until the end.] Before I go into the formalities, I think some intuition about what these statements are saying is in order. I will only consider problem (i). Write the statement as P(n) = 2\|(n2 - n). Let's consider what this statement is saying about the first few nonnegative integers. You have already correctly shown that P(0) is true. Consider: P(1) = 2\|(12 - 1) = 2\|0 P(2) = 2\|(22 - 2) = 2\|(4 - 2) = 2\|2 P(3) = 2\|(32 - 3) = 2\|(9 - 3) = 2\|6. Clearly, each of these is true, but we want to prove that P(n) is true for any nonnegative integer n. This is where induction comes into play; here is the general idea. Given some statement P(n) about nonnegative integers: (1) Base case: You prove that P(0) is true. (2) Inductive step: You prove that if P(k) holds for any nonnegative integer k, then it follows that P(k+1) holds. Then, since P(k) implies P(k+1) for any k, we have P(0) implies P(1), P(1) implies P(2), and so on. Since we have already proven P(0), we can follow the chain of implications to arrive at P(n) for any n. Informally, since we have P(0) and [P(0) implies P(1)], we conclude that P(1) holds. Then, since we have P(1) and [P(1) implies P(2)], we conclude that P(2) holds, and so on. The proof structure for the inductive step is somewhat complicated for a student facing proofs for the first time.[A] There are two basic assumptions you make: (a) You assume that k is a nonnegative integer (but not any particular nonnegative integer). Hence, we are only allowed to use properties that hold for any nonnegative integer to prove statements about k, and anything we can prove about k must hold for any nonnegative integer. (b) For an inductive proof, the statement that we want to prove about k is that P(k) implies P(k+1). So we assume that P(k) is true [with (i), this is the statement 2\|(k2 - k)], and, in the context of this assumption, we prove P(k+1).[B] Note that, although this can be a legitimate approach, we do not necessarily manipulate P(k) to arrive at P(k+1). Rather, we attempt to prove P(k+1), and we are permitted to use our assumption that P(k) holds as part of the proof. Now, returning to problem (i), let's attempt to carry out this procedure. (1) Base case: You have already shown P(0). (2) Inductive step: Assume P(k) for some arbitrary nonnegative integer k; i.e., 2\|(k2 - k).[C] Now you want to show P(k+1). This is the statement 2\|((k+1)2 - (k+1)). We're most of the way there, so I'll give one more hint and leave the rest to you. Try to algebraically manipulate the expression (k+1)2 - (k+1) so that it is the sum of the expression (k2 - k) from the inductive hypothesis and some other term or terms that must necessarily be divisible by 2. [A] Depending on your background, you may find it helpful to review propositional and predicate logic in more detail than is typically covered at the beginning of an undergraduate course in discrete maths. I highly recommend Carnegie Mellon OLI's course in propositional logic for the former. [B] This proof pattern for implications works because the only situation in which an implication of the form A implies B is false is when A is true and B is false. Hence, if we can show that B must be true when A is true, the implication always holds. [C] If your course has defined divisibility more formally, this means k2 - k = 2p for some integer p, and you want to show that (k+1)2 - (k+1) = 2q for some integer q. Use the fact that integers are closed under addition and multiplication -- that is, if you add or multiply two integers, you get another integer.
Concepts of Calculus with Applications KEY BENEFITS Martha Goshaw's Concepts of Calculus with Applications is the next generation of calculus textbook for the next generation of students ...Show synopsisKEY BENEFITS Martha Goshaw's Concepts of Calculus with Applications is the next generation of calculus textbook for the next generation of students and instructors. Martha is a new kind of textbook author, drawing from her many successful years in the classroom to bring calculus to life. This text is written in Martha's natural classroom voice, using a cheerful, student-friendly presentation to engage non-majors in the modern applied calculus course. With her deep knowledge of how students think and study, Martha's approach helps students with every homework assignment and exam, with ample algebra review before every topic and multiple types of study tools. Now for the first time ever, MyMathLab(R) makes available a wide array of online homework, tutorial, and assessment tools, making the most of both students' and instructors' time. KEY TOPICS Function review, Limits and Derivatives, Applications of the Derivative, The Integral and its Applications, Multivariable Calculus. MARKET For all readers interested in Calculus
Grade 8 Math Worksheets Geometry gets much more difficult at this level. Algebra begins to take part in the mix and is expected to be understood. Three step problems become common place and are required to complete the majority of the problem types that you will encounter. Functions become very routine and students need to have a full grasp of the difference between equations and expressions. Worksheets By Email: Find Any Errors, Please Let Me Know! I would appreciate everyone letting me know if you find any errors. I'm getting a little older these days and my eyes are going. Please contact me, to let me know. I'll fix it ASAP. Check my Google Page to see the sheets that I add regularly.
Physics Text I'm looking for a textbook that I can use to re-learn physics on my own. The last physics course I took was years ago, an AP course in high school. I also haven't taken Calculus in the same length of time. I'd be interested in trying to relearn both simultaneously. Is there a physics text that people would recommend? Whatever you settle on, pick up a copy of Paul Hewitt's Conceptual Physics too. Work through a section in Hewitt and then tackle the corresponding section in whatever text you get (I had Giancolli for alg/trig physics and Halliday in calc-based physics). The problem most people have with physics is that they try to manipulate formulas before they understand the relationships they represent. Try Hewitt; it's fun and you'll learn a lot. I am about to start on "Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics) Morris Kline" It's teaching Calculus from a Physics perspective. Let me give you a few tips. I took Calculus twenty years ago and got an A. We learned how to take Integrals, Derivatives, etc. I re-took Calculus last Summer to knock the rust off, and barely switched to Audit in time to avoid a disaster. It's not being taught the same way today. If you get a chance, ask a teacher who's taught for more than twenty years and see if he remembers. NOW, it's taught using "Rigor". You know, as in Rigor Mortis; "stiff". The first month of the class was a very cursory Algebra review. Then it was a crash introduction to Proofs, something you don't need until much later. After that, instead of teaching Integrals or Derivatives, the book we used tried to make introductory Calculus students re-invent Calculus by studying how Newton/Liebnitz did it. This is "Rigor". As in stupid. The right way to teach Math is by doing problems over and over until they become routine. Let the third-year Calc students explore the origins of Calculus, and second year students tackle Proofs, not in a single assignment, but a full semester's worth. I purchased the Morris book because a) it's about actually solving real-world problems, not the intricate math puzzles mathematicians gloat over; b) Morris has the same scathing opinion of "Rigor" and Proofs that I have developed, and c) it was written before Rigor became the defacto standard. Somebody should tell today's math teachers that the point is learning to use it, not confounding the students with puzzles a year more advanced than they know how to solve. The result is, many people turn away from Math in disgust, feeling like they're not smart enough. I think if teachers were using the Morris book, they'd engage the students better and graduate more people able to use Math. Halliday Resnick. I used Fundamentals of Physics in a correspondence course (over 2 semesters) and would recommend physics books from them. This one: Physics, Parts I and II (Parts 1 & 2) is under two dollars. I am assuming you could use and old edition.
A physics primer, with equations The mantra for popular-science books is to minimize the use of equations. In The Theoretical Minimum: What You Need to Know to Start Doing Physics, authors Leonard Susskind and George Hrabovsky have taken the opposite approach by producing a physics book for the educated general public that emphasizes the mathematics needed to solve physics problems. When I first heard about the premise of the book, I was intrigued. Is there a group of people who want to solve physics and mathematics problems, and not simply read about the gee-whiz physics that is the standard fare of most popular-science books? To my surprise, apparently there is. The Theoretical Minimum is the product of a series of lectures that Susskind presented for the general public in the Stanford area – all of which can be found video-recorded on the Web – and these lectures attracted a large following of people who were, in Susskind's words "hungry to learn physics". Indeed, Hrabovsky himself was one of those people. Now president of the Madison Area Science and Technology organization, which is devoted to research and education, Hrabovsky has no formal scientific training but taught himself physics and mathematics – presumably through courses and books similar to The Theoretical Minimum. This thirst for academic learning outside of a conventional university degree reminded me of the recent and rapid growth of so-called massive open online courses, or MOOCs: open-access (i.e. free) university courses that give people of any age or background the chance to learn about a subject that interests them, at their own pace (see p9 of the print edition). Like MOOCs, The Theoretical Minimum allows knowledge-lovers to get their teeth into the kind of physics and mathematics problems that one would normally face during a university degree. As Susskind puts it, it is intended for "people who once wanted to study physics, but life got in the way". The book is written in the form of 11 short lectures that cover classical mechanics, plus a final chapter on electromagnetism. Though replete with equations, it remains very readable. Abstract concepts are well explained, usually in a couple of different ways to give the reader a good conceptual overview of the principle at hand. For example, one does not need to understand every detail of a given equation in order to comprehend its power and its use, since these are explained in the text. In addition, each lecture includes several exercises, allowing readers to put their problem-solving skills into practice. (Solutions to the exercises are posted on the Web.) The first three chapters include mathematical interludes on trigonometry, vector notation, differentiation and integration. These discussions are complete, and would serve as a good reminder for someone who is already familiar with calculus; however, they are also rather terse, and would likely be too advanced for someone who wishes to learn it for the first time. I found it satisfying to finally gain a basic understanding of Lagrangian and Hamiltonian mechanics Is this really just the minimum you need to know to start doing physics? To me, the answer is an emphatic "no": this book covers far more than the minimum. The first five chapters cover the core classical mechanics principles of motion and dynamics, including conservation of energy and momentum, while the material covered in the second half of the book (chapters 6–12) is usually considered "advanced classical mechanics". This material – which includes Lag As such, I can attest to the readability of the book: I was able to understand what an equation that I had never seen before represents, without having to pick apart and understand every term that makes it up. In fact, I found it satisfying to finally gain a basic understanding of Lagrangian and Hamiltonian mechanics, since I had sometimes wished we had covered these subjects in my degree. I even felt like I had been partially duped during my degree after reading Susskind's comment that the Euler–Lagrange equations comprise "all of classical physics in a nutshell"! There is, however, a flip side to my satisfaction at filling in some holes left by my undergraduate degree: I found myself wondering how much someone who has not had formal mathematics or physics training would really get out of The Theoretical Minimum. The concepts presented in it are not only advanced, but also abstract and unintuitive, and I would imagine they would be quite daunting to someone new to the subject. At the very least, they would leave newcomers scratching their heads. The book is really about explaining mathematics and abstract physics and does very little to relate these concepts back to everyday life. In addition, in many instances I thought that the explanation would benefit from a diagram or two. Susskind is one of the fathers of string theory, arguably one of the most abstract and theoretical areas of physics. However, the rest of us are not: we need a more tangible way to learn. In summary, although this book probably offers more than many readers will have bargained for, it does provide a clear description of advanced classical physics concepts, and gives readers who want a challenge the opportunity to exercise their brain in new ways. Thanks to the breadth of accompanying information (for example, exercises and video-recorded lectures on the Web), it also enables them to learn at their own pace, and hopefully most will get some fun and satisfaction from it. If members of the general public really are pulling for these types of courses, ones that offer rigour and a challenge, I enthusiastically encourage them. About the author Lowry Kirkby is a PhD student in biophysics at the University of California, Berkeley, US, and the author of Physics: a Student Companion (2011 Scion Publishing) 14 comments Minimum When Susskind uses the term "minimum" in the video lectures he qualifies by saying "it's the minimum you need to know before you can move to the next concept [video/series]". So, especially when you get to his series on General Relativity, the mathematics can become quite intimidating (co-variant/contra-variant derivates and christoffel symbols for example) but he tries to give the minimum amount of information you need to start to understand what the equations are saying. For me, this means re-watching the same video a couple of times to fully grasp the concepts. Once understood though, you are able move on. Lenny's Latest The original stringer has hit one out of the park again. I would love to teach an undergrad course out of his book, & feast on the math-physics fusion. Lenny/Stanford has a full-spectrum of adv. physics courses on Utube, well worth viewing. Has anybody noticed that Lenny is a Dead Ringer for Galilei ? Any doubts see the Mar 2009 cover of PW. Teaches the Character of Physical Law I loved this book. As an old guy with an undergraduate degree in physics, I was amazed by how lucid, pithy, and intelligent the book is. (I'm just starting to watch the videos.) The aesthetic attraction of the book is that he exposes the reader to the essence of modern theoretical physics by explaining mathematically the link between symmetries and conservation laws. Although this text deals with classical physics, Susskind and Hrabovsky are setting the stage for quantum field theory by developing the powerful tools that will be used there. In QFT, all forces are explained by different gauge symmetries (broken or otherwise) which must leave the Lagrangian invariant. The change in the style of physics is represented here: when asked what was the most essential concept that could be passed to a civilization that was rebuilding from scratch, Brian Greene said that it was that the laws of physics are based on symmetries whereas Feynman would convey the fact that the world is built of atoms. Pedagogical treatment If and when one makes clear pedagogically the physics of a given natural phenomenon, the algebric equations expressing it become memorably expressive and transparent leading to creative thinking and questioning. A physics primer, with equationsCalculus - They language that God talksAlgebric Equation If there is something that cannot be but godly and it is Algebra with its Algebric Equation. Wthout this Algebric Equation, all the disciplines of science, would have been struggling in an utter stone ageMathematics is the Language of PhysicsI could not agree with you more. Physics without the mathematics is akin to painting without paints. Although Physics is highly experimental, you need math to understand the process and outcome. For instance: you can take a ball and throw it and see the laws of physics and its flight path and say it is due to gravity and the balls mass and the velocity it is moving. But how can you describe that on paper? What are the exact properties at play? Only the mathematics behind it can tell you exactly.... gravity is -9.8 m/s^2. The velocity is explained through v=v-nought+aΔt. I could go on. Point being, I want to reiterate that although physics is a science and can be shown through experiments, it is shown beautifully through mathematics as well. The world is a canvass, physics is the brush, and mathematics is the paint/colors.I have no intention of disrespecting or critcizing anyone and above all Prof Susskind.I was just mentioning a fact that in all schools and even at university level maths is not accepted as comfortably as other subjects but please look around and note that every scientist or teacher in the field of physics is good in maths.Maths has to be a core subject and only through regular serious practice the subject can be mastered.This has to be done very firmly in schools from very beginning whether the students or their parents like it or not.Very rarely someone is mathematically challenged and mostly the main reason for weakness in maths is social environment and failure of policy makers in field of education. Equations have power to predict but you must know your maths well enough to extract any information or even to set up equations.If anyone cannot calculate and give quantative information then your physics is incomplete. All points noted, pradeep. And I reiterate that maths is a vital tool for physics. But look at masseffected20's post above. Maths will tell him about the ball's trajectory, but it doesn't tell him how gravity works. He doesn't know how gravity works, because he lacks the conceptual understanding. His physics is incomplete too. Physics needs mathematics and concepts. Sorry, I do know minimum But I have question if exist opposite of Furier transformation ( so we could get eaquations in ussual form ) and also if we can have some Furier transformation of Enstein most known eaqution E=mcc for its relativistic version? What then means mathematical row for addition of m0 sum? graphic expression of equations Analytical mechanics... Quote: Lag Yes I too remember this rather glaring omission at Oxford (although to be fair I think it was part of some "theory" option somewhere). Perhaps it's skipped in Britain because Lagrange was (arguably) French and Hamilton was Irish :-) As a result I had some catching up to do when starting graduate work in the US. As for the book, I notice that it only covers 1/6 of Susskind's "theoretical minimum" lectures at Stanford - there were also lectures on quantum mechanics, statistical mechanics, relativity etc. All of which are well worth checking out, as there are many interesting insights, even for experts.
Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century Book Description: This new approach to mathematics---the utilization of advanced computing technology in mathematical research---is often called experimental mathematics. The computer provides the mathematician with a "laboratory" in which she can perform experiments---analyzing examples, testing out new ideas, or searching for patterns. This book presents the rationale and historical context of experimental mathematics, and includes a series of examples that best portray the experimental methodology. For more examples and insights, the book, "Experimentation in Mathematics: Computational Paths to Discovery" is a highly recommended companion
More About This Textbook Overview Shortly after the invention of differential and integral calculus, the calculus of variations was developed. The new calculus looks for functions that minimize or maximize some quantity, such as the brachistochrone problem, which was solved by Johann Bernoulli, Leibniz, Newton, Jacob Bernoulli and l'Hopital and is sometimes considered as the starting point of the calculus of variations. In Woodhouse's book, first published in 1810, he has interwoven the historical progress with the scientific development of the subject. The reader will have the opportunity to see how calculus, during its first one hundred years, developed by seemingly tiny increments to become the highly polished subject that we know today. Here, Woodhouse's interweaving of history and science gives his special point of view on the mathematics. As he states in his preface: ''Indeed the authors who write near the beginnings of science are, in general, the most instructive; they take the reader more along with them, show him the real difficulties and, which is the main point, teach him the subject, the way they themselves learned it.''
Master Math : Business and Personal Finance Math today's fast-paced and evolving financial environment it is essential for you to have a strong understanding of mathematics to succeed both personally and professionally. MASTER MATH: BUSINESS AND PERSONAL FINANCE MATH teaches you the mathematics required for success in today's world in an easy-to-read, user-friendly format. It covers all the need-to-know information and skills in business math and personal finance topics. The book's approach to math concepts and skills is straightforward and introduces new concepts step-by-step. This allows you to build confidence before you try it on your own. In addition to reviewing the basic operations of arithmetic, topics include gross and net pay, banking, credit and loans, owning a car or home, insurance and investments, as well as budgets, business costs, sales and marketing, managing people and inventory and business profit and loss. Chapters are organized logically and in short lessons for ease of learning.
This new program from Houghton Mifflin will help you understand the best uses for the technology supplements that accompany your textbook. Use the grid below to fnid HM mathSpace™ resources by textbook. HM mathSpace™ Technology Guide This new program from Houghton Mifflin and its accompanying technology guide will help you understand the best use for the technology supplements that accompany your textbook. You can access any of the web-based products in HM mathSpace™ by visiting math.college.hmco.com/students, and going to your textbook's companion web site. SMARTHINKING™ PASSKEY/SMARTHINKING™ live online tutoring (Included in technology guide) If you don't have time to see your instructor, or office hours aren't convenient, this is your chance to get the help you need when you need it. Through state-of-the-art tools and a two-way whiteboard, you can communicate in real-time with qualified e-structors who can help you understand difficult concepts and guide you through the problem solving process while you study or complete your homework. eduSpaceฎ Passkey (Included in technology guide) eduSpaceฎ is a text-specific online learning environment which combines an algorithmic tutorial program with homework capabilities. Specific content is available to help you further understand your textbook and varies depending on the book. Tutorials help you review concepts that you may miss because of an absence from class; or use them to review for upcoming quizzes or tests. Practice Exercises allow you to reinforce skills and concepts not yet mastered by working on a variety of exercise types. Homework Assignments can be accessed, completed, and submitted online if you instructor assigns them. Quizzes can be used for practice or taken for a grade if you instructor assigns them. HM3 Student CD-ROM HM3 reinforces material presented in class with animated lessons, video clips, and an unlimited number of algorithmically generated practice exercises and quizzes. You can use it to reinforce your understanding of concepts and master skills by following a guided, three-step process: Study the Lesson presents a concept then demonstrates step-by-step problem solving, often with animated solution steps. Take the Quiz is completed without hints, with feedback and summaries after you receive your scores. Real Deal UpGrade Student CD-ROM This CD-ROM includes resources to help you achieve success in your course including: ACE self-quizzes (1 per section) Chapter Summaries Chapter Objectives Chapter Tests (with solutions) A link to your textbook's web site Learning Tools CD-ROM This comprehensive CD contains text-specific support and materials to help you study outside of class. Brief descriptions are as follows (each CD may contain other features as well): CD-ROMs for College Algebra, Algebra & Trigonometry, Precalculus, and Trigonometry An unlimited number of practice exercises for testing your knowledge and reinforcing concepts through optional hints, step-by-step solutions, and lessons A graphing calculator for exploring and visualizing data and equations when working with the tutorials A large bank of data sets for experimenting and sharpening skills with Minitab, the TI-83 Plus Graphing Calculator, or Microsoft Excel™ The interactive ComputerStat program for demonstrating statistical concepts and processes data. mathSpace™ Student CD-ROM This new tutorial CD-ROM allows you to practice skills and review concepts as many times as necessary, by algorithmically generating exercises and step-by-step solutions for practice. CalcChat.com This web site delivers step-by-step solutions to all odd-numbered exercises in the Larson Calculus textbook series in an interactive, online chat room format. You can access detailed solutions to the odd-numbered exercises in the Larson Calculus texts and interact with peers and/or a moderator to solve problems together. Houghton Mifflin Mathematics Instructional DVDs These DVDs provide careful explanations of key concepts, examples, exercises, and applications in a lecture-based format. Ideal if you miss a lecture or need more step-by-step explanations. Also a great tool for reviewing before an upcoming class, quiz, or test.
Posts Tagged 'gmat math' Inequalities on the GMAT should be approached in the same way as regular equations. We can manipulate inequalities the same way that you can manipulate equations. As with equations on the GMAT, you first must simplify the equation in order to answer the... To succeed on the GMAT, there is a general rule of Algebra that you should know: to solve for all variables in a system of equations, you need as many distinct linear equations as variables. So if you get 2 variables, you need two... You might remember back in the day in Algebra class that you learned how to work with systems of linear equations. These are problems when you have multiple equations and multiple variables, and you have to find a way to solve for each variable.... Basic math content knowledge, such as the formula for the area of a triangle or the equation for calculating an average, is often the wolf in sheep's clothing on the GMAT – test takers who lack proficiency in the basics find it very challenging to... Before students begin studying for the GMAT – before they even know anything about it beyond that it tests math and verbal – one question type worries students more than any other: a question about two trains traveling on parallel tracks. Every time I start toRemember how to find the volume of a cylinder? It's okay most people don't; grade school was a long time ago! Knewton teacher Cole Entress helps you refresh your memory. Also, in honor of the World Cup(!), we're discounting our GMAT course by 10% through Monday night...
Mathematical Induction - Explains the process of making and proving conjectures about the behavior of equations that a repetitive trait, such as summation formulas. Includes the rules for a valid induction and some examples. Miss Lindquist: The Online Algebra Tutor for Word Problems - An intelligent tutoring system funded through a grant from the National Science Foundation to build software that is more like human tutors. This program will tutor students presenting them with progressively harder problems and will help me when needed.
Calculus is a branch of Mathematics which examines change. It has two major disciplines: differential and integral calculus, with one being concerned with rates of change, while the other focuses on the accumulation of quantities. Thus, it can be seen that the applicability of this study extends into economics, engineering as well as any science. Although Calculus does not stand apart from Algebra, both of these branches can be used to solve different problems. Algebra deals with structures utilizing letters and symbols to represent specific relationships between each other. However, since the relationship is fixed, it may not be applicable to use algebra to solve problems dealing with continuously changing relationships. Thus, calculus in this context can be a very useful as there are many non-theoretical relationships which rarely stay the same. Exploring the basic terminology, a derivative is a measure of how the output of a specific function, which is not limited to y or f(x), changes as the input changes. An integral, also known as an antiderivative, is a function F whose derivative is the given function f. Both of these form the basic tools of calculus with numerous applications in everyday life. Thus, understanding basic Calculus may prove to be a practical tool for anyone. 1. A heated object is allowed to cool in a room temperature which has a constant temperature of To. a. Analyse the cooling process. b. Formulate mathematical model for the cooling process. 2. At time t= 0 water begins to leak from a tank of constant cross-sectional area A. The rate of outflow is proportional to h, the d An even function is defined as f(x) = f(-x), and an odd function has -f(x) = f(-x). The domain of a function is the set of input data that keeps the function defined. Determine if the function f(x) = -2x^2 * absolute value(-6x) is even, odd, or neither. Find the average rate of change for the function f(x) = 4/(x+3) between t Consider the function: y = 15/4 - x/2 - x2/4. a) Present the function in the turning point form. b) Find the equation of the axis of symmetry and coordinates of the turning point. Determine whether there is a function maximum or minimum at this point? Substantiate 1. Evaluate the following indefinite integrals: See attached 2. On a dark night in 1915, a German zeppelin bomber drifts menacingly over London. The men on the ground train a spotlight on the airship, which is traveling at 90 km/hour, and at a constant altitude of 1 km. The beam of the spotlight makes an angle θ with the This question considers the motion of an object of mass m sliding on the outside of a cylinder of radius R whose axis is horizontal. The motion occurs in the vertical plane, and the surface of the cylinder is rough — the coefficient of sliding friction is μ'. The diagram below shows the position of the object when it is at an We wish to determine whether the following integral is path-dependent: I = f_c - 2ycos2xdx - sin2xdy In the practice problems, you must: - Determine if statement is correct - Calculate the Jacobian of transformation - Evaluate triple intergrals Please see attachment for following problems. Assume that un (sub n) belongs to the complete real normed vector space (V, ll.ll) for each n E N and that the series from n=1 to infinity - abs value( un+1 - un) converges. Show that the sequence {un} n=1 to infinity converges. Hint: make use of the Cauchy criterion V_cell = (I_cell)(R_esr) + (I_cellR_p)(1 - exp(-t/((R_p)(C_t))) Calculate the equation for V_cell when R_p > infinity Is the new equation the same as below? If yes, show how you arrive at this: V_cell = (I_cell)(R_esr) + (I_cell)(t/C_t) The population sizes of a prey, X, and a predator, Y (measured in thousands) are given by x and y, respectively. They are governed by the differential equations ẋ = −pxy + qx and ẏ = rxy - sy (where p, q, r and s are positive constants (p ≠ r). In the absence of species Y (i.e. y = 0), how would I find a solution 1. Consider the Dirichlet Problem where the temperature within a rectangular plate R is steady-state and does not change with respect to time. Find the temperature u(x,y) within the plate for the boundary conditions below and where (See attached) 2. Solve the Dirichlet problem for steady-state (constant with respect to t excuse me, at room temperature 20 degree, the result is near to the accept value? Johan - this was insanely helpful. The problem is a lot more straight forward than I than expected. Your solution really helped me understand this unit Thank you for your answer. I do have some questions though. Why is it that in DBD the microdischarge channels form? I know it is due to voltage being applied across the gas, but how/why do these channels form? Does it have to do with AC voltage, and if so, can a DC voltage be applied to counteract the AC and get uniform illumination? Also, what would be the method of correctly applying the RF waves to be uniformly distributed across the gas? Sorry to bother you, but I was looking for a more in-depth answer. Your answer was great, by the way. There are currently 136 Experts Providing Help for Mathematics at BrainMass View Details Converting units using dimensional analysis is one aspect of chemistry that tends to give students trouble in the beginning stages of their education. It is the goal of this book to provide a simple pathway to mastering this extremely useful techniq... READ MORE »
There are twelveThere are nine units, all at level four,… The twelve units in this book from Nuffield National Curriculum Mathematics build on previous work and are at NC level six. They are suitable for students working towards an Intermediate GCSE. Each unit provides information for the student to read and questions and activities for them to do. The units are in short sections and a… There are nine units, all at level four, in this book from the Nuffield National Curriculum Mathematics series. Each unit provides information for the student to read and questions and activities for them to do. The units, which are in short sections, have detailed content descriptions at the top of each page. These descriptions… There are nineThe nine handling data units, all at level five, in this Nuffield National Curriculum Mathematics book are: The mean and the range Collecting data Probability Picture this That's just typical Comparing distributions Using databases Predicting the outcome Projects. Each unit provides information for the student… The level six units, from Nuffield National Curriculum Mathematics, in this students' book cover the topics of: Parallel lines Three dimensions flattened Area of simple shapes Quadrilaterals Volume Enlargements Drawing with Logo Circles, perimeter and area Maps and scale drawings. Each unit provides information… The nine units, all at level five, in this book from the Nuffield National Curriculum Mathematics series are: Area and volume Angles Circles All about boxes Construction Common sense measuring Polygons Practical measuring Networks. Each unit provides information for the student to read and questions and activities… This shape, space and measures book at level seven, from the Nuffield National Curriculum Mathematics series, was suitable for students following an intermediate GCSE course. It has nine units of work, each with information for students to read and questions and activities to do. The units, which are in short sections, have detailed… This book at level seven, from the Nuffield National Curriculum Mathematics series, was suitable for students following an intermediate GCSE course. It has nine units of work, each with information, questions and activities. The units, which are in short sections, have detailed content descriptions at the top of each page. These…
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations. This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading. Customer Reviews: A must read for all those who hate PDE's By raddy@bu.edu - May 6, 1998 We all had to go through the drudgery of PDE's in undergraduate courses and except if you're a math major your knowledge of the methods of solution will probably stop at separation of variables, Laplace transform and D'Alembert. This book is an excellent review of a host of methods for solution but what is more important is the physical interpretation of the PDE's the author insists on. Most of the physical examples are drawn from the fields of heat and mechanics but they can be easily applied to electromagnetic and semiconductor charge transport problems. Every aspiring senior in an engineering discipline should study this book for his own good. Very Good By Alberto Dominguez - May 8, 2003 Unbeatable as far as breadth. Covers a lot of ground, conceptually it's extremely well organized, and the explanations are very easy to follow. This text is ideal for self-study.The two major shortcomings are (1) slight lack of depth and (2) the exercises, which are far too few and far too simple. A rare gem By Atul Sharma - May 25, 2000 Partial differential equations can be obscure, and are often not dealt with at all at the undergraduate level. Assuming only a reasonable familiarity with calculus and ordinary differential equations, this book is extraordinarily clear and even enjoyable. Divided into neat, digestible segments suitable for self-study, I found it a very useful introduction to PDE's, covering a very broad range of topics and examples. My only suggestion for improvement would be a more up-to-date review of numeric methods using a computer algebra system. Nonetheless, even this section (examples intended to be worked by hand) is very clear and makes alternate texts much easier to absorb. I would recommend it to anyone wishing to be more comfortable with PDEs. The subject of this book is estimating parameters of expectation models of statistical observations. The book describes the most important aspects of the subject for applied scientists and engineers. ... This text serves as an introduction to the programming language Java for scientists and engineers, as well as experienced programmers wishing to learn Java as an additional language. The authors have ...
Titu Andreescu and Dorin Andrica The book aims at an audience of (I quote from the back cover) "undergraduates, high school students and their teachers, mathematical contestants … and their coaches, as well as anyone interested in essential mathematics." That is about the same audience as some other books on the market, notably L.-s. Hahn's Complex Numbers & Geometry from the MAA, with which it has, inevitably, a nonempty overlap. It's certainly not a book on Complex Analysis. As the authors mention in the Introduction, the symbol eit appears nowhere in the book. The book also misses on Möbius transform which takes about 20% of Hahn's book. It does not refer to any plane curves, not even cycloids. Still, I do not quite understand why the authors seem to have hesitated in adopting a less ambiguous title; say, "Complex Numbers from A to Z." The book is a real treasure trove of nontrivial elementary key concepts and applications of complex numbers developed in a systematic manner with a focus on problem solving techniques. Much of the book goes to geometric applications, of course, but there are also sections on polynomial equations, trigonometry, combinatorics… The book is organized into six chapters, Glossary, authors' and subject indices and a bibliography list. The chapters are as follows Complex Numbers in Algebraic Form (pp. 1-28). Complex Numbers in Trigonometric Form (pp. 29-52). Complex Numbers and Geometry (pp. 53-88). More on Complex Numbers and Geometry (pp. 89-160). Olympiad-Caliber Problems (pp. 161-252). Answers, Hints and Solutions to Proposed Problems (pp. 253-306). Chapter 5's caption is somewhat misleading. It may create an impression that the previous chapters dealt with trivial matters or that Chapter 5 offers exclusively mathematical chestnuts only worthy of olympiad experience. Neither will be true. Problems constitute an integral part of the book alongside theorems, lemmas and examples. The problems are embedded in the text throughout the book, partly as illustrations to the discussed concepts, partly as the testing grounds for the techniques just studied, but mostly I believe to emphasize the centrality of problem solving in the authors' world view. Some problems, especially in chapters 3 and 4, have already been plucked from various olympiads and competitions: IMO, nationals, Putnam… By the time the interested reader reaches Chapter 5, the time may be ripe to tackle "Olympiad-Caliber" problems. On the other hand, even Chapter 5 contains plenty of problems that are introductory in nature. The book is really about solving problems and developing tools that exploit properties of complex numbers. The accumulation of the toolchest can be surmised from the subsection captions. For example Section 3.5 is split into: Equation of a line, Equation of a line determined by two points, The area of a triangle, Equation of a line determined by a point and a direction, The foot of a perpendicular from a point to a line, Distance from a point to a line. Section 4.6 sports such a sequence of subsections as The Distance OI, The Distance ON, The Distance OH. Aided by a subject index and a glossary, such a detailed table of contents makes the book very searchable. If you are looking for the formula for the area of a triangle, for example, then it is right there, in the table of contents. Characteristically, though, you'll find not only the formula itself, but also some of its applications. Say, the Area of a triangle subsection contains two solved problems of which one applies immediately to proving Menelaus' theorem. In Chapter 4 the reader is treated to some unusual notions of the real and complex products of two complex numbers: These are none other than the scalar and vector products expressed in complex terms. E.g., u.u = \|u\|2. In a book on Complex Numbers their use is a real eye opener. I am aware of only one other book where complex numbers are mixed with the scalar product. This is Euclidean Geometry and Transformations by C. W. Dodge, where the basic object is the vector enhanced with the complex number symbolism. The book under review introduces the two products directly for the complex number objects. However simple and natural this usage is, this is something I have not seen done before. For example, the usual condition for the orthogonality of two lines UV and WZ (where a low case letter denotes the complex number corresponding to the point assigned the same letter in upper case) is commonly expressed as meaning that in order for UV and WZ to be orthogonal the quotient (u - v)/(w - z) must be purely imaginary. (This is demonstrated in Chapter 3.) The common condition is immediately seen to be equivalent to (u - v).(w - z) = 0 which is more suitable for algebraic manipulation. It is also delightfully efficient. An application proved to be effortless. Say, two triangles are called orthologic if the perpendiculars from the vertices of one onto the "opposite" sides of the other are concurrent. If we deal with triangles ABC and A'B'C', then the orthogonality condition is given by (1) (z - a).(b' - c') = 0 (z - b).(c' - a') = 0 (z - c).(a' - b') = 0, where z is just a variable. Taking it to be the point of concurrency, we add the three equations, eliminate z and obtain a concurrency condition (2) a.(b' - c') + b.(c' - a') + c.(a' - b') = 0. This is because, going backwards, (2) is equivalent to (3) (z0 - a).(b' - c') + (z0 - b).(c' - a') + (z0 - c).(a' - b') = 0, for any z0. Assuming z0 satisfies the first two equations in (1), we see from (3) that it also satisfies the third equation. With little effort, (2) can be rearranged into (2') a'.(b - c) + b'.(c - a) + c'.(a - b) = 0 which shows that the relation is indeed symmetric. This fact is known as Maxwell's theorem after J. C. Maxwell who published a paper on the subject with an ingeniously beautiful proof (See, D. Pedoe Geometry: A Comprehensive Course, 114-116.) The theorem has also elicited interest from J. Steiner who proved it in 1827. The reader will find a good deal of elegant and simple sample problems and even a greater quantity of technically taxing ones. The book supplies many great tools to help solve those problems. As the techniques go, the book is truly "From A to Z". Problem and example selection of course has been governed by authors' taste and experience. I would certainly include a lovely problem due to the late M. Klamkin (Mathematics Magazine, 28, 1955, 293) Prove that cos(5o) + cos(77o) + cos(149o) + cos(221o) + cos(293o) = 0. Its omission is hardly a point of contention, though. But there are a couple of things worth complaining about. Annoyingly, William Wallace's name is consistently misspelled as Wallance. It is misspelled in a short biographical footnote, in the Index and throughout the book whenever the Simson-Wallace line has been mentioned. The formulation of Proposition 1 in section 4.5 is obviously incorrect: Consider the point X(x) in the plane of triangle ABC (with the circumcenter at the origin.) Let P be the projection of X onto BC. Then the coordinate of P is given by where R is the circumradius of triangle ABC. Clearly the projection of a point on BC does not depend on A, whereas R does. To correct the formulation, X is to be taken on the circumcircle of triangle ABC. The mishap, if noticed by the clever mathematical contestants, will probably amuse, rather than disorient, them. On every occasion where the proposition is referred to, X is assumed to be in the right place. Less committed readers may get frustrated. But the book is for a committed reader. It is for the readers who seek to harness new techniques and to polish their mastery of the old ones. It is for somebody who made it their business to be solving problems on a regular basis. These readers will appreciate the scope of the methodological detail the authors of the book bring to their attention, they will appreciate the power of the methods and the intricacy of the problems. Those who look for the "neglected mathematical beauty" may enjoy more the "guided tour" which is offered by L.-s. Hahn's book. A high school mathematics teacher and a team coach will do well owning both books, irrespective of their topical overlap. Alex Bogomolny is a business and educational software developer who lives with his wife and two sons — 26 and 6 — in East Brunswick, NJ. Past December, his web site Interactive Mathematics Miscellany and Puzzles has welcomed its 16,0000,000th visitor.
Latest Newsletter Mathematics (Yr 10-12) Year 10 Three courses are offered to Year 10 students, they closely follow the Senior Mathematics curriculum. Mathematics A covers arithmetic, trigonometry, statistics, co-ordinate geometry and some basic algebra; it concentrates on mathematics in real life situations, practical problem solving and communicating mathematically. Students completing this course will be go on to study Mathematics A or Prevocational Mathematics (if offered) in QSA. Mathematics A does not lead into Mathematics Studies (Standard Level) in the IB Diploma. Mathematics B is designed to prepare students for the study of Mathematics B in Years 11 and 12, as well as Mathematical Studies (Standard level) in the IB Diploma Programme. Mathematics B covers topics such as advanced algebra, trigonometry and co-ordinate geometry with an emphasis on Mathematical applications. Mathematics C is designed to extend the top Mathematics students. The course covers advanced algebra, trigonometry, co-ordinate geometry and the study of functions as well as extension topics such as surds, matrices and vectors. The emphasis will also be on mathematical applications. Students in this course will go on to study Mathematics B (and Mathematics C) for QSA in senior years or Mathematics (Standard Level or Higher) in the IB Diploma. Year 11-12 Students in Years 11 & 12 at Townsville Grammar School can choose from the following Mathematics subjects: Mathematics A is an Authority subject and develops the skills needed to make decisions which affect students' everyday lives, providing a good general background for many areas of tertiary study. Topics covered include Managing Money, Data Collection and Presentation, and Maps and Compasses. Mathematics B is an Authority subject in which advanced mathematical skills are developed and is designed to raise the students' competence in and confidence with mathematics. The subject outline includes topics such as Rates of Change, Periodic Functions and Applications, and Logarithmic Functions and Applications and Statistics. Mathematics C gives the students the opportunity to develop their full mathematical potential and is an Authority subject. Topics studied include Real and Complex Number Systems, Matrices and Applications of Calculus. Prevocational Mathematics is an Authority Registered subject. It is designed to provide students with a relevant and practical mathematical base for life after school. Years 11-12 - International Baccalaureate Mathematics (For students studying the International Baccalaureate) IB Mathematics SL This course caters for students who already possess knowledge of basic mathematical concepts and who have the skills needed to apply simple mathematical techniques correctly. The majority of these students will expect to need a sound mathematics background for future studies in subjects such as chemistry, economics, psychology and business administration. The Mathematics SL course covers the topics of algebra, functions, calculus, matrices, vectors and statistics. The level of calculus in this course includes basic rules for differentiation and integration with applications to finance, area, volume, optimisation, curve sketching and kinematics. IB Mathematical Studies SL This course caters for students with varied backgrounds and abilities in Mathematics; they are equipped with fundamental skills and a rudimentary knowledge of basic processes. It is designed to build confidence and encourage an appreciation of mathematics in students who do not anticipate a need for mathematics in their future studies. Students taking this course need to be already equipped with fundamental skills and a rudimentary knowledge of basic processes. Note: All Year 10 Extension/Mathematics B and Years 11 and 12 Mathematics B students use a Casio Graphics Calculator as the technology requirement of their courses. Please consult the relevant booklist for the make and model numbers. Further information on Mathematics subjects are contained in the Subject Selection Handbooks available here. IB Mathematics HL This course caters for students with a good background in mathematics who are competent in a range of analytical and technical skills. Students embarking on this course will develop insight into mathematical form and structure, and should be intellectually equipped to appreciate the links between concepts in different topic areas. The majority of these students will be expecting to include mathematics as a major component of their university studies, either as a subject in its own right or within courses such as physics, engineering and technology. The nature of the subject is such that it focuses on developing important mathematical concepts in a comprehensible, coherent and rigorous way. Students are encouraged to apply their mathematical knowledge to solving problems set in a variety of meaningful contexts. Development of each topic will feature justification and proof of results.
books.google.de - The primary goal of these lectures is to introduce a beginner to the finite-dimensional representations of Lie groups and Lie algebras. Intended to serve non-specialists, the concentration of the text is on examples. The general theory is developed sparingly, and then mainly as useful and unifying language... Theory
Due to health reasons you might have not been able to attend a few lectures at school, but what if I can you can simulate your classroom, in your house? In fact, right on the computer that you are working on? All of us have missed some lectures at some point or the other during our life, but thanks to Algebrator I've never been left behind. Just like a teacher would explain in the class, Algebrator solves our queries and gives us a detailed description of how it was answered. I used it basically to get some help on poems on slope y=mx+b and binomials. But it works well for all the topics.
Run a Quick Search on "Elementary Geometry for College Students" by Daniel to Browse Related Products: Short Desription Building on the success of its first four editions, the Fifth Edition of this market-leading text covers the important principles and real-world applications of plane geometry, with a new chapter on locus and concurrence and by adding 150-200 new problems including 90 designed to be more rigorous. Strongly influenced by both NCTM and AMATYC standards, the text takes an inductive approach that includes integrated activities and tools to promote hands-on application and discovery. If You Enjoy "Elementary Geometry for College Students (Hardcover)", May We Also Recommend:
"Mathematics is the alphebet with which God created the universe" – Galileo Menu MM1H The Composite Function. This video introduces the composite function and explains how it works. The video was prepared for Year 12 students of Mathematical Methods CAS in the State of Victoria, Australia. This course is fully prescribed by the Vitorian Curriculum and Assessment Authority. MM1H The Inverse Function. This video introduces the inverse function and demonstrates how to find an inverse, both graphically and algebraically. The video was prepared for students undertaking Mathematical Methods CAS Units 3 and 4 in Year 12. Maths Methods CAS is a course which is fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australi MM1B Relations and Functions. This video introduces students to the concept of Relations and Functions; what they are and now to distinguish between a Relation and a Function. One-to-one functions are dealt with in more detail, as these are important from the perspective of inverse functions. The video was prepared for students undertaking Year 12 Mathematical Methods Units 3 and 4, a course fully presribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia. This video provides worked solutions for the 2006 VCAA Mathematical Methods (CAS) Units 3 and 4 Examination 1. This subject is for Year 12 students of Mathematical Methods (CAS) in Year 12. The examination is of duration one hour and it is technology-free. The course is fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia. SM2A Linear Dependence of Vectors. This video introduces the concept of linear dependence for both two vector and three vector sets and demonstrates how to prove or disprove linear dependence in them. The video was prepared for Year 12 students studying Specialist Mathematics, a science and engineering mathematics discipline, as fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia. MM9D The Chain Rule. This video introduces the chain rule for use in differentiating functions in the area of calculus. The video was prepared for Year 12 students studying Mathematical Methods (CAS). This course is fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia The video was produced for Year 12 Mathematical Methods (CAS) students. This course is fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia.
Ripples in Mathematics The Discrete Wavelet Transform 9783540416623 ISBN: 3540416625 Pub Date: 2001 Publisher: Springer Verlag Summary: This book gives an introduction to the discrete wavelet transform and some of its applications. It is based on a novel approach to discrete wavelets called lifting. The first part is a completely elementary introduction to the subject, and the prerequisites for this part are knowledge of basic calculus and linear algebra. The second part requires some knowledge of Fourier series and digital signal analysis. The conne...ctions between lifting and filter theory are presented and the wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals. The problems with finite length signals are treated in detail. MATLAB is used as the computational environment for examples and implementation of transforms. The book is well suited for undergraduate mathematics and electrical engineering students and engineers in industry. Jensen, A. is the author of Ripples in Mathematics The Discrete Wavelet Transform, published 2001 under ISBN 9783540416623 and 3540416625. Six hundred twenty nine Ripples in Mathematics The Discrete Wavelet Transform textbooks are available for sale on ValoreBooks.com, one hundred ten used from the cheapest price of $12.03, or buy new starting at $67.67
Information for Students Which course should I take for Gen Ed? We offer many courses that give you a chance to explore some of the cool things you can do with math. All of these courses are offered every semester. Math 105 (Math for Decision Making): Looking for a course in mathematics that focuses on applications? This course gives applications of math involving probability, mathematics of finance, and various types of optimization problems. Math 107 (Fundamentals of Applied Calculus): Calculus is a way of describing how quickly quantities change. This version of calculus is tailored to business and economics students and focuses on modeling data with technology with less emphasis on algebra. Math 108 (Calculus for Decision Making): Looking for a course in calculus that focuses on applications? This course explores calculus without worrying about the theoretical underpinnings of calculus. Applications include drug concentrations in the body via daily medication, credit card debt, and population growth. This course is offered every semester. Math 111 (Calculus 1): Roughly 300 years ago, Newton and Leibniz asked three important questions: What is instantaneous rate of change? What is the area under a curve? And what is the amazing relationship between the first two questions? The answers to these questions helps solve problems in fields from physics to economics, from biology to the business world! Math 112 (Calculus 2): Population growth and differential equations, physics and integrals, finance and series. This and much more is explore as we apply calculus to problems in the real world. Math 144 (Stats for Business, Economics, and Management): Statistics are used frequently in the world of business and finance; this class will help you understand where these statistics come from and how to use them yourself. This class is targeted at students in the business school but will be useful for everyone! Math 145 (Stats for Health/Life Sciences): Similar to Math 144, this class looks at statistics as it's used in the health, life, and natural sciences. Math 152 (What is Mathematics?): What is the role of mathematics in our world? What does infinity really mean? How small is small? Questions like this (and many more) are explored in this course. We explore what mathematics means to us as individuals and as a culture. Math 155 (Basic Statistical Reasoning): Statistics are increasingly used in the news and on the internet. This class will help you make sense of all the stats. It's a little less technical than Math 144/145, so it's perfect for students looking for gen ed credit. Math 161 (Math and Society): How does we manage credit card debt or choose the right loan? How do we share a cake in a fair way? These questions and many more in this course show us how mathematics helps us function as a society.
Beginning Algebra - Text Only - 04 edition Summary: Miller/O'Neill Beginning Algebra is an insightful text written by instructors who have first-hand experience with students of developmental mathematics. The authors have placed an emphasis on graphing, by including special sections called, "Connections to Graphing" at the end of Chapters 1-5, before the formal presentation of Graphing appears in Chapter 6. The "Connections to Graphing" sections may be considered optional for those instructors who ...show moredo not prefer an early introduction to graphing. For those who do prefer graphing early, instructors can use the "Connections to Graphing" sections together where they prefer to introduce graphing. A section on geometry appears in "Chapter R" for instructors who look for such content in Beginning Algebra. Applications that incorporate geometric concepts may also be found throughout the text. Chapter R also contains a section on study skills. This section provides easy to digest tips (in list format) for course success. The authors have crafted the exercise sets with the idea of infusing review. In each set of practice exercises, instructors will find a set of exercises that help students to review concepts previously learned, and in this way, students will retain more of what they have learned. The exercise sets also contain "translation" exercises which provide students with an opportunity to convert from English phrases to mathematical symbols and from mathematical symbols to English phrases, thus helping students to strengthen their command of mathematical language. Moreover, the applications found in the exercise sets are based on real-world data, which helps to promote students' interest in mathematics, and in turn, may serve to motivate and engage them more effectively. Other features include mid-chapter reviews and classroom activities. The classroom activities are of special value, in that through their use, students may begin to take greater ownership over their learning. The classroom activities were designed to be quick activities students could perform in class (either individually, or collaboratively in groups). In short, the Miller/O'Neill Beginning Algebra text offers enriching applications, a high level of readability, and excellent opportunities for students to become actively engaged in their exploration of mathematics. Features :
Academics Middle School Mathematics Philosophy The objectives in Middle School mathematics are the maintenance, expansion, and refinement of arithmetic skills; the acquisition of a comprehensive mathematical vocabulary, including terminology and symbolism; and an acquaintance with problem-solving techniques necessary for success in the study of algebra. An experiment-based, interdisciplinary math/science project is conducted second term, leading to the Middle School Math-Science Night when projects are exhibited. Grade Five Skills using arithmetic operations, including work with fractions and decimals, are refined and expanded. Geometry lessons include perimeter, area, and volume. Individual projects help students to realize the everyday use of mathematics outside the classroom. Text: Prentice Hall, Mathematics: Course 1. Grade Six The mathematics vocabulary continues to expand, and terms dealing with symbols and notation are presented. Estimation skills as well as fraction, decimal, and percent skills are reviewed and expanded. Measurement systems, number theory, geometry, ratio, proportions, and exponents are also studied. Positive and negative numbers and algebra are introduced. Text: Prentice Hall, Mathematics, Course 2. Form I Skills necessary for the understanding of algebra and more advanced arithmetic concepts are introduced. Work with rational numbers and variables leads to the use of algebraic expressions necessary for the solution of linear equations. Defining variables and building equations are applied to problem solving. The geometry unit revisits lines, angles, and triangles, and introduces perimeter, area and volume. Some concepts of elementary statistics are introduced. Form II: Algebra I In this course, students learn to solve systems of equations and linear and quadratic equations, aswell as learning to simplify, add, subtract,multiply, and divide polynomials. Other topicswe cover include graphing, slope, exponents, and square roots. Most topics include word problems with practical applications. Text: Addison Wesley, Algebra I, Classic Edition.
College Algebra - 6th edition Summary: Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE ALGEBRA, Sixth Edition. This straightforward and easy-to-use algebra book will help you learn the fundamentals of algebra in a variety of practical ways. The book features new tools to help you succeed, such as learning objectives before each section to prepare you for what you're about to learn, and a list of formulas and key concepts after each section that help reinf...show moreorce what you've learned. In addition, the book includes many real-world examples that show you how mathematics is used to model in fields like engineering, business, physics, chemistry, and biology. ...show less Lothar Redlin Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology. Saleem Watson Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional6th Edition. Used - Good. Used books may have used stickers on the cover, and do not include online codes or other supplements unless noted. Choose EXPEDITED shipping for faster delivery! n145151.45 +$3.99 s/h VeryGood ocbookstx Richardson, TX 1111990166152.25
This textbook is written primarily for undergraduate mathematicians and also appeals to students working at an advanced level in other disciplines. The text begins with a clear motivation for the study of numerical analysis based on real-world problems. The authors then develop the necessary machinery including iteration, interpolation, boundary-value problems and finite elements. Throughout, the authors keep an eye on the analytical basis for the work and add historical notes on the development of the subject. There are numerous exercises for students. Class tested and based on a course taught by the authors at Oxford University Reviews & endorsements "This book is a solid text in the basics of numerical mathematics, using more of a theoretical background than most. If you are looking for a book to use in a course in numerical analysis where there is an emphasis on the theoretical background, then this one will serve your needs." Journal of Recreational Mathematics
Mathematics Modules Mathematics module courses are for students needing to improve their skills for college-level work. These courses are available at the Learning Commons in Glen Ellyn. Individualized, Appointment-Based Courses Mathematics module courses are offered in an individualized appointment-based format through the Learning Commons in Glen Ellyn. Students meet with an instructor once a week and follow a syllabus to guide instruction. The instructor acts as a facilitator of instruction, and the student does study work at home or in one of the Learning Commons using a wide variety of print material, computer-delivered programs or audio/video presentations. Please call (630) 942-2131 for more
Arun Prakash. School of Civil Engineering. 7.2 Introduction to MATLAB File Processing . Using computers to solve (engineering) problems of our interest is called Computing. In. The solution of a system of equations Ax = b is given by x = A?1 b. disp@'9"ot—l num˜er of students in the ™l—ss a9 numPstr@nA"A Encribd is NOT affiliated with the author of any documents mentioned in this site. All sponsored products, company names, brand names, trademarks and logos found on this document are the property of its respective owners.
Elementary Mathematical Modeling: A Dynamic Approach, 1st Edition ELEMENTARY MATHEMATICAL MODELING uses mathematics to study problems arising in areas such as Genetics, Finance, Medicine, and Economics. Throughout the course of the book, students learn how to model a real situation, such as testing levels of lead in children or environmental cleanup. They then learn how to analyze that model in relationship to the real world, such as making recommendations for minimum treatment time for children exposed to lead paint or determining the minimum time required to adequately clean up a polluted lake. Often the results will be counterintuitive, such as finding that an increase in the rate of wild-life harvesting may actually decrease the long-term harvest, or that a lottery prize that is paid out over a number of years is worth far less than its advertised value. This use of mathematics illustrates and models real-world issues and questions, bringing the value of mathematics to life for students, enabling them to see, perhaps for the first time, the utility of mathematics the
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
This case study unit offers strategies for working with students with disabilities who have difficulty with beginning algebra. It provides information on strategies such as using algebra manipulatives, teaching vocabulary, and implementing graphic organizers.(Secondary) This case study unit offers strategies for working with students with disabilities who have difficulty with algebra. It provides information on strategies such as using intermediate algebra manipulatives, teaching vocabulary, and implementing graphic organizers.(Secondary) This webcast focuses on the need for challenging mathematics courses—especially algebra—and mathematics instructional strategies to help students learn. Geared toward researchers, mathematics teachers at the middle school and high school levels, district-level mathematics experts, principals, and preservice educators, the hourlong webcast addressed the following questions: "Just what is 'algebra'?" and "Why are students having trouble with it in our schools?"
Elementary Linear Algebra - 6th edition ISBN13:978-0618783762 ISBN10: 0618783768 This edition has also been released as: ISBN13: 978-0547004815 ISBN10: 0547004818 Summary: The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system.The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding tec...show morehnology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice. ...show less Ships same day or next business day! UPS(AK/HI Priority Mail)/ NEW book $89.39 +$3.99 s/h New Premier Books BN Romulus, MI 0618783768 Brand New. Exact book as advertised. Delivery in 4-14 business days (not calendar days). We are not able to expedite delivery. $155.00 +$3.99 s/h New bluehouse acton, MA Brand new. $308.42 +$3.99 s/h New Bookeyez2 snellville, GA Brand New Title. We're a Power Distributor; Your satisfaction is our guarantee! $315.95 +$3.99 s/h New Textbook Barn Woodland Hills, CA Hardcover New 0618783768
algebra 1, prealgebra and algebra 1, geometry and reading biology
Books Geometry & Topology What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics. The new and improved Tutor in a Book's Geometry. Designed to replicate the services of a skilled private tutor, TIB's Geometry, presents a teen tested visual presentation of the course and includes more than 500 well illustrated, carefully worked out proofs and problems with step by step explanations. Throughout the book, time tested solution and test taking strategies are demonstrated and emphasized. The recurring patterns that make proofs doable are explained and illustrated. Dozens of graphic organizers that help students understand, remember and recognize the connection between concepts are included. With the intent to level the playing field between students who have tutors and those that don't, long time successful private mathematics tutor and teacher, Jo Greig, packed 294 pages with every explanation, every drawing, every hint, every memory tool, examples of the right proofs and problems, and every bit of enthusiasm that good tutors impart to their private tutoring students. Ms. Greig holds a bachelors' degree in mathematics. Dr. J. Shiletto, the book's mathematics editor, holds a Ph.D in mathematics. time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences. Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series—Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence—it makes ancient wisdom and its astonishing interconnectedness accessible to us today. Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th century mathematician Oliver Byrne employed the color scheme for the figures and diagrams in his most unusual 1847 edition of Euclid's Elements. The author makes it clear in his subtitle that this is a didactic measure intended to distinguish his edition from all others: "The Elements of Euclid in which coloured diagrams and symbols are used instead of letters for the greater ease of learners." As Surveyor of Her Majesty's Settlements in the Falkland Islands, Byrne had already published mathematical and engineering works previous to 1847, but never anything like his edition on Euclid. This remarkable example of Victorian printing has been described as one of the oddest and most beautiful books of the 19th century. Each proposition is set in Caslon italic, with a four-line initial, while the rest of the page is a unique riot of red, yellow, and blue. On some pages, letters and numbers only are printed in color, sprinkled over the pages like tiny wild flowers and demanding the most meticulous alignment of the different color plates for printing. Elsewhere, solid squares, triangles, and circles are printed in bright colors, expressing a verve not seen again on the pages of a book until the era of Dufy, Matisse, and Derain. The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy student and teacher sewn softcover edition in one volume, with minimal notes and a new index/glossary. This survey of topics in Non-Euclidean Geometry is chock-full of colorful diagrams sure to delight mathematically inclined babies. Non-Euclidean Geometry for Babies is intended to introduce babies to the basics of Euclid's Geometry, and supposes that the so-called "Parallel Postulate" might not be true. Mathematician Fred Carlson believes that it's never too early to introduce children, and even babies, to the basic concepts of advanced mathematics. He is sure that after reading this book, the first in his Mathematics for Babies series, you will agree with him! This is one of two versions of this title. The interior of both books is identical, but the cover design on this one is done in Pretty Pink, perfect for babies who prefer the color pink instead of blue. The Baby Blue edition can be found here: Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship betweenThree-time New York Times bestselling author Danica McKellar now makes it a breeze to excel in… Geometry! Hollywood actress and math whiz Danica McKellar has completely shattered the "math nerd" stereotype. For years, she's been showing girls how to feel confident and ace their math classes – with style! With Girls Get Curves, she applies her winning techniques to geometry, giving readers the tools they need to feel great and totally "get" everything from congruent triangles to theorems, and more. Inside you'll find:
High School Probability Tutor High School Probability Tutor Specifically designed to meet the needs of high school students, REA's High School Probability Tutor presents hundreds of solved problems with step-by-step and detailed solutions. Almost any imaginable problem that might be assigned for homework or given on an exam is covered. Topics include the basic concepts of probability, counting, discrete distributions, binomial and multinomial distributions, continuous distributions, conditional probability, expectation, joint distributions, functions of random variables, and sampling theory. Fully indexed for locating specific problems rapidly.
Demystified is your solution for tricky subjects like trigonometry. If you think a Cartesian coordinate is something from science fiction or a hyperbolic tangent is an extremeexaggeration, you need Trigonometry DeMYSTiFieD , Second Edition, to unravel this topic's fundamental concepts and theories at your own pace. This practical guide eases you... more... Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious. The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical t ? whether you need a supplement to your textbook... more... From angles to functions to identities - solve trig equations with ease Got.... more... Trigonometry has always been an underappreciated branch,...
Summary:This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to multiply and divide signed numbers. By the end of the module students should be able to multiply and divide signed numbers and be able to multiply and divide signed numbers using a calculator. Summary:This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter Addition and Subtraction of Whole Numbers and contains many exercise problems. Odd problems are accompanied by solutions. Summary: ... by another.[Expand Summary] a calculator to multiply one whole number by another.[Collapse Summary] Summary: ... subtract decimals.[Expand Summary] to use the calculator to add and subtract decimals.[Collapse Summary] Summary:ThisSummary:This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module reviews the key concepts from the chapter "Introduction to Fractions and Multiplication and Division of Fractions." Summary: ... geometry problems.[Expand Summary] method to solve number problems and geometry problems.[Collapse Summary] Summary: ... whole number.[Expand Summary] fundamental principle of arithmetic and find the prime factorization of a whole number.[Collapse Summary]
First of all, let me make it very clear that all of the content in our books is available for free on Coolmath.com. We just have books because we've gotten a lot of requests over the years from people with limited Internet access and from people who, like me, just like the feel of a book in their hands when they are learning! Even though they use the term "Algebra" in kindergarten now - and don't even get me started on that one! (wink) - that's not the "Algebra" that in these books. This is the Algebra a student starts to do in middle or high school when their class is called "Algebra." So, for our Algebra books, the most common question I get from parents is, "Which ones do I need?" Middle and high schools break up their Algebra programs in different ways. Some have Algebra 1 and Algebra 2 while others have Algebra 1A, Algebra 1B... and, then, you have community colleges that break it up as Beginning Algebra and Intermediate Algebra! There is also a LOT of overlapping in these courses. Oy. Because of this, I've just broken my books down by chapter topics, put them in the most reasonable order that you'd learn in and separated them into three books because two would have been just too thick. :-) Also, there are some textbooks and some teacher who throw weird extra stuff in there. To avoid confusing everyone (mostly the students), I've left the fringe out. As close as I can guess for you, for Algebra 1 (and Beginning Algebra), my Part 1 and Part 2 books should cover most of the material. For Algebra 2 (and Intermediate Algebra), my Part 2 and Part 3 books should cover most of the material. For Precalculus, you'll probably want Part 2, Part 3 and my Precalculus Review book. If you or your child have been through the math wringer and feel all beat up, you should definitely get my Math Survival Guide, because I've been there and know how you feel. This book will help the battered student get past the mental obstacles and move forward to success. Go here to see the table of contents of these books and make a purchase:
Think Bayes by Allen B. Downey Publisher Comments If you know how to program with Python and also know a little about probability, youre ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use... (read more) Visions of Infinity: The Great Mathematical Problems by Ian Stewart Publisher Comments... (read more) Lattice: Multivariate Data Visualization with R (Use R) by Deepayan Sarkar Publisher Comments Written by the author of the lattice system, this book describes lattice in considerable depth, beginning with the essentials and systematically delving into specific low levels details as necessary. No prior experience with lattice is required to read... (read more) Great Ideas of Modern Mathematics by Jagjit Singh Publisher Comments An internationally famous expositor discusses such topics as differential equations, matrices, groups, sets, transformations, mathematical logic and other important areas of modern mathematics. His clear-cut explanations for both lay readers and... (read more) Cartoon Guide to Statistics by Larry Gonick Publisher Comments If you have ever looked for P-values by shopping at P mart, tried to watch the Bernoulli Trails on "People's Court," or think that the standard deviation is a criminal offense in six states, then you need The Cartoon Guide to Statistics to put you on the... (read more) Singapore Math Practice, Level 3b (Singapore Math Practice) by Not Available (na) Publisher Comments Welcome to Singapore Math––the leading math program in the world! This workbook features math practice and activities for fourth grade students based on the Singapore Math method. An introduction at the front of the book explains Singapore Math... (read more) Sacred Number: The Secret Quality of Quantities by Miranda Lundy Publisher Comments Numbers permeate every aspect of our lives; very little happens without a basic ability to manipulate the simple whole numbers we all take for granted. Beautifully illustrated with old engravings as well as contemporary imagery, Sacred Number introduces... (read more) Professor Stewart's Cabinet of Mathematical Curiosities by Ian Stewart Publisher Comments Knowing that the most exciting math is not taught in school, Professor Ian Stewart has spent years filling his cabinet with intriguing mathematical games, puzzles, stories, and factoids intended for the adventurous mind. This book reveals the most... (read more) Introducing Mathematics (Introducing) by Ziauddin Sardar Publisher Comments Introducing Mathematics traces the story of mathematics from the ancient world to modern times, describing the great discoveries and providing an accessible introduction to topics such as algebra and chaos theory
Math 149 - Precalculus Syllabus for section OC1 & OC2 – Fall, 2012 Instructor: Jennifer Strehler Office: DP 2741 E-mail: strehler@oakton.edu Website: Textbook: Lial, Precalculus – 5th edition MyLabsPlus (not MyMathLab) is required for this section. Calculator: A graphing calculator is strongly recommended (TI 83 suggested) A calculator without the ability to graph (and without trig/log functions) is required. Office Hours Since this is an online class, most of our communication will be online. If you have a question about a specific problem in the homework, please use the "ask my instructor" link in the homework software (I get a copy of the problem you're working on this way!) I will also be on the Des Plaines campus: 2741 - or by phone: (847)376-7071 during the following times: Tuesday: 10:00 – 10:50 Thursday: 10:00 – 10:50 Saturday: 12:00 – 2:50 Prerequisites MAT 053 or geometry proficiency; and MAT 110 or the equivalent with a grade of C or better, or an appropriate score on the Mathematics Assessment Test. It is presumed that you recall Intermediate Algebra, as there is no time to review in this course. Course (catalog) Description This course surveys algebraic and transcendental functions. Content includes polynomial, rational, exponential, logarithmic and trigonometric functions; conic sections, series, parametric equations, and polar equations. Technology will be integrated throughout the course. Learning Objectives It is presumed that students will spend a minimum of 10 hours per week in independent study (reading the text, doing homework, working unassigned problems) in order to meet the following objectives: A. Understand the concepts of relations and functions. B. Understand the basic characteristics and graphs for the following functions: polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric. C. Apply algebraic techniques to trigonometric expressions, identities, and triangles. D. Understand the basic characteristics and graphs of the conic sections. E. Understand the concepts associated with vectors and their operations. F. Apply the concepts of sequences and series. G. Understand parametric equations. H. Understand polar equations. I. Use technology for graphing and evaluating functions. 1. Generate the complete graph for the elementary functions. 2. Solve equations involving elementary functions. Academic Integrity Students, Faculty and administration at Oakton Community College are required to demonstrate academic integrity and follow Oakton's Code of Academic Conduct. This code prohibits: cheating, plagiarism (turning in work not written by you or lacking proper citation), falsification and fabrication (lying or distorting the truth), helping others to cheat, making unauthorized changes in official documents, pretending to be someone else or having someone else to pretend to be you, making or accepting bribes, special favors, or threats, and any other behavior that violates academic integrity. There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students with a fair hearing if a complaint is made. If you are found to have violated the policy, the minimum penalty is failure on the assignment and a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years. Details of the Code of Academic Conduct can be found in the Student Handbook. Course Expectations  I expect that you will log into MyLabsPlus and work regularly (at least two times each week) toward the successful completion of this course.  I expect that your schedule will allow you to complete all assignments and take the exams /quizzes when they are scheduled. All exams, quizzes and assignments have firm due dates and requests for extensions will NOT be granted. The exams will be available in the testing center the week prior to the exam due date. Quizzes and homework can be completed early.  Academic integrity. All work is expected to be your own.  Ask for help when you need it. The tutoring centers (room 2400 DP in Des Plaines and A135 in Skokie), the free publisher-provided tutoring and my office hours are excellent resources for help. The tutoring centers are available Monday – Thursday from 8am – 8pm, Friday from 8am - 4pm & Saturday 10am – 2pm.  A calculator without the ability to graph (and without trig/log functions) is required for the exams. As such, it is best to practice solving problems in the method described in the text. For example, you will need to memorize the unit circle and use it from memory to answer questions on the exams without the use of a calculator with trig functions. Communication  I will send several e-mails to the entire class during the course of the semester. It is your responsibility to ensure that the e-mail address on file with the registrar is the address to which you wish to receive course communication.  Please use e-mail as your primary means of communication. I will read and respond to e-mail at least once a day during the week. The time I check my e-mail is likely to be irregular. If you send me a message at 8:30 am & I checked my e-mail at 7:30 that morning, I may not get your message until whenever I check e-mail the next day. It is not guaranteed that I will check e-mail on weekends.  I am teaching more than one course this term. Make sure you put MAT 149 in the subject line of your e-mail so that I know which class you are in (and that your e-mail is not spam!)  Please use complete sentences and avoid textspeak in your e-mail. Assignments, Quizzes and Exams All homework, quizzes and exams have firm dates. Extensions will NOT be granted. Date Due 08/31/12 Chapter 2 (incl. 1.6) homework and quiz 09/10/12 Chapter 3 homework and quiz 09/19/12 Chapter 4 homework and quiz 09/15/12 – 09/21/12 Exam 1 (chapters 2, 3 & 4) available 09/28/12 Chapter 9 homework and quiz 10/08/12 Chapter 10 (incl. 2.2) homework and quiz 10/17/12 Chapter 11 homework and quiz 10/13/12 – 10/19/12 Exam 2 (chapters 9, 10 & 11) available 10/26/12 Chapter 5 homework and quiz 11/07/12 Chapter 6 homework and quiz 11/03/12 – 11/09/12 Exam 3 (chapters 5) available 11/19/12 Chapter 7 homework and quiz 11/28/12 Chapter 8 homework and quiz 11/17/12 – 11/30/12 Exam 4 (chapters 7 & 8) available 12/01/12 – 12/07/12 Final exam (chapters 2 – 11) available  Homework will be done through MyLabsPlus and is based on chapters 2 – 11 of the textbook. Homework must be completed according to the schedule above.  There will be ten chapter quizzes, which will be administered through MyLabsPlus. Quizzes must be completed according to the schedule above. In order to take a quiz, you must have completed all homework for that chapter with a score of at least 70%. If you do not have at least a 70% on each assignment, you will not be able to take that chapter quiz.  There will be five exams that will be administered at the testing center located on the Des Plaines campus of Oakton Community College. o The hours of our testing center are: Mon – Thurs: 8:00 – 8:00 Friday: 8:00 – 4:00 Saturday: 10:00 – 2:00 o If you need to take the exam at the Skokie campus, it is your responsibility to inform me no later than 9/15. If you are not able to take the exams at one of our campuses, please contact Robin Nash at rnash@oakton.edu in order to make alternative arrangements as soon as possible. Arrangements must be made with the facility that will proctor your exam no later than 9/15. o You will be given 2 hours to complete each of the first 4 exams. If you arrive within 2 hours of the close of the testing center, you will only be allowed to work on the exam until the testing center closes and no additional time will be given for the exam. You will have 3 hours for the comprehensive final and should arrive at the testing center at a time that will allow you to complete the exam. The dates that these exams are available are listed below. Grading MyLabsPlus shows a current average that is never accurate. Course grades will be computed as follows: Exam 1 Available 09/15/12 – 09/21/12 10% Exam 2 Available 10/13/12 – 10/19/12 10% Exam 3 Available 11/03/12 – 11/09/12 10% Exam 4 Available 11/17/12 – 11/30/12 10% Final Exam Available 12/01/12 – 12/07/12 20% Homework Average 20% Quiz Average 20% Course grades will be determined as follows: 90% - 100% A 80% - 89% B 70% - 79% C 60% - 69% D Less than 60% F A grade if "I" (Incomplete) must be formally requested of the instructor by the student and may be granted only if the student has missed no more than one test for the entire term and the student's course average is at least 70. The decision to grant the "I" grade will be made by the instructor alone. No incomplete grades will be given without documented evidence of serious illness or circumstances. Other Course Information If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the ASSIST office in Instructional Support Services. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program. Important Dates August 20 Fall, 2012 semester classes begin. August 25 Last day to submit proof of residency, business service agreements and (noon) chargebacks/joint agreements. September 3 Labor Day holiday. College closed. September 16 Last day to withdraw and have course dropped from record. Last day to change to audit. September 30 Incomplete (I) grades from Summer, 2012 semester for which faculty have not submitted final grades will become an "F" after this date. October 6 (noon) Last day for filing Graduation Petitions October 14 Last day to withdraw with a "W" from 16-week courses; Students will receive a grade in all courses in which they are enrolled after October 14. November 11 Veterans' Day holiday. College closed. November 19 Registration opens for Spring, 2012 semester November 24, 25 Thanksgiving recess. College closed. Outline of Topics A. Functions and their graphs 1. Operations on functions: combinations 2. Graphing techniques 3. Translations and rotations 4. Inverse functions B. Polynomial Functions: Graphs and Zeros 1. Quadratic functions 2. Polynomial functions of higher degree 3. Remainder and factor theorems 4. Complex zeros of polynomial functions 5. Fundamental Theorem of Algebra 6. Applications C. Rational Functions and Conic Sections 1. Rational functions and their graphs 2. Conic sections a. Center at origin b. Translations D. Exponential and Logarithmic Functions 1. Exponential functions and their graphs 2. Logarithmic functions and their graphs 3. Properties of logarithms 4. Solving exponential and logarithmic equations 5. Applications E. Find the intersection of two polynomials (Substitution Method) F. Sequences and Series 1. Fundamentals of sequences and series 2. Arithmetic sequences 3. Geometric sequences 4. Applications G. Trigonometric Functions 1. Measurement of angles 2. Circular functions 3. Graphs of sines and cosines 4. Graphs of the other trigonometric functions 5. Inverse trigonometric functions and their graphs 6. Trigonometric identities a. Pythagorean identities b. Sum and difference formulas c. Multiple and half angle formulas d. Sum-to-product; product-to-sum 7. Solving trigonometric equations 8. Applications a. Complex numbers and their trigonometric form b. Solving right triangles c. Law of Sines, Law of Cosines d. Roots and powers of complex numbers e. Polar coordinates f. Parametric equations H. Vectors 1. Geometric and algebraic representation of vectors 2. Basic operations with vectors I. Technology 1. Generate the complete graph of each trigonometric and inverse trigonometric function including setting a proper window, tracing and zooming. 2. Graphically locate the x-intercepts, the relative extrema and determine asymptotic behaviors. 3. Solve equations graphically, numerically and/or symbolically
500 Ways to Achieve Your Best Grades. We want you to succeed on your college linear algebra midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and get your best grades. These questions and answers are similar to the ones you'll findon a typical college... more... Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries... more... An advanced Practice Makes Perfect workbook for linear algebra, designed to reinforce ideas and concepts, to provide 500 exercises and answers, to offer hundreds of solved problems--making this workbook the ideal complement to class study or self-study. more...
97803879627 Calculus (Undergraduate Texts in Mathematics) In a first calculus course, students typically are exposed to a watered down version of calculus, with little or no emphasis on basic concepts. Students must make a large leap from such a course to a rigorous, substantive analysis course, and it is the purpose of this book to aid such a transition. While examining the fundamental concepts of calculus, the author stresses motivation and stimulating examples, and endeavors to let the student discover for himself something about the nature of calculus. The exercises are often provided with helpful hints and, in some cases, with outlined solutions
books.google.com - Advanced Mathematics fully integrates topics from algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis. Word problems are developed throughout the problem sets and become progressively more elaborate. With regular practice, high-school level students will be able to solve... Mathematics Advanced Mathematics: An Incremental Development Advanced Mathematics fully integrates topics from algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis. Word problems are developed throughout the problem sets and become progressively more elaborate. With regular practice, high-school level students will be able to solve challenging problems such as rate problems and problems involving abstract quantities. Conceptually oriented problems help prepare students for college entrance exams such as the ACT and SAT. - Publisher. I hated taking this in high school, but when I graduated, I asked if I could buy a new copy to keep with me. I'm re-reading through it to freshen up on my advanced math, and now I'm glad I decided to keep this book :-).Read full review
Geometry Reasoning, Measuring, Applying Author: Unknown ISBN-13: 9780395937778 ISBN: 0395937779 Edition: 10 Pub Date: 2000 Publisher: Houghton Mifflin College Div Summary: The theorems and principles of basic geometry are clearly presented in this workbook, along with examples and exercises for practice. All concepts are explained in an easy-to-understand fashion to help students grasp geometry and form a solid foundation for advanced learning in mathematics. Each page introduces a new concept, along with a puzzle or riddle which reveals a fun fact. Thought-provoking exercises encourag...e students to enjoy working the pages while gaining valuable practice in geometry
Algebra book : 529 results priced between £5.00 and £150.00 Algebra book Sort: 529Algebra book£5.00£150.00/l/Algebra-book Algebra I Workbook for Dummies 2nd Edition The Title "Algebra I Workbook for Dummies " is written by Mary Jane Sterling . This book was published in the year 2011. The ISBN number 1118049225\|9781118049228 is assigned to the Paperback version of this title. The book displayed here is a 2nd Edition edition. This book has total of pp. 312 (Pages). The publisher of this title is John Wiley & Sons . We have about 123734 other great books from this publisher. Algebra I Workbook for Dummies is currently Available with us. This handbook is designed as a work of reference, and provides a convenient source of basic definitions and formulae for use throughtout the three blocks. In addition to this it also contains a quick reference guide to Maple commands; and summaries of the main concepts, definitions and techniques of each of the units. Helps students connect mathematics to every day examples through the use of relevant applications and real data. This title features Enhanced WebAssign, which provides interactive, visual learning support with examples and practice exercises that reinforce the text's pedagogical approach. From radical problems to rational functions -- solve equations with ease Do you have a grasp of Algebra II terms and concepts, but can't seem to work your way through problems? No fear -- this hands-on guide focuses on helping you solve the many types of Algebra II problems in an easy, step-by-step manner. Purchase Mystery Math: A First Book of Algebra by David A Adler,Edward Miller and Read this Book on Kobo's Free Apps. Explore Kobo's Vast Collection of eBooks - Over 3 Million Titles, Including 2 Million Free Books! This that are... A Collection of Problems in Algebra with Solutions, Book, 2 Matrices and Vector Spaces Problem solving is an art that is central to understanding and ability in mathematics. With this series of books the authors have provided a selection of problems with complete solutions and test papers designed to be used with or instead of standard Textbooks on algebra. For the convenience of the reader, a key explaining how the present books may be used in conjunction with some of the major textbooks is included. Each Book of problems is divided into chapters that begin with some notes on notation... Can, on to advanced concepts such as inner product spaces and normality. All of this occurs by way of a series of 164 problems, each with hints and, at the back of the book, full solutions. This book... Product Description Schaum's has Satisfied Students for 50 Years.Now Schaum's Biggest Sellers are in New Editions!Schaum's Outlines-Problem SolvedMore than... AS Use of Maths: Algebra and Graphs (incorporating Applying Maths): Core Book In stock at one or more sellers. The mathematics is presented in contexts relevant to students' studies, linking maths to other areas of the curriculum with a strong focus on integrating ICT. This work includes advice on developing the assessed portfolio and practice exam questions at the end of each chapter. Full colour comprehensions provide practice for the Applying Maths exam. * The Guided Notebook is an interactive workbook that guides students through the course by asking them to write down key definitions and work through important examples for each section of the eText. This resource is available in a three-hole-punched, unbound format to provide the foundation for a personalized course notebook. Students can integrate their class notes and homework notes within the appropriate section of the Guided Notebook. Instructors can customize the Guided Notebook files found... Product Description Conf... Sham is a famous author for several Kids Books,Kids Puzzles,Children Puzzles, Children Questions, Children Games,Kids...... The Title "Algebra A Combined Approach, Books a la Carte Plus MML/MSL Student Access Code Card 4th Edition" is written by Elayn Martin-Gay. This book was published in the year 2011. The ISBN number 0321772008\|9780321772008 is assigned to the Loose-leaf version of this title. The book displayed here is a 4th Edition edition. The publisher of this title is Longman Group . We have about 12182 other great books from this publisher. Algebra A Combined Approach, Books a la Carte Plus MML/MSL Student Access... Charles P. "Pat" McKeague earned his B.A. in Mathematics from California State University, Northridge, and his M.S. in Mathematics from Brigham Young University. A well-known author and respected educator, he is a full-time writer and a part-time instructor at Cuesta College. He has published twelve textbooks in mathematics covering a range of topics from basic mathematics to trigonometry. An active member of the mathematics community, Professor McKeague is a popular speaker at regional conferences... DESCRIPTION: This name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information... The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has considerable mathematical significance, with applications in various fields: e.g., in computer science---databases, specification theory, AI---and in anthropology, economics, physics, and philosophical logic.This comprehensive treatment of the theory of relation algebras and the calculus of relations is the first devoted to a systematic development of the... The first part of this monograph is an elementary introduction to the theory of Fr��chet algebras. Important examples of Fr��chet algebras, which are among those considered, are the algebra of all holomorphic functions on a (hemicompact) reduced complex space, and the algebra of all continuous functions on a suitable topological space.The problem of finding analytic structure in the spectrum of a Fr��chet algebra is the subject of the second part of the book. In particular, the author pays attention... Linear Algebra: An Introduction With Mathematica uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Mathematica. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Mathematica. The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer... This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required. Volume II completes the description of the main aspects of the theory, covering representation questions, model theory and decision problems for them, translations from logic to algebra and vice-versa, and relationships with other algebraic versions of logic. The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as ...
more details Developmental mathematics is the gateway to success in academics and in life. George Woodbury strives to provide his students with a complete learning package that empowers them for success in developmental mathematics and beyond. The Woodbury suite consists of a combined text written from the ground up to minimize overlap between elementary and intermediate algebra, a new workbook that helps students make connections between skills and concepts, and a robust set of MyMathLab resources. Note: this item is for the textbook only; supplements are available separately.
Did It Mathematics 3 (Paperback) I Did It Mathematics, an activity-based and interactive course, has been prepared in conformity with the latest NCERT syllabus and the National Curriculum Framework (2005). It presents mathematical concepts in a logical and comprehensive manner and with high degree of clarity. It also encourages students to think, discuss and assimilate ideas and concepts with great ease. The simple and lucid manner of presentation of contents coupled with large number of illustrative examples facilitate easy grasp of concepts. The in-text activities in the books provide opportunity to students to relate mathematical concepts with everyday life. Key Features" Overview to help teachers develop comprehensive lesson plans" Vocabulary Learnt to help students learn the mathematical terms " Word Attack to develop skills for applying mathematics in day-to-day life" Maths Lab Activities to reinforce the concepts learnt in each chapter A separate Activity Book with full colour stickers is available. Details Of Book : I Did It Mathematics 3 Book: I Did It Mathematics 3 Author: Mahesh ISBN: 052118519X ISBN-13: 9780521185196 Binding: Paperback Publishing Date: 2010
The student workbook includes a set of lesson review boxes accompanied by questions that provide practice for previously taught concepts and the concepts taught in the lesson. "Exploring Math Through..." sections help students understand how ordinary people use algebraic math, providing concrete examples of how math is useful in life. Students will need to supply paper to work the problems. 333 pages, softcover. The teacher's guide includes the main concepts, lesson objectives, materials needed, teaching tips, the assignment for the day, and the reduced student pages with the correct answers supplied. Each lesson will take approximately 45-60 minutes, and is designed to be teacher-directed. Softcover. Arranged by assignment category, the test & resource book includes 16 tests, 4 quarter tests, lesson worksheets, formula strips, nets supplements, and algebra tiles. Tests are designed to be given after all the lesson material is presented, generally after 10 days. Softcover. Customer Reviews for Horizons Math Algebra (Grade 8) Complete Set This product has not yet been reviewed. Click here to continue to the product details page.
Math lessons i should know for 2D Game Developing? Hello, i recently just started off with SFML and i stumbled upon a math lesson known as the 'Vector Algebra', i believe it's a Grade-12 mathematics lesson and i'm still a 2nd year student so i didn't know what it is, anyways, after spending quiet some time learning this lesson on khanAcademy, i would like to know what are some other mathematics lessons that are most likely going to appear after this one? also, is there like a book that teaches you math but the 'games developing' perspective? 'rather than learning the entire lesson, that way you could just learn a portion of it (the one that you're going to need for games only) Thank you. I'm pretty sure there's both a math and physics book "for game designers/developers". I own one of them, but my books are packed up for the moment. Trigonometry, vectors, matrices...depending on whether you're doing soley 2d graphics or 2d transforms in a 3d system Knowing the maths is half of the game, you also have to learn how to properly implement it (if I got a penny for every time a game implemented their gravity so the player follows an awkward "triangle curve" and not a parabola, I'd be rich). Looking at other people's code is the best thing you can do to learn that. You don't have to understand everything, but you can look at specific sections of code to better understand how they did it, and then compare it to yours. Try some of our maths articles -- in particular, the "math for game developers" series provide some good video-based explanations of useful topics. Beyond basic maths, vector algebra, and perhaps trigonometry a lot of maths topics are only useful for specific games rather than generally useful in every game; your best bet is to simply start out with different game ideas and then learn whatever you need to know to proceed. It really depends on your game design though. If you're making othello you don't need linear algebra and even physics, unless you want player to throw a ball and make a mess on the board, realistically, then you need those. If you're making action game like Odin Sphere/Muramasa: The Demon Blade, you need all of those (some of the physics). It really depends on your game. But honestly you need linear algebra and some physics.
Cranston Calculus also when the infamous "word problem" gets introduced. Algebra II extends what is covered in Algebra I, and typically includes more quadratic equations, and introduction to advanced factoring, and more simultaneous equations. It's fun too!
Mathematics After a competency test and evaluation by the Academic Director, students are placed in the appropriate class. PRE-ALGEBRA: MA50 (1 Credit) This course lays the foundation for entry into the algebra sequence. Emphasis is placed on developing numeracy (an intuitive grasp of how numbers interrelate) as well as proficiency in manually performing more difficult problems. The nine units introduce concepts that will be fully developed in Algebra I and Geometry. These topics include variables, expressions, solving equations, multi- step equations, inequalities, factors, fractions, exponents, rational numbers, ratio, proportion, probability, percents, linear functions, real numbers and right triangles. ALGEBRA 1: MA150 (1 Credit) This course gives a solid foundation in algebra. The emphasis is on problem solving. Topics covered include variables and groups, real number operations, first degree equations, polynomials, factoring, rational and irrational fractions and the application of these to linear equations and systems. INTEGRATED MATH I: MA200 (1 Credit) This course covers the arithmetic of whole numbers, fractions, decimals as they are used in algebra; graphing, number sets, real numbers, complex numbers, ratio, proportion, percent, roots, algebraic expressions, equations both linear and quadratic; manipulating and evaluating functions are topics covered in depth in this course. Some students will move independently through this course and also cover basic geometry of lines, points, planes, angles, polygons, circles , triangles, area, constructions, Pythagorean theorem, basic proofs. ACCELERATED ANALYTICAL GEOMETRY MA250 (1 Credit) Analytic Geometry is a college preparatory course in planar geometry taught in the classic Euclidean method of two-column proofs. Base knowledge is built through the introduction and application of certain axioms, definitions, postulates, and theorems all common to the study of geometry. The course generally targets 9th or 10 grade students who have had an approved full year course in Algebra I for credit and is intended to bridge the curriculums of Pre-Algebra and Algebra II. ALGEBRA 2: MA300 (1 Credit) This course begins with a thorough review of algebraic expressions, inequalities, absolute value and linear equations. The main focus is the development of skills in the use of linear, quadratic and polynomial functions. Other topics studied include use of the real, irrational and complex number systems. Graphing calculators are required. TRIGONOMETRY: MA350 (1 Credit) This course is intended to follow sequentially after Algebra 2. It begins with a brief review of algebraic expressions, inequalities, absolute value and linear equations and in the use of linear, quadratic, and polynomial functions. The main focus is development of skills using exponential, and logarithmic and polynomial functions. Other topics studied include use of the real and complex number systems, conic sections, systems of equations in two and three variables, trigonometry, polar equations and graphs, sequences and series. Graphing calculators are required. ALGEBRA 2/TRIG: MA400 (1 Credit) This is a rigorous course that begins with a brief review of algebraic expressions, inequalities, absolute value and linear equations. The main focus is development of skills in the use of linear, quadratic, polynomial, exponential, and logarithmic functions. Other topics studied include use of the real and complex number systems, conic sections, systems of equations in two and three variables, trigonometry, polar equations and graphs, sequences and series. Graphing calculators are required. PROBABILITY & STATISTICS: MA500 (1 Credit) The goal of statistics is to explore, analyze and present data. Numbers can speak volumes if we organize, display and summarize them well. Numbers can also be misleading, however. We will spend time analyzing how statistics are often manipulated to draw conclusions that serve the needs of a company or individual. In this statistics course you will learn how to draw valid conclusions by assessing variation and uncertainty. CALCULUS: MA550 (1 Credit) This course covers differentiation and integration of algebraic, geometric, exponential, logarithmic and trigonometric functions with theoretical and practical applications. Vector algebra, differential equations as well as sequences and series are briefly introduced.
Survey of Mathematics with Applications balances solid mathematical coverage with a comprehensive overview of mathematical concepts as they relate to varied disciplines. The text provides an appreciation of mathematics, highlighting mathematical history, and applications of math to the arts and sciences. It is an ideal book for students who require a general overview of mathematics, especially those majoring in liberal arts, the social sciences, business, nursing and allied health fields. Let us introduce you to the practical, interesting, accessible, and power... MOREful world of mathematics today-the world of "A Survey of Mathematics with Applications, "Expanded 8e.""
Refine Your Search: Comment: The Multiplication Properties of Exponents presented the correct concepts and models. Vocabulary and symbols that are used... see more Comment: The Multiplication Properties of Exponents presented the correct concepts and models. Vocabulary and symbols that are used throughout the lesson are defined and examples are provided to get a deeper understanding. Options for decoding text is evident with the teacher circling and highlighting key elements of the lesson. Highlighting and emphasizing key elements in the text and diagrams helps the students to distinguish between what it important and relevant to lesson. Options in the scaffolds for practice and perfomance are provided so that the student can develop the skill of expanding and evaluating exponents. Assessment is relevant, assessible, and timely. Tips are offered to help students toward answering the question correctly and mastering a skill. Technical Remarks:A good majority of the information was confusing to follow. Words were on top of other words, which made it difficult to follow. Could have been that the file was not compatible to my computer. Comment: Students are to decide which cell phone plan best fits their need. Students will use linear equations and actual cell phones... see more Comment: Students are to decide which cell phone plan best fits their need. Students will use linear equations and actual cell phones plans from cell phone providers to offer a real world connection. Using the internet helps students gain more knowledge about cell phones, rate plans, and text messaging. This lesson is rich in technology, having students explore many cell phone websites and youtube videos over making wise decisions. The lesson is meaningful to the students. Most of todays society is driven by the use of cell phones. It applies to the appropiate audience, Algebra students who will need access to a computer lab and a projector to show video clips. Comment: How to Design using ProEngineer defines vocabulary terms such as axis and sketch, that are essential in the steps of... see more Comment: How to Design using ProEngineer defines vocabulary terms such as axis and sketch, that are essential in the steps of designing. The tutorial provide options that guide information processing. Prompts for each steps are provided with an example of what the model robot, boat, and car should look like. The teacher understands how students vary in skill and abilitry level. Students have options of an easy robot, a medium level car, and hard boat, and an advanced level. Easy gives you step by step, medium gives minimum help, and hard gives no help. Comment: The lesson looks at the need to make computer science and engineering more exciting to students. Technology is growing and... see more Comment: The lesson looks at the need to make computer science and engineering more exciting to students. Technology is growing and changing everyday which and students need to be able to keep up. Four instructional objectives are reached during the lesson. They include performing skills, recalling facts, indentifyng concepts and applying pricniciples. The lesson strengthens the students ablility to collaborate within groups, promote creativity and independent thinking. The intended audience is elementary through high school who will be able to communicate through a safe social place by the name of Edmodo. In this lesson, students will need access to a school computer or home computer, CAD software, and access to email, google docs, and the internet. Author: Marcus Clark (Teacher (K-12)) Date Added: Dec
This collection of free worksheets provides practice in a variety of algebra topics, generating ten problems at a time for users to solve. Each worksheet is printable and comes with an answer key. To... More: lessons, discussions, ratings, reviews,... Students are given an input like f(3) and asked to move a point to the location on a given graph. Feedback is given. Students are also given the output, and asked to place the point properly, for ex... More: lessons, discussions, ratings, reviews,... This game explores functions in a different way: a and b = f(a) are drawn in a unique numerical line. When the user changes a, b = f(a) changes following a rule. The objective of the game is to discovLulu, one of the Alive Maths microworlds, is primarily a problem-posing and problem-solving environment where students are invited to look for numerical relationships and spatial patterns on the coordWindows software which allows the display of 2D and 3D diagrams both on one, and on different screens. Display 2D diagrams in the Cartesian and polar systems of coordinates. Display 3D diagrams in t... More: lessons, discussions, ratings, reviews,... Highlight the language of domain and range, and the ideas of continuity and discontinuity, with this tool that links symbolic and graphic representations of each interval of a piecewise linear functio
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
An Introduction to Partial Differential Equations with MATLAB Written for junior- and senior-level undergraduates in mathematics, physics, and engineering, this text provides a basic introduction to partial differential equations with a focus on Fourier series and integrals. Each chapter includes a prelude that introduces the topic and its historical background. MATLAB is used throughout the book to solve numerous example problems. Free Mathematical Modeling Technical Kit Learn how you can quickly build accurate mathematical models based on data or scientific principles.
Swampscott Calculusetermine or clarify the meaning of unknown and multiple-meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies. - Use context (e.g., the overall meaning of a sentence or paragraph; a word?s position or function in a sentence) as a clue to the... ...In addition to fundamental concepts, the study of physics develops the ability to think mathematically, and apply mathematical methods to many problems of interest, including outside of physics. Pre-calculus is the gate-keeper course for transition to calculus, and is therefore as important as c...
PTS Newsletter Booker Profiles in Mathematics Numeration And Computation The Booker profiles consist of: numeration (104 items covering aspects of numeration for whole numbers up to seven digits); and computation (184 items covering three concept items, 20 basic fact items, 20 algorithms, and 3 problem-solving items per operation). The material has been designed to identify and describe the origin of students' errors. The final profile analysis may demonstrate that although certain skill areas are present, the student does not know how to apply these skills and shows a lack of concept and/or process. The profile then provides direction for programming and remediation. registration-level: A age: 7+ Country of origin: Australia Copyright: Booker, 1994 administration: Individual timing: 30-45 minutes each part Product code Product title Registration level Certification level Price Quantity 8026BPMC Booker Profiles in Mathematics - Numeration And Computation Complete set
Jaap Suter released a new Geometric Algebra Primer on his web site. Available in PDF and PS format, this 64-page document offers an introduction to geometric algebra, complete with examples relevant for computer graphics. Here's a snippet from the site: "Geometric algebra is a new way of dealing with geometrical concepts and relations. It is based on Clifford algebra and has already been adopted with great enthusiasm in physics. Its elegance and ease of use is unparalleled. By introducing two simple concepts, the multivector and its geometric product, we obtain an algebra that allows subspace arithmetic. It turns out that being able to 'calculate' with subspaces is extremely powerful, and solves many of the hacks required by traditional methods. This paper provides an introduction to geometric algebra. The intention is to give the reader an understanding of the basic concepts, so advanced material becomes more accessible."
Lial Series has helped thousands of students succeed in developmental mathematics by providing the best learning and teaching support to students and instructors. The Lial Serieshas helped thousands of students succeed in developmental mathematics by providing the best learning and teaching support to students and instructors. 6.3 Using the Percent Proportion and Identifying the Components in a Percent Problem 6.4 Using Proportions to Solve Percent Problems 6.5 Using the Percent Equation 6.6 Solving Application Problems with Percent 6.7 Simple Interest 6.8 Compound Interest 7. Measurement 7.1 Problem Solving with U.S. Measurement Units 7.2 The Metric System – Length 7.3 The Metric System – Capacity and Weight (Mass) 7.4 Problem Solving with Metric Measurement 7.5 Metric—U.S. Measurement Conversions and Temperature 8. Geometry 8.1 Basic Geometric Terms 8.2 Angles and Their Relationships 8.3 Rectangles and Squares 8.4 Parallelograms and Trapezoids 8.5 Triangles 8.6 Circles 8.7 Volume 8.8 Pythagorean Theorem 8.9 Similar Triangles 9. Basic Algebra 9.1 Signed Numbers 9.2 Adding and Subtracting Signed Numbers 9.3 Multiplying and Dividing Signed Numbers 9.4 Order of Operations 9.5 Evaluating Expressions and Formulas 9.6 Solving Equations 9.7 Solving Equations with Several Steps 9.8 Using Equations to Solve Application Problems 10. Statistics 10.1 Circle Graphs 10.2 Bar Graphs and Line Graphs 10.3 Frequency Distributions and Histograms 10.4 Mean, Median, and Mode Marge Lial became interested in math at an early age–it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology; trips to various digs and ruin sites produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. We dedicate the new editions of the paperback developmental math series to Marge in honor of her contributions to the field in which she helped thousands of students succeed. Stan Salzman is a long time resident of Sacramento, California. Stan has taught at American River College for many years, where he was a member of the business department. He is the author of Business Math and Essential Math, published by Pearson Education, Inc., and is coauthor of Basic Math. Diana Hestwood lives in Minnesota and has taught at Metropolitan Community College in Minneapolis for two decades. She has done research on the student brain and is an expert on study skills. She is the author of Lial/Hestwood's Prealgebra and coauthor of Lial/Salzman/Hestwood's Basic Math and Lial/Hestwood/Hornsby/McGinnis's Prealgebra and Introductory Algebra.
AP Physics 1 and AP Physics 2 2014–15 Guided by National Research Council and National Science Foundation recommendations, the AP Program spent several years collaborating with master AP teachers and faculty members from universities and colleges to evaluate and revise the AP Physics B course. This collaboration led to a decision to replace AP Physics B with two new courses, AP Physics 1: Algebra-Based and AP Physics 2: Algebra-Based. Higher education officials have endorsed the new courses enthusiastically. The courses will benefit all members of the AP community. AP will begin offering the courses in the 2014-15 academic year, and it will discontinue the AP Physics B program following the 2013-14 academic year. Overview of Revisions AP has implemented key recommendations by replacing AP Physics B with two new courses: AP Physics 1 and AP Physics 2. An in-depth study by the National Research Council (NRC) concluded that AP Physics B is a very broad course that "encourages cursory treatment of important topics in physics" rather than cultivating a deeper understanding of key foundational principles. The NRC further concluded that students should study Newtonian mechanics, including rotational dynamics and angular momentum, topics not covered in AP Physics B. The NRC also emphasized the need for an instructional approach that supports in-depth, student-led inquiry of topics. To achieve these important goals, and to provide the much-needed time for teachers to accomplish them, the NRC recommended spreading the course material over two years. After confirming this recommendation through college curriculum studies, higher education validations, reviews of state standards, and AP teacher timing trials, the AP Program is replacing AP Physics B with two separate full-year courses. AP Physics 1: Algebra-Based and AP Physics 2: Algebra-Based debut in fall 2014, followed by the first exam administrations in May 2015. Students have the time needed to explore and deepen understanding. Splitting the AP Physics B course into two separate, full-year courses allows students to achieve in-depth understanding. They will have more time for hands-on explorations of physics content and inquiry labs. The full year also allows time for inclusion of physics content specified by state standards. Educators teach each course over a full academic year. AP Physics 1: Algebra-Based is the equivalent to a first-semester college course in algebra-based physics. The course covers Newtonian mechanics (including rotational dynamics and angular momentum); work, energy, and power; and mechanical waves and sound. It will also introduce electric circuits. AP Physics 2: Algebra-Based is the equivalent to a second-semester college course in algebra-based physics. The course covers fluid mechanics; thermodynamics; electricity and magnetism; optics; and atomic and nuclear physics. A new curriculum framework clarifies what knowledge and skills students should demonstrate to qualify for college credit and placement. AP developed the AP Physics 1: Algebra-Based and AP Physics 2: Algebra-Based Curriculum Framework in close consultation with college and university faculty and master AP teachers. The new framework differs from the AP Physics B "list of learning objectives" in significant ways and is: Organized around seven foundational big ideas in physics that structure the courses. Focused on a series of learning objectives that clarify the knowledge and skills students should demonstrate to qualify for college credit and placement. Each learning objective combines physics content with one or more of seven foundational science practices. The science practices are emphasized. The ability to develop and use physics knowledge by applying it to the practice of scientific inquiry and reasoning is at the heart of the new physics courses and exams. Focusing on these skills enables teachers to use the principles of scientific inquiry to promote a more engaging and rigorous experience for AP Physics students. Inquiry-based investigations are emphasized. The amount of instructional time devoted to laboratory investigations has increased from 20 to 25 percent. These investigations now foster student engagement in the practice of science through experimenting, analyzing, making conjectures and arguments, and solving problems in a collaborative setting, where they direct and monitor their progress toward an academic goal. Exam questions are based on the learning objectives as described in the curriculum framework. The new curriculum framework includes measurable learning objectives, each of which combines the science practices with specific content to provide teachers with a clear and detailed description of what knowledge and skills students should demonstrate upon completing the courses. The new exams: Reduce the multiple-choice section from 70 to 50 questions, giving students more time to apply reasoning skills to questions on key concepts. Emphasize the ability to use symbolic and proportional reasoning, and the ability to translate between multiple representations. Reduce the number of free-response questions, allowing time to articulate qualitative and quantitative explanations, reasoning, and justifications of answers. Include an experimental-design question that demonstrates understanding of the science practices. The redesigned courses align with the knowledge and skills valued by college faculty members and department chairs. College department chairs and subject matter experts reviewed each element of the redesigned courses and revised exams. They identified the key concepts and skills students should learn — and confirmed that the design of the new AP Physics courses offer students a solid foundation for further science coursework in college. The AP Course Audit AP teachers will need to revise their course syllabus, based on the current course requirements, and have it authorized through the AP Course Audit. The audit process ensures that teachers have a thorough understanding of the redesigned course requirements and receive the support they need to create a syllabus for each course. To make the process of updating syllabi as straightforward as possible, teachers have the following options: Option 1: Design and submit a syllabus aligned with the new curricular requirements using the resources available on the AP Course Audit website. Option 2: Adopt and submit one of the Annotated Sample Syllabi. The AP Course Audit will begin accepting syllabi for review in March 2014. During the transition, AP will support teachers in completing the AP Course Audit and will provide many resources online to help them plan for 2014-15, including practice exam questions, syllabus development guides, sample syllabi, course planning and pacing guides, and more. Please visit AP Course Audit Information for details. Professional Development AP offers a wide range of professional development options to ensure that teachers have access to the training they need to implement AP Physics 1 and AP Physics 2. These options include one-day, face-to-face workshops and AP Summer Institutes, where participants learn practical ways to design a rigorous curriculum and prepare students for success on the exams. Beginning in June 2013, AP Physics B workshops and AP Summer Institutes devote approximately 20 percent of the sessions to previewing the new courses, supporting the transition to the new curriculum framework. Additional one-day workshops focus specifically on building students' reasoning skills. Beginning in June 2014, AP Physics workshops and AP Summer Institutes will focus on the new courses only. Available now: Teachers can join the AP Physics Teacher Community, an online forum moderated by fellow educators where AP teachers can connect with colleagues, share classroom materials, and exchange ideas. Related Links Timeline Starting September 2013 One-day, face-to-face workshops are available throughout the year. They focus 80 percent of the content on AP Physics B and 20 percent previewing the redesigned courses. Additional one-day workshops focus specifically on building students' reasoning skills. October 2013 Course planning and pacing guides for AP Physics 1 are available on this site. February 2014 The AP Physics 1: Algebra-Based and AP Physics 2: Algebra-Based Course and Exam Description, additional course planning and pacing guides for AP Physics 1,and course planning and pacing guides for AP Physics 2 are available on this site.
Algebra and Trigonometry Book Description: The Eighth Edition of this highly dependable book retains its best features–accuracy, precision, depth, and abundant exercise sets–while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Trigonometric Functions; Exponential and Logarithmic Functions; Analytic Geometry; Analytic Trigonometry; Counting and Probability; and more. For individuals with an interest in learning algebra and trigonometry as it applies to their everyday lives
Publisher's Description REA's Crash Course for the AP* Calculus AB & BC Exams Calculus AB & BC exams yet? How will you memorize everything you need to know before the tests? Do you wish there was a fast and easy way to study for the exams AND boost your score? If this sounds like you, don't panic. REA's Crash Course for AP* Calculus AB & BC is just what you need. Our Crash Course gives you: Targeted, Focused Review - Study Only What You Need to Know The Crash Course is based on an in-depth analysis of the AP* Calculus AB & BC course description outline and actual AP* test questions. It covers only the information tested on the exams, so you can make the most of your valuable study time. Written by experienced math teachers, our easy-to-read format gives you a crash course in functions, graphs, units, derivatives, integrals, and polynomial approximations and series. Expert Test-taking Strategies Our authors share detailed question-level strategies and explain the best way to answer AP* questions you'll find on the exams. By following their expert tips and advice, you can boost your overall point score Calculus AB & BC student must have. When it's crucial crunch time and your Advanced Placement* exam is just around the corner, you need REA's Crash Course for AP* Calculus AB & BC! Author Bio Flavia Banu graduated from Queens College of the City University of New York with a B.A. in Pure Mathematics and an M.A.in Pure Mathematics in 1997. Ms. Banu was an adjunct professor at Queens College where she taught Algebra and Calculus II. Currently, she teaches mathematics at Bayside High School in Bayside, New York, and coaches the math team for the school. Her favorite course to teach is AP* Calculus because it requires "the most discipline, rigor and creativity." Joan Marie Rosebush is teaching calculus courses at the University of Vermont. Ms. Rosebush has taught mathematics to elementary, middle school, high school, and college students. She taught AP* Calculus via satellite television to high school students scattered throughout Vermont. Ms. Rosebush earned her Bachelor of Arts degree in elementary education, with a concentration in mathematics, at the University of New York in Cortland, N.Y. She received her Master's Degree in education from Saint Michael's College, Colchester, Vermont.
This book, the first of a two-volume basic introduction to enumerative combinatorics, concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. Richard Stanley covers those parts of enumerative combinatorics with the greatest applications to other areas of mathematics. The four chapters are devoted to an accessible introduction to enumeration, sieve methods--including the Principle of Inclusion-Exclusion, partially ordered sets, and rational generating functions. A large number of exercises, almost all with solutions, augment the text and provide entry into many areas not covered directly. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference. "Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets"--Provided by publisher.… (more)
The importance of linking math to the real world There's not one comprehensive list of math skills all children must learn, and math education should be changed to reflect that reality, two math experts argue in this opinion piece. Replacing the traditional, abstract curriculum -- algebra, geometry, pre-calculus and calculus -- with applied math such as finance or engineering would better prepare most students for the real world, write Brown University emeritus math professor David Mumford and Sol Garfunkel, the executive director of the Consortium for Mathematics and Its Applications.
Summary A flexible program with the solid content students need Glencoe Algebra 1strengthens student understanding and provides the tools students need to succeedfrom the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests.
More About This Textbook Overview The theory of integer partitions is a subject of enduring interest as well as a major research area. It has found numerous applications, including celebrated results such as the Rogers-Ramanujan identities. The aim of this introductory textbook is to provide an accessible and wide-ranging introduction to partitions, without requiring anything more than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints. Related Subjects Meet the Author George E. Andrews is Evan Pugh Professor of Mathematics at the Pennsylvania State University. He has been a Guggenheim Fellow, the Principal Lecturer at a Conference Board for the Mathematical Sciences meeting, and a Hedrick Lecturer for the MAA. Having published extensively on the theory of partitions and related areas, he has been formally recognized for his contribution to pure mathematics by several prestigious universities and is a member of the National Academy of Sciences (USA). Kimmo Eriksson is Professor of Mathematics at Mälardalen University College, where he has served as the dean of the Faculty of Science and Technology. He has published in combinatorics, computational biology and game theory. He is also the author of several textbooks in discrete mathematics and recreational mathematics, and has received numerous prizes for excellence in teaching. Read an Excerpt Mathematics as a human enterprise has evolved over a period of ten thousand years. Rock carvings suggest that the concepts of small counting numbers and addition were known to prehistoric cavemen. Later, the ancient Greeks invented such things as rational numbers, geometry, and the idea of mathematical proofs. Arab and Chinese mathematicians developed the handy positional system for writing numbers, as well as the foundation of algebra, counting with unknowns. From the Renaissance and onward, mathematics has evolved at an accelerating pace, including such immensely useful innovations as analytical geometry, differential calculus, logic, and set theory, until today's fruitful joint venture of mathematics and computers, each supporting the other. We will delve into, or at least touch upon, many of these modern developments - but really, this book is about mathematical statements of a kind that would have made sense already to the cavemen! One could imagine a petroglyph or cave painting of the following kind: The concepts involved here are just small counting numbers, equality of numbers, addition of numbers, and the distinction between odd and even numbers. What is shown in the table is that for at least up to four animals, they can be lined up in rows of odd lengths in as many ways as in rows of different lengths. Written on today's blackboard instead of prehistoric rock, the table would have a more efficient design: 1 + 1 2 1 + 1 + 1 3 3 2 + 1 1 + 1 + 1 + 1 3 + 1 4 3 + 1 The fact that there will always be as many items in the left column as in the right one was first proved by Leonhard Euler in 1748. But it is quite possible that someone observed the phenomenon earlier for small numbers, since it takes no more advanced mathematics than humans have accessed since the Stone Age. Nowadays, objects such as 3 + 1 or 5 + 5 + 3 + 2 are called integer partitions. Stating it differently, an integer partition is a way of splitting a number into integer parts. By definition, the partition stays the same however we order the parts, so we may choose the convention of listing the parts from the largest part down to the smallest. Euler's surprising result can now be given a more precise formulation: Every number has as many integer partitions into odd parts as into distinct parts. The table continues for five and six: 1 + 1 + 1 + 1 + 1 3 + 1 + 1 5 5 4 + 1 3 + 2 1 + 1 + 1 + 1 + 1 + 1 3 + 1 + 1 + 1 3 + 3 5 + 1 6 5 + 1 4 + 2 3 + 2 + 1 EXERCISES 1. Continue the table from seven up to ten and check for yourself that Euler was correct! See if you can obtain some intuition for why the numbers of integer partitions of the two kinds are always equal. (Difficulty rating: 1) Statements of the flavor "every number has as many integer partitions of this sort as of that sort" are called partition identities. The above partition identity of Euler was the first, but there are many, many more. It is an intriguing fact that there are so many different and unexpected partition identities. Here is another, very famous, example: Every number has as many integer partitions into parts of size 1, 4, 6, 9, 11, 14,... as into parts of difference at least two. The numbers 1, 4, 6, 9, 11, 14,... are best described as having last digit 1, 4, 6, or 9. Another way to put it is that when these numbers are divided by 5, the remainder is 1 or 4. Counting with remainders is called modular arithmetic and will appear several times in this book. In fact, it is striking that partition identities, their proofs and consequences, involve such a wide range of both elementary and advanced mathematics, and even modern physics. We hope that you will find integer partitions so compellingly attractive that they will lure you to learn more about these related areas too. The last identity above was found independently by Leonard James Rogers in 1894 and Srinivasa Ramanujan in 1913. The tale of this identity is rich and has some deeply human aspects, one of which is that Rogers was a relatively unknown mathematican for a long time until the amazing prodigy Ramanujan rediscovered his results twenty years later, thereby securing eternal fame (at least among mathematicians) also for Rogers. The field of integer partitions comes with an unusually large supply of life stories and anecdotes that are romantic or astonishing, or simply funny. They are best presented, and best appreciated, in conjunction with the mathematics itself. Welcome to the wonderful world of integer partitions! Chapter 2 Euler and beyond In this chapter, we will show how identities such as Euler's, and many more, can be proved by the bijective method. However, although the bijective method is elegant and easy to understand, it is not the method Euler himself used. Euler worked with an analytic tool called generating functions, which is very powerful but demands a bit more mathematical proficiency. We will return to Euler's method in Chapter 5. Highlights of this chapter We introduce basic set theory: union, intersection, and cardinality of sets. We show how bijections (one-to-one pairings of two sets) can be used to prove identities. A bijective proof of Euler's identity is given (the number of partitions into distinct parts equals the number of partitions into odd parts) using merging of equal parts, the inverse of which is splitting of even parts. Euler's identity is generalized to other "Euler pairs," that is, sets M and N such that the number of partitions into distinct parts in M equals the number of partitions into parts in N. 2.1 Set terminology We will need some concepts from set theory. In particular, a set is a collection of distinct objects, usually called elements. We can describe a set by listing its elements within curly brackets. For example, {1, 2, 4, 5} is a set of four elements, all of which are integers. It is important to remember that the order of the elements implied by the list is not part of the set; thus the lists {4, 5, 2, 1} and {1, 2, 4, 5} describe the same set. If you discard some elements of a set and retain the rest, you obtain a subset. The symbol ⊂ means "is a subset of." For instance, {2, 5} ⊂ {1, 2, 4, 5}. The intersection of two sets N and N′ is the set of those elements that lie in both sets, denoted by N ∩ N′. Two sets are disjoint if they have no element in common, that is, if their intersection is empty. The union of two sets N and N′ is the set N ∪ N′ containing all elements found in any or both of these sets. Thus if N = {1, 4} and N′ = {2, 4, 5}, then their intersection is N ∩ N′ = {4} and their union is N ∪ N′ = {1, 2, 4, 5}. Intersections and unions are conveniently illustrated by so-called Venn diagrams, such as: The number of elements in a set N is denoted by \|N\| and is often called the cardinality (or just the size) of the set. EXERCISE 2. In the above example, we had \|N\| = 2, \|N′\| = 3, \|N ∩ N′\| = 1, and \|N ∪ N′\| = 4. It is no coincidence that 2 + 3 = 1 + 4; in fact, for any sets N and N′, it is always true that \|N\| + \|N′\| = \|N ∩ N′\| + \|N ∪ N′\|. Why? Draw the conclusion that the size of the union of two sets equals the sum of their respective sizes if, and only if, the two sets are disjoint. (Difficulty rating: 1) 2.2 Bijective proofs of partition identities In order to formulate partition identities precisely and concisely, some notation is needed. Let p(n) denote the number of integer partitions of a given number n. The function p(n) is called the partition function. For example, we have p(4) = 5, since there are five partitions of the number four: 4, 3+1, 2+2, 2+1+1 and 1+1+1+1. In partition identities, we are often interested in the number of partitions that satisfy some condition. We denote such a number by p(n \| [condition]). For example, Euler's identity takes the form p(n \| odd parts) = p(n \| distinct parts) for n ≥ 1. (2.1) Now let us reflect a moment on how such an identity can be proved. For every single value of n, we can verify the identity by listing the partitions of both kinds, counting them, and finding the numbers to be equal. But the identity is stated for an infinite range of values of n, so we cannot verify it case by case; instead we must find some general argument that holds for each and every positive value of n. A natural idea would be to find a general way of counting the partitions, yielding an explicit expression, the same for both sides of the identity. In other words, if we could show that p(n \| odd parts) equals, say, n2 + 2 (or some other expression), and if we likewise could show that p(n \| distinct parts) equals the same number, then we would of course have proved that the identity holds. But can we find such an expression for these functions? From the partition tables in the previous chapter, including Exercise 1, we can compute the first few values: The tabulated values do not seem to suggest any simple function such as a polynomial in n. Consequently this approach fails to prove the identity. But we fail because we try to accomplish more than we actually need! If we want to verify that the number of objects of a type X is equal to the number of objects of a type Y, then we do not need to find the actual numbers - it is enough to pair them up and show that every object of type X is paired with a unique object of type Y and vice versa. The "cave paintings" of Chapter 1 constitute such a pairing between partitions of n into odd parts and partitions of n into distinct parts, for n = 2, 3, 4. Such a one-to-one pairing between two sets is called a bijection. Hence, in order to prove a partition identity, we just need to find a bijection between the partitions in question. It is not obvious what a bijection between partitions could look like. An integer partition of n is just a collection of parts summing up to n, so a bijection between partitions must be described in terms of operations on parts. A simple operation is splitting an even part into two equal halves. The inverse of this operation is merging two equal parts into one part twice as large. This gives an immediate bijective proof of a partition identity: p(n \| even parts) = p(n \| even number of each part) for n ≥ 1. (2.2) Study how the bijection works for n = 6: (2.3) EXERCISE 3. For odd n, there can be no partitions into even parts, nor into parts with an even number of each size. Why? For even n ≥ 2, find an alternative bijective proof of the above identity by finding bijections for each of the two equalities p(n \| even parts) = p(n/2) = p(n \| even number of each part). (2.4) (Difficulty rating: 2) 2.3 A bijection for Euler's identity Returning to Euler's identity, what must a bijection look like? It must have the property that when we feed it a collection of odd parts, it delivers a collection of distinct parts with the same sum. Its inverse must do the converse. From odd to distinct parts: If parts are distinct, there are no two copies of the same part. Hence, if the input to the bijection contains two copies of a part, then it must do something about it. As we have seen above, a natural thing to do is to merge the two parts into one part of double size. We can repeat this procedure until all parts are distinct - since the number of parts decreases at every operation, this must occur at the latest when only one part remains. For example, Tracing our steps back to odd parts: The inverse of merging two equal parts is the splitting of an even part into two equal halves. Repeating this procedure must eventually lead to a collection of odd parts - since the size of some parts decreases at every operation, this must occur at the latest when all parts equal one. For example, It might seem that there is an arbitrariness in the order in which we choose to split (or merge) the parts. However, it is clear that splitting one part does not interfere with the splitting of other parts, so the order in which parts are split does not affect the result. Neither does the order of merging, since merging is the inverse of splitting. Above, we have described a procedure of repeated merging of pairs of equal parts that we can feed any partition into odd parts, and that will result in a partition into distinct parts. Inverting every step gives a procedure of repeated splitting of even parts that takes any partition into distinct parts and results in a partition into odd parts. Hence, this procedure is a bijection proving Euler's identity. For n = 6, the bijection works as follows: (2.5) A common feeling among combinatorial mathematicians is that a simple bijective proof of an identity conveys the deepest understanding of why it is true. Test your own understanding on a few exercises! EXERCISES 4. Why does the same bijection also prove the following stronger statement for n ≥ 1? p(n \| even number of odd parts) = (2.6) p(n \| distinct parts, number of odd parts is even), (2.7) as well as the same statement with both "even" changed to "odd." (Difficulty rating: 2) 5. In the bijection, we are merging pairs of equal parts. Change "pairs" to "triples"! If we merge triples of equal parts until no such triples remain, how can we describe the resulting partitions? The inverse would be to split parts that are divisible by three into three equal parts. When does this process stop? What identity is proved by this new bijection? (Difficulty rating: 1) 6. Generalize the idea of the previous exercise and show that for any integers k ≥ 2 and n ≥ 1, p(n \| no part divisible by k) = p(n \| less than k copies of each part). (2.8) (Difficulty rating: 1) 2.4 Euler pairs The merging/splitting technique for proving Euler's identity is versatile. We can let it operate on other sets of partitions, say A and B, as long as the splitting process takes all partitions in A to partitions in B and the merging process takes all partitions in B to A. For instance, let A be the set of partitions of n into parts of size one. The number of partitions in A is p(n \| parts in {1}) = 1, since the only partition of n satisfying the condition is the sum 1 + 1 + ⋯ + 1 of n ones. The merging process will merge pairs of ones into twos, then merge pairs of twos into fours, then merge pairs of fours into eights, and so on until all parts are distinct. Consequently, the corresponding set B must be the set of partitions of n into distinct parts in {1, 2, 4, 8, ...} (powers of two). Now we must check that the splitting process will take every partition in B to A. Clearly any power of two (say 2k) is split into a pair of powers of two (2k-1 + 2k-1). Since the only power of two that is odd is 20 = 1, the process will go on until all remaining parts are ones. Hence, we have a bijection that proves that for any n ≥ 1, p(n \| parts in {1}) = p(n \| parts are distinct powers of two). (2.9) And since the left-hand expression has the value one, we have proved that every positive integer has a unique partition into distinct powers of two. This is called the binary representation of integers. For example, (2.10) where (bkbk-1... b0)2 is the number written with binary digits (bits). This is the common mode for computers to store numbers in
Currently Out Of Stock! You May Consider This Alternative Texas Instruments TI34 MultiView Sci Calculator Product Details Texas Instruments TI34 MultiView Sci Calculator The TI-34 MultiView scientific calculator was designed with educator input in mind for use in these middle grades math and science classes: Middle School Math Pre-Algebra Algebra I & II Trigonometry General Science Geometry Biology In Classic mode, the TI-34 MultiView can be used in the same classrooms as the TI-34 II Explorer Plus as the screen appears identical to the TI-34 II Explorer Plus in this mode. Get the TI-34 MultiView today. What It Is And Why You Need It MultiView Display View multiple calculations on a 4-line display and scroll through entries with ease. See math expressions and symbols, including stacked fractions, exactly as they appear in textbooks Up to 4 lines of Display Enter multiple calculations to compare results and explore patterns, all on the same screen. Fraction Exploration The TI-34 MultiView scientific calculator comes with the same features that made the TI-34 II Explorer Plus so helpful at exploring fraction simplification, integer division and constant operators. Data List Editor Enter statistical data for 1- and 2-var analysis as well as for exploring patterns via list conversions to see different number formats like decimal, fraction and percent side-by-side
In order to better prepare our students for much of the assessments we have.DMS will offer a math class called ALEKS.This class will occur in a computer lab with a licensed math teacher.The entire class is web based and uses a variety of methods to help students understand math better.This class will increase our studentsí knowledge in all areas of math. Assessment and LEarning in Knowledge Spaces is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics she is most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained. ALEKS courses are very complete in their topic coverage and ALEKS avoids multiple-choice questions. A student who shows a high level of mastery of an ALEKS course will be successful in the actual course he/she is taking. ALEKS also provides the advantages of one-on-one instruction, 24/7, from virtually any Web-based computer. The hope of offering this class is to give students more support in math so they are better prepared for the increase in demand for math knowledge in our society to that we can compete better globally.
The Entry Level Math (ELM) requirement Most MAT 03 students take the course to satisfy part of the ELM requirement. Students may satisfy the ELM requirement by earning CR grades in our math sequence MAT 03 and MAT 09. There are other ways to satisfy the ELM requirement. For example, one may satisfy the ELM requirement by earning a score of 50 or above on the ELM exam, or a score of 550 or higher on the math SAT. You may repeat the ELM exam as many times as necessary to earn a passing score. Please consult the University Advisement Center http: or the Testing Office for details. Preparation for Courses for Math and Science Majors MAT 03 & MAT 09 are not enough to prepare students for the more demanding courses like MAT 153 Pre-Calculus or MAT 191 Calculus I that are required in math and science majors. MAT 03 & 09 are designed only to prepare students for general education math courses MAT 105 and MAT 131 and general education science courses. Students with rusty math skills who are planning to major in science or math should take a full course in Intermediate Algebra at a local community college. MAT 03 meets for three hours of lecture per week for sixteen weeks. It is a pre-collegiate course. It is graded on a CR/NC basis and does not count toward the Bachelor's degree. Prerequisites MAT 03 has no prerequisites and is intended for students who scored less than 42 on the current ELM exam. Student Learning Outcomes After completing MAT 03 the student will be able to: Perform arithmetic with signed numbers and fractions. Translate sentences into equations with variables. Use the distributive law to transform expressions. Solve simple linear equations and inequalities. Model realistic problems with simple linear equations. Graph linear equations and inequalities. Calculate slopes of lines and understand what they mean. Find an equation for the line given two points on the line, or one point and a slope. Graph two-variable inequalities in the plane. Add, subtract, and multiply polynomials Use and understand integer exponents (including negative exponents). Factor by grouping or patterns and factor trinomials Method of Evaluating Outcomes Evaluations are based on homework, class participation, quizzes, and scheduled examinations covering students' understanding of the topics covered in MAT 03. MAT 03 is a CR/NC class. Grading Policy: 10% of grade = Online Homework. 10% of grade "You Try" Exercises 10% of grade = Quizzes and Online Quiz Followups 5% extra credit Class participation 70% of grade = 2 Midterms (20% each) 1 Final (30%) Exams Midterms and the final exam are cumulative common exams written and graded by the math department. Online homework, extra problems, and practice tests are common. You Try exercises are in the eBook or textbook, are checked and corrected by the student, and shown to the instructor to check off as done. Quizzes and quiz follow-ups are written and graded by the instructor. To receive credit for the course, a minimum score of 70% is required. Midterm dates are listed on the calendar at the end of this syllabus. Final exams are given according to the CSUDH final exam schedule. There are no makeup exams. Homework and Class Participation Online Homework Through Connect: Times of completion are listed for each assignment, generally before the next class session after the topic is covered. Take homework seriously! It is the main vehicle for learning in math classes. You Try Exercises: Several "You Try" exercises appear in each section of the eBook or textbook. Do these exercises in a notebook, showing your work. Then check your answers against the answers at the end of the section and correct as needed. At the beginning of the class after the section has been covered, instructor will check that you have done the exercises and give you your credit. Again, take homework seriously! It is the main vehicle for learning in math classes. Attendance: Students are expected to attend every scheduled class, arriving on time, and staying to the end of class. It is the student's responsibility to keep informed of any announcements, syllabus adjustments, or policy changes. Students who miss the first week of classes will be dropped. Missing class, or arriving late or leaving early will have negative impact on your grade. Behavior: The most important rule for this class is RESPECT THE RIGHTS OF YOUR FELLOW STUDENTS. Therefore, no disruptive behavior will be permitted during class time; this includes but is not limited to discussing non-class matters with other students, use of cell phones or other communication devices (such as the ringing of phones or alarms) and listening to music. All cell phones, IPODs, and other communication devices must be turned off and remain out of sight. Participation: Student participation is expected such as contributing to group and class discussions, and putting problems on the board. 5 Minute Meeting: All students are required to meet with their instructor for a 5-minute meeting within the first three weeks of the semester. Policy on Due Dates and Make-Up Work Assignments are due at the start of the class. There are no exceptions; no late or make-up work will be accepted. It is the student's responsibility to do the online homework on time, and to bring the You Try exercises to class by the start of class on the due date. Quiz follow-ups must be done online by their due date. There are no makeup tests except in an extreme emergency, but then proof of the emergency must be provided when requesting a makeup and you must contact the instructor directly, by email, or voice mail as soon as possible; do not wait until the next class to ask about a makeup test since the test may be discussed during that class time. Withdraw/Drop Information Last day to drop without record of enrollment is Thursday September 13. Even though the last day to drop a course with a "Withdraw" on the student's record is Thursday November 15, the Mathematics Department will not grant a withdraw to any student under any circumstances unless he/she is withdrawing from the University. Academic Integrity The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".) Accommodations for Students with Disabilities Cal State Dominguez Hills adheres to all applicable federal, state, and local) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028. Creating Conditions for Successful Learning Research shows success in math class depends very much on two factors: the amount of time spent working on the material, and the student's beliefs about mathematics and what it means to understand and do mathematics. With this in mind, here are some suggestions: Be in class, every class, and be on time. Be prepared to participate in group work and discussions every day so that class time is not wasted, and Spend at least 1 hour every day, not including class time, working on homework assignments, and studying. Realize that mathematics is not just a set of procedures, and that mathematical concepts involve a lot of thinking and reasoning. Consequently, being able to execute procedures accurately is only one part of doing well in this class. Realize that success in mathematics is less about "ability" and more about willingness to think and to work hard to make sense of things. In addition, you need to have: your assignments with you and ready to turn in on the day they are due the phone numbers and emails of at least 3 classmates (preferably "study buddies") who will work with you in partnership to collect any handouts and inform you of important information should you miss a class. Classroom Norms As we will spend a lot of time working in partnerships, in groups, and in class discussions, here are some rules to help you navigate what may be an unfamiliar experience in a math class. Never call out an answer until the person leading the classroom has given permission. Raise your hand. This is a safe environment. That means that you should feel free to ask a question or offer an opinion or an answer, and no one will make fun of you for what you say. If you are working with classmates, work with them. Do not wait and hope that others will do your work for you, and do not move on to other assignments while your classmates are struggling to understand the current one. Be considerate of others. In addition to the ways to be considerate listed above, do not dominate group or class discussions. Remember that everyone needs an opportunity to share his/her ideas. Do not expect me to validate your answers or those of anyone else. You are responsible for making sense of answers and solution methods, and you should always look for ways to verify your work. Cell phones should be off or set to "vibrate." Do not place a call during class, and do not answer a phone call without first leaving the room. These rules are meant to benefit the entire class, and to ensure that everyone has the opportunity to contribute and to learn. Practice Problems can be found in four locations. The first is online assignments, the second is You Try exercises within the text, the third is at the end of each section, and the fourth is either at the end of the mid-chapter review or the chapter review. It is highly recommended that you first view some of the online tutorial videos associated with each chapter before completing the online homework exercises. The advantage of doing online exercises for homework is that you will be provided with instant feedback and hints on how to properly complete the exercise. TORO Learning Center (TLC) The Toro Learning Center is CSUDH's tutoring center. Stop by our new center at our new location in LIB C532, the north side of the University Library. The center offers free tutoring sessions for currently enrolled CSUDH students. A valid CSUDH student ID card is required to access services and to schedule a 25 minute tutoring session. Same day appointments can be made when available, but scheduling earlier is strongly recommended. Peer tutors are available for on campus sessions to help students enhance and enrich their long term academic skills. Please contact us at (310) 243-3827 or stop by the center in LIB C532. Feel free to visit our website for more information, our hours of operation, and our tutoring policy:
This is a free, online textbook that provides information on dimensions, from longtitude and latitude to the proof of a... see more This is a free, online textbook that provides information on dimensions, from longtitude and latitude to the proof of a theorem of geometry. There are 9 chapters, each 13 minutes long. The book contains a total of 117 minutes of video, but can also be read as an ordinary textbook.The film can be enjoyed by anyone, provided the chapters are well-chosen. There are 9 chapters, each 13 minutes long. Chapters 3-4, 5-6 and 7-8 are double chapters, but apart from that, they are more or less independent of each other. According to the website, "Mathematics is a language, specifically it is the language of Science. Like any language, mathe-... see more According to the website, "Mathematics is a language, specifically it is the language of Science. Like any language, mathe- matics has letters (known as numbers) that are used to make up words (known as expressions), and sentences (known as equations). The punctuation marks of mathematics are the differ- ent signs and symbols that are used, for example, the plus sign (+), the minus sign (-), the multiplication sign (×), the equals sign (=) and so on. There are also rules that explain how the numbers should be used together with the signs to make up equations that express some meaning.״
Practical Problems in Mathematics for Drafting and CAD enhance math skills of the reader in the field of drafting, this completely updated fourth edition of Practical Problems in Mathematics For Drafting and CAD presents a comprehensive overview of contemporary drafting problems, CAD drawings, and industry applications and practices. This text provides a variety of integrated math problems and CAD operations in order to facilitate critical thinking, problem solving, and basic mathematics literacy. Filled with real-world applications and designed to cover a range of skills and levels of ... MOREdifficulty, the fourth edition includes updated figures, illustrations, problem sets, examples, and solutions in order to give you the skills you need to succeed in the field of drafting. Designed to enhance the math skills of students in the field of drafting, this completely updated fourth edition of Practical Problems in Mathematics For Drafting and CAD provides students with a comprehensive overview of contemporary drafting problems, CAD drawings, and industry applications and practices.
Linear Algebra Projects Linear algebra, as a field of mathematics, can be approached both theoretically and as a useful tool. Our major goal this semester is to learn the mathematics that makes linear algebra work, but it is also important to see how the subject works for other fields of study. We will see at least four applications of linear algebra during the semester. I will lecture on two of them, and you will do projects on another two. Each project consists of reading a section of the text, distilling the information into your own words, and organizing the topic into a 5-10 page paper. Paper Guidelines Each paper should be 5-10 pages, typed, single spaced, with 10- or 12-pt type and approximately 1" margins. Mathematica is a reasonable word processor as well as a useful computer program for linear algebra, but any technology is acceptable. It must be converted to a file format that I can read and sent through Blackboard. The paper should contain your own title, introduction, conclusion, references, and other labeled sections as needed. You are encouraged to include pictures, computer output, and an outside reference. Each of the two papers counts 5% of your semester grade. The topics and due dates are: Lecture 1 Games of Strategy, section 11.8 Friday 9/13, in class Project 1 Graph Theory, section 11.7 Due Monday 9/23, 11:59 pm Lecture 2 Cubic Spline Interpolation, section 11.5 Friday 10/11, in class Project 2 Curve Fitting, section 11.1 Due Monday 10/21, 11:59 pm Lecture 3 Computed Tomography, section 11.13 Monday 12/2, in class There are three papers available to you in both hard and soft copies. You should read these for several reasons. First, they contain examples of applications of linear algebra. I hope it will be interesting to find out how the math you are studying is used. Second, the papers contain Mathematica code that you may find useful. Third, you can change and execute the code in the soft copy to see what happens. This is a good way to learn both the topic and Mathematica. Fourth, each is an example of an acceptable paper for this class. Feel free to cut and paste examples of code or text formatting that you want to use in your own paper. But please do not copy text content from these or any other sources. Keep in mind the policy on Academic Honesty designed to help you avoid plagiarism and other forms of cheating. To save a file to disk, right click on the link and choose Save Link As.... Then open the file from Mathematica.
Lecture 22: Math 65 - Lesson 11b Embed Lecture Details : Special Forms and Factoring Summary Course Description : Introductory Algebra - Second Term Introduces algebraic concepts and processes with a focus on function, linear systems, polynomials, and quadratic equations. Applications, graphs, functions, formulas, and proper mathematical notation are emphasized throughout the course. A scientific calculator is required. The TI-30X II is recommended.
More About This Textbook Overview This package consists of the textbook plus an access kit for MyMathLab/MyStatLab. Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Algebra: A Combined Approach, Fourth Edition was written to provide students with a solid foundation in algebra and help them effectively transition to their next mathematics course. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success. MyMathLab provides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online. Related Subjects Meet the Author El Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most "teachable moment"—as they prepare for a test—along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Elayn is the author of 12 published textbooks and numerous multimedia interactive products, all specializing in developmental mathematics courses. She has participated as an author across a broad range of educational materials: textbooks, videos, tutorial software, and courseware. This offers an opportunity for multiple combinations for an integrated teaching and learning package, offering great consistency for the
Effective Mathematics Instruction The Importance of Curriculum. Abstract A two-year study was conducted in two fourth grade classrooms to evaluate the effectiveness of two mathematics curricula. During the first year, Teacher A used a Direct Instruction program, Connecting Math Concepts (CMC (Common Messaging Calls) A programming interface specified by the XAPIA as the standard messaging API for X.400 and other messaging systems. CMC is intended to provide a common API for applications that want to become mail enabled. 1.), and Teacher B used a traditional math basalbasal /ba·sal/ (ba´s'l) pertaining to or situated near a base; in physiology, pertaining to the lowest possible level. ba·sal adj. 1.textbooktextbook Informatics A treatise on a particular subject. See Bible. published by Scott, Foresman. During the first year, the CIVIC group scored significantly higher on the computationComputation is a general term for any type of information processing that can be represented mathematically. This includes phenomena ranging from simple calculations to human thinking. subtest of the National Achievement Test and on curriculum-based tests constructed from the CMC and basal programs as well as on a multiplicationmultiplication, fundamental operation in arithmetic and algebra. Multiplication by a whole number can be interpreted as successive addition. For example, a number N multiplied by 3 is N + N + N. facts test. The next year Teacher B also used the CMC program, and achievement in Teacher B's classroom was significantly greater than the previous year, on the curriculum-based tests and the multiplication facts test. This suggests that the curriculum was the critical variable responsible for higher student achievement. Implications for textbook adoption and selection are discussed. What is the best route to improved mathematics outcomes? In response to criticisms of math texts, some have suggested that textbooks be set aside in favor of upon the side of; favorable to; for the advantage of. See also: favor more life-like, problem-solving mathematics instruction. Despite attempts to deemphasize the role of textbooks through projects and interdisciplinaryin·ter·dis·ci·pli·nar·y adj. Of, relating to, or involving two or more academic disciplines that are usually considered distinct. interdisciplinary Adjectivethematicthe·mat·ic adj. 1. Of, relating to, or being a theme: a scene of thematic importance. 2. instruction, textbooks still "dominate instruction in elementary and secondary schools" (Farr, Tulley, & Powell, 1987, p. 59). Even though good teachers provide instructional opportunities that go beyond the textbook, 75% to 90% of classroom instruction is organized around textbooks (Tyson & Woodward, 1989; Woodward & Elliott, 1990). With this fact in mind, it seems wise to explore the possibilities of improving textbooks rather than abandoning them (Grossen & Carnine, 1996). Osborn, Jones, and SteinStein , William Howard 1911-1980. American biochemist. He shared a 1972 Nobel Prize for pioneering studies of ribonuclease. (1985) argued that "improving textbook programs used in American schools is an essential step toward improving American schooling" (p. 10). Improved textbooks, if available, would need to be selected by state or local textbook adoption committees However, current textbook adoption processes are not research based. According toaccording to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. Tyson-Bernstein (1988), selections are more likely to be guided by political and economic factors than by qualities that are known to benefit students. Moreover, adoption committees are often poorly trained for the task of analyzing textbooks. Evaluation of textbooks is not as objective as regulations and policy statements suggest and it is based primarily on professional judgment rather than any objective rating system (Five & Cook, 1994) Pedagogy and educational research are seldom mentioned as factors that influence decisions (Courtland et al., 1983; Powell, 1985). Even if adoption committee members were better trained, they would find that (a) field-test data and program evaluationProgram evaluation is a formalized approach to studying and assessing projects, policies and program and determining if they 'work'. Program evaluation is used in government and the private sector and it's taught in numerous universities. data are infrequentlyin·fre·quent adj. 1. Not occurring regularly; occasional or rare: an infrequent guest. 2. reported and (b) textbooks are very similar. Texbook similaritySimilarity is some degree of symmetry in either analogy and resemblance between two or more concepts or objects. The notion of similarity rests either on exact or approximate repetitions of patterns in the compared items. has occurred because 22 states, most notably and Texas, have statewide adoption procedures that require textbook adoption. Because adoption by large states is critical for profits, publishers tailor their textbooks to meet the requirements of these states. The result is that the textbooks published by different companies are "very careful to be comprehensive in their coverage of topics, but they are seeminglyseem·ing adj. Apparent; ostensible. n. Outward appearance; semblance. seeming·ly adv.indifferent INDIFFERENT. To have no bias nor partiality. 7 Conn. 229. A juror, an arbitrator, and a witness, ought to be indifferent, and when they are not so, they may be challenged. See 9 Conn. 42. to the conceptual coherencecoherence, constant phase difference in two or more Waves over time. Two waves are said to be in phase if their crests and troughs meet at the same place at the same time, and the waves are out of phase if the crests of one meet the troughs of another. of the content and the pedagogicalped·a·gog·ic also ped·a·gog·i·cal adj. 1. Of, relating to, or characteristic of pedagogy. In the current study, two curricula were compared in preparation for an adoption decision in a small school district. The two curricula that were experimentally compared are Invitation to Mathematics (1988) published by Scott Foresman and Connecting Math Concepts. (Engelmann, Engelmann, & Carnine, 1993). The two differ in important ways as summarized in Table 1. Scott Foresman Organization The most prominent feature of the Scott Foresman (SF) mathematics curricula is its spiralspiral /spi·ral/ (spi´ral) 1. helical; winding like the thread of a screw. 2. helix; a winding structure. design. In a spiral design, texthooks are organized into 10-20 chapter or unit topics and each topic is revisited each year (Stein, Silbert & Carnine, 1997). The intent of the spiral design is that topics will be treated with increasing depth and s each year, building on the previous year's learning. However, as Miller and Mercermer·cer n.Chiefly British A dealer in textiles, especially silks. [Middle English, from Old French mercier, trader, from merz, merchandise, from Latin merx explain,"... in reality the result seems to be superficialsuperficial /su·per·fi·cial/ (-fish´al) pertaining to or situated near the surface. su·per·fi·cial adj. 1. Of, affecting, or being on or near the surface. 2. coverage of many different skills" (1997, p. 51). The International Mathematics and Science Study (TIMSS TIMSS Trends in International Mathematics and Science Study TIMSS Third International Math and Science Study ) Curriculum and Textbook Analysis project reported that their analysis of 628 texthooks from roughly 50 countries showed that American math textbooks covered more topics than almost any other country in the world, but little was covered in depth (Schmidt, McKnight, & Raizen, 1996). Referring to the spiral designed curriculum, the National Council of Teachers of Mathematics The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally. (NCTM NCTM National Council of Teachers of Mathematics NCTM Nationally Certified Teacher of Music NCTM North Carolina Transportation Museum NCTM National Capital Trolley Museum NCTM Nationally Certified in Therapeutic Massage , 1989) noted the need to change the "repeti tion of topics, approach, and level of presentation in grade after grade" (p. 66). Porter (1989) found over 70% of the math concepts in the elementary curriculum received cursorycur·so·ry adj. Performed with haste and scant attention to detail: a cursory glance at the headlines. [Late Latin curs instruction, defined as less than 30 minutes instructional time during; the entire school year. As an example of the spiraling design, the concept that fractions are part of a whole occupies only one lesson in the Scott, Foresman (SF) fourth grade text. Conducting that lesson will give students less than 30 minutes instruction during all of 4th grade, which is insufficient for many below average to average students to understand the concept. A curriculum that spirals may result in teaching for exposure. "Skill mastery is unlikely, because new skills are introduced too quickiy in an attempt to 'get through the book"" (Miller & Mercer, 1997, p. 51). Another problem is that the rate at which new concepts are introduced is often either too fast or too slow. One objective is stated for each lesson in SF and each lesson has a new objective. For example, Objective 119 has to do with addition of fractions with like denominators and Objective 120 with addition of fractions with unlike denominators. Assuming the daily math period is the same length of time, there will be too much time for Objective 119 leading to wasted instructional time, and there will not be enough time to introduce, let alone master, Objective 120. Strategies The SF curricula relies upon discovery learning rather than explicit presentation of specific strategies for solving problems. In discovery leaming, the teacher sets up a situation in which students are to discover important concepts through the use of inductive reasoning Inductive reasoning The attempt to use information about a specific situation to draw a conclusion. . The SF teacher's manual provides suggestions for using "concrete materials" to help students understand important concepts and poses questions or situations to motivate students. Some teaching suggestions are offered such as "write the example on the board," "point out...," "explain..," and "encourage students to discuss." Process involved in finding a solution to a problem. Many animals routinely solve problems of locomotion, food finding, and shelter through trial and error. Scott Foresman includes problem-solving activities in each chapter. Throughout the text, they remind students to use a general problem solving strategy that is prompted by a penguinpenguin, originally the common name for the now extinct great auk of the N Atlantic and now used (since the 19th cent.) for the unrelated antarctic diving birds. holding a sign. The general problem-solving strategies include the following: make a table, find a pattern, use physical modes, use logical reasoning The three methods for logical reasoning, deduction, induction and abduction can be explained in the following way: [1] Given preconditions α, postconditions β and the rule R1: α ∴ β (α therefore β). , work backward, list all possibilities, try and check, draw a diagramdiagram /di·a·gram/ (di´ah-gram) a graphic representation, in simplest form, of an object or concept, made up of lines and lacking pictorial elements. , and make a graph. Mastery The teacher's guide for the SF curricula does not include any discussion of mastery. The text is organized so that a new concept is introduced daily, so some students may not receive enough practice to develop mastery. In addition, there is minimal review after the unit in which the skills are introduced. For example, learning how to tell the time from a clock is presented on pages 90-91 of the fourth grade SF text, but is never seen again in the remaining 256 pages of the text. Fractions are presented in Chapter 11 of the 4th grade, but students do not see any fractions again until Chapter 10 of the 5th grade textbook. The fourth grade SF text has a test at the end of each chapter, occasional "maintenance" problems and cumulative tests for Chapters 1-6, 1-9, and 1-12. There are also extra problems at the back of book for both calculation and problem-solving However, the cumulative review involves a limited number of problems, it is not integrated and it occurs infrequently. Most lessons do include an error analysis, which alerts teachers to common errors and makes suggestions for extra practice. Facts Instruction Chapter 1 of the SF text includes a review of single digit A single character in a numbering system. In decimal, digits are 0 through 9. In binary, digits are 0 and 1. digit - An employee of Digital Equipment Corporation. See also VAX, VMS, PDP-10, TOPS-10, DEChead, double DECkers, field circus. addition and subtractionsubtraction, fundamental operation of arithmetic; the inverse of addition. If a and b are real numbers (see number), then the number a−b is that number (called the difference) which when added to b (the subtractor) equals . Chapter 5 reviews multiplication and Chapter 8 introduces division. There are no mastery activities or timed tests of math facts. Field Testing No field testing was described in the SF teacher's manual or in the literature. Connecting Math Concepts Organization The curriculum design of the Direct Instruction program, Connecting Math Concepts (CMC) is very different from SF. The fact that each lesson is organized around multiple concepts and skills, rather than around a single unit, is the most unusual aspect of the design of CMC. Each concept/skill is addressed for only 5- to 10-minutes in any given day's lesson, but is revisited day-after-day for many lessons. Organizing lessons so that concepts / skills are revisited for a few minutes a day over many days is referred to as a "." organization. Many important curriculum goals are made easier by organizing lessons into strands, such as sequencing of dozens of preskills, cumulatively introducing skills, and treating topics in depth. The presentation of key concepts in strands which run through several lessons allow the concepts to be arranged in a logical scope and sequence. Thus preskills can be taught prior to being integrated into more complex mathematical concepts. For example, before students are taught to find equivalent fractions (e g., 1/3 - 3/9) by multiplyingmul·ti·ply 1 v.mul·ti·plied, mul·ti·ply·ing, mul·ti·plies v.tr. 1. To increase the amount, number, or degree of. 2. Mathematics To perform multiplication on. by a fraction of one (e.g. x 3/3), they learn the necessary multiplication facts and that multiplying by a fraction equal to one doesn't change the value of a number and how to write fractions equal to one. With a strand design the variations in amount of time needed for learning each concept are easily accommodated by adjusting the number of minutes and the number of consecutive days spent teaching it. The strand design thus accommodates the problems associated with variability in the time needed to learn each skill/concept (and the related issue of the rate of introduction of concepts). (See Stein, Carnine, & Dixon, 1998) or (Caninecanine or canid Any domestic or wild dog or doglike mammal (e.g., wolf, jackal, fox) in the family Canidae, found throughout the world except in Antarctica and on most ocean islands. , Jones, & Dixon 1994) for a more thorough discussion of the design features of CMC). Strategies CMC uses explicit strategies to teach both basic operations and problem solving. Within a strand the amount of structure is gradually decreased each day moving from the initial teaching presentation through guided practice to independent practice. Because each lesson contains many strands, a balance between new learning and practice is maintained. The teacher's manual provides specific teaching procedures including wording and error correction procedures. The purpose of the teaching scripts is to assure that the explicit strategies are presented in clear and unambiguous language of instruction. This represents a radical departure from traditional texts and for teachers who are used to a more freewheelingfree·wheel·ing adj. 1. a. Free of restraints or rules in organization, methods, or procedure. b. Heedless of consequences; carefree. 2. Relating to or equipped with a free wheel. delivery style. Problem solving Students work on solving comparison and classification problems using addition and subtraction, multistep problems and problems involving fractions including probability. Strategies are systematically presented in a word problems strand throughout the year. Explicit instruction is provided to help students discriminatedis·crim·i·nate v.dis·crim·i·nat·ed, dis·crim·i·nat·ing, dis·crim·i·nates v.intr. 1. a. among problem types so that they know when to apply each strategy. Mastery An important advantage of strand organization is that it enables gradual mastery of concepts by repeating and extending information over many lessons rather than teaching by a single exposure. Strands allow distributed review of skill in which only a few problems are presented daily over a long period of time. This distribution over time allows systematic, brief review of concepts until they are integrated with other more complex mathematical procedures. Such distributed practice allows students to become both accurate and rapid in their responses. Distributing practice across several days facilitates mastery better than massing practice in one day's lesson (Dempster, 1991), and it is easy to schedule when lessons are designed in strands. Mastery is critical to success in CMC because the strand design requires that students use everything that has been taught. If students are weak on a particular skill, they will most certainly have trouble later in the program when that skill becomes a component in a more complex operation. The teacher's guide provides criteria for "passing" each test and makes specific suggestions for remediation. In addition, teachers are given specific suggestions for correcting different types of errors and specific procedures for "firming" students on concepts within each lesson. Facts Instruction Addition and subtraction facts are assumed to have been mastered as they were practiced in previous levels. Mastery of multiplication and division facts is FACTS I Federal Agencies' Centralized Trial-Balance System emphasized in lessons 1-90 including a variety of oral mastery activities and timed tests. Uniquely, CMC has received extensive field-testing prior to being marketed (Engelmann, Englemann, & Carnine, 1993). For example, evaluations of the third grade text prior to publication indicated that low-income minority students scored two years above grade level after using CMC (Carnine & Engelmann, 1991). In another prepublicationpre·pub·li·ca·tion adj. Of or relating to the time just before a publication date, especially of a book: The marketing department was amazed by the number of prepublication orders. investigation, high performing third graders were better able to solve word problems and make connections between various math concepts than other high performing students (Carnine & Engelmann, 1991). Since its publication empirical data supporting its effectiveness continues to accumulate Accumulate Broker/analyst recommendation that could mean slightly different things depending on the broker/analyst. In general, it means to increase the number of shares of a particular security over the near term, but not to liquidate other parts of the portfolio to buy a security . The CMC program and a basal math program were separately used at two schools in Camden, NJ with beginning first graders from predominantlypre·dom·i·nant adj. 1. Having greatest ascendancy, importance, influence, authority, or force. See Synonyms at dominant. 2. educationally at-risk backgrounds. After two years, CMC-taught students scored significantly higher on math computation than the basal group on both the California Test of Basic Skills and the Metropolitan Achievement Tests (BrentBrent, outer borough (1991 pop. 226,100) of Greater London, SE England. The area is a rail and industrial center. Its manufactures include automobile parts, clocks and watches, and electrical equipment. & DiObilda, 1993). In an educationally at-risk elementary schoolelementary school: see school. in Kalamazoo, MI, two third-grade classes, and a fifth-grade class participated in a pilot study using CMC. Students taught with CMC: (a) achieved average to above-average rates of progress in both math calculation and application on the Kaufman Tests of Education Achievement; (b) came close to the 50 on the Iowa Tests of Basic Skills although other students displayed significant percentile declines between second and third grade; and (c) were more sophisticated at math problem solving (Vreeland, et al., 1994). As a consequence, CMC was implemented in other math classes. At the end of the second implementation year, the outcomes were overwhelmingly positive (Vreeland, et al., 1994). CMC was implemented in the first and fourth grades in eight elementary schools in a Pennsylvania school district, during the 1992-93 school year (Wellington, 1994), Teacher-designed posttests for the fourth grade showed significant differences between students educated with CMC compared to the "traditional basals," consequently CMC was adopted district-wide in grades 1-5. Although Wellington (1994) did not find significant differences in favor of the CMC group in the first grade, Tarver and Jung; (1995) found that first grade students using CMC outperformed students using Math Their Way and cognitively guided instructionOverview Cognitively Guided Instruction is an instructional method most often found in elementary math programs. Centered around the belief that all children come to school with informal or intuitive math knowledge, CGI involves learning with manipulatives or through the (CGICGI in full Common Gateway Interface. Specification by which a Web server passes data between itself and an application program. Typically, a Web user will make a request of the Web server, which in turn passes the request to a CGI application program. ) on the CTBS CTBS Comprehensive Tests of Basic Skills CTBS Certified Tissue Bank Specialist CTBS California Tests of Basic Skills Math subtests. Furthermore, statistically significant differences increased after the second year of implementation when the CMC group scored more than one grade level above the CGI groupCGI Group Inc. (TSX: GIB.A, NYSE: GIB) is a Canadian-based information technology (IT) management and business process services (BPS) company. Founded in 1976 as Conseillers en Gestion et Informatique on the CTBS. Furthermore, 20% of the CMC students scored at the ceiling of the test although none of the CGI students did so. The study reported herein began as the result of two teachers' willingness to conduct a pilot study for one year to evaluate CMC, in which one used CMC (Teacher A) and the second (Teacher B) served as a control group by continuing to use the same Scott, Foresman textbook the two had been using for years. Then the second year, when Teacher B wanted to use CMC also, we had an opportunity to examine the effect of the curriculum independent of teacher effect by comparing with Teacher B's previous scores. Conducted the year prior to the district's consideration of a new mathnew math n. Mathematics taught in elementary and secondary schools that constructs mathematical relationships from set theory. Also called new mathematics. basal curriculum, this study's purpose was to provide local empirical data useful for making a decision to adopt and to add to a growing body of small-scale program evaluations supporting the effectiveness of CMC. Within this framework, CMC was compared to a traditional basal, namely the Scott, Foresman (SF) text Invitation to Mathematics on several norm-referenced and curriculum-based measures. The addition of the second year's data from Teacher B enabled us to make the same comparisons independent of the effect of the teacher. To our knowledge the question of the effectiveness of CMC has not been previously examined by comparing the achievement of a teacher's own classes before and after implementation. Methodology Materials The instructional materials used were Connecting Math Concepts (Engelmann, et al, 1993) Level D and Invitation to Mathematics (1988) published by Scott, Foresman. Both curricula were designed for 4th grade students. The CMC curriculum included a teacher's guide, teacher presentation books A and B, an answer key, and student textbooks and workbooks SF included a teacher's guide and a student textbook. The content of both curricula contained considerable overlap, but was not identical. The SF text included chapters on addition and subtraction facts, numbers and place value, addition and subtraction, measurement, multiplication facts, multiplication, geometrygeometry [Gr.,=earth measuring], branch of mathematics concerned with the properties of and relationships between points, lines, planes, and figures and with generalizations of these concepts. , division facts, division, decimals, fractions, and graphing. Each chapter in the SF text interspersed a few activities on using problem solving strategies. CMC included strands on multiplication and division facts, calculatorcalculator or calculating machine, device for performing numerical computations; it may be mechanical, electromechanical, or electronic. The electronic computer is also a calculator but performs other functions as well. skills, whole number operations, mental arithmetic the art or practice of solving arithmetical problems by mental processes, unassisted by written figures. See also: Mental , column multiplication, column subtraction, division, equations and relationships , place value, fractions, ratios and proportions, number families, word problems, geometry, functions, and probability. Despite the differences in content and organization, both programs covered math concepts generally considered to be important in 4th grade--addition and subtraction of multi-digit numbers, multiplication and division facts and procedures, fractions, and problem solving with whole numbers. Other subjects and activities sometimes interfered with time set aside for math instruction, and some lessons took longer than the one lesson per day typically expected. As a result, neither group had time to complete their respective curricula. During year 1, the CMC group completed 90 out of 120 lessons, and the SF group completed 10 out of 12 chapters. During year 2, Teacher A completed 105 lessons in the CMC curriculum and Teacher B completed 95 lessons. Measures Four measures were used, with the same versions used for both pretestpre·test n. 1. a. A preliminary test administered to determine a student's baseline knowledge or preparedness for an educational experience or course of study. b. A test taken for practice. 2. and posttestpost·test n. A test given after a lesson or a period of instruction to determine what the students have learned. . The National Achievement Test (1989) (NAT (Network Address Translation) An IETF standard that allows an organization to present itself to the Internet with far fewer IP addresses than there are nodes on its internal network. ) is a timed standardized test A standardized test is a test administered and scored in a standard manner. The tests are designed in such a way that the "questions, conditions for administering, scoring procedures, and interpretations are consistent" [1] battery designed to be administered to groups of students. The math section consists of three subtests--computation, concepts, and problem solving, with concepts and problem solving combined for scoring. Its norms are based on a stratifiedstratified /strat·i·fied/ (strat´i-fid) formed or arranged in layers. strat·i·fied adj. Arranged in the form of layers or strata. random sample of 150,000 twelfth-grade students in public schools in five geographical areas. Test-retest reliabilitytest-retest reliability Psychology A measure of the ability of a psychologic testing instrument to yield the same result for a single Pt at 2 different test periods, which are closely spaced so that any variation detected reflects reliability of the instrument on the mathematics subtests and total for Level F were all reported as r = .90 or higher (Wick, 1990). A cumulative curriculum-based measure was drawn from each of the two curricula. The first test, (SF test), which was published by Scott, Foresman to go along with the Invitation to Mathematics text, was the complete Cumulative Test for Chapters 1-12 and was intended to be comprehensive as well as cumulative. The SF test consisted of 22 multiple-choice items (four choices) which assessed the range of concepts presented in the 4th grade SF textbook. For the CMC measure the first author designed a test that consisted of 55 production items for which students computed answers to problems, including both computational Having to do with calculations. Something that is "highly computational" requires a large number of calculations. and word problems. The CMC test was comprehensive as well as cumulative; problems were examples of the entire range of problems found in the last quarter of the CMC program. Problems were chosen from the last quarter of the program because the various preskills taught in the early part of the program are integrated in problem types seen in the last quarter of the program. Students did not use calcula tors on any of the tests. Fluencyflu·ent adj. 1. a. Able to express oneself readily and effortlessly: a fluent speaker; fluent in three languages. b. in recall of basic multiplication facts is an essential objective for fourth grade and was assessed by an experimenter-designed test. The three-minute, timed-test consisted of 72 simple multiplication facts, and students completed as many as possible within the time limit. Students took the test three times on three different days and their mean score was recorded. Participants All the students in the 4th grade of a school in a small community in Wisconsin were randomly assignedas·sign tr.v.as·signed, as·sign·ing, as·signs 1. To set apart for a particular purpose; designate: assigned a day for the inspection. 2. to one of two fourth grade classrooms prior to the study. Data were collected on all who had permission to participate. In year 1, 23 students were in each class (two students in each class did not wish to participate, so their data were excluded from the analysis). Percentile scores on the NAT indicated the classes began the year slightly below average in math skills with the CMC class in the 43rd percentile and the SF class in the 44th. In year 2, there were 19 students in each 4th grade class. Both classes were heterogeneous Not the same. Contrast with homogeneous. heterogeneous - Composed of unrelated parts, different in kind. Often used in the context of distributed systems that may be running different operating systems or network protocols (a heterogeneous network). and included the full range of abilities including learning disabled and gifted students. Thewas low. In year 1, one CMC student left in midyearmid·year n. 1. The middle of the calendar or academic year. 2. a. An examination given in the middle of a school year. b. midyears A series of such examinations. and returned later in the year. In year 2, a total of four of Teacher B's students moved out and four moved in. Scores for these students were not included in the data analysis. Teachers Teacher A, a female with 14 years of experience had taught 4th grade in the school for the previous three years. Teacher B, a male with 11 years of experience, had taught 4th grade in the school for his entire career. Both teachers were considered by their peers and administrators to be caring and competent. Teacher A taught the CMC curriculum during Years 1 and 2. She had taught from SF during the previous years and had no previous experience with CMC or any other Direct Instruction programs. She received 4 hours of training at a workshop in August and about three hours of additional training from the experimenters. Teacher B had 11 years of experience with the SF text and taught from it during year 1. He received minimal training before teaching CMC during year 2. He attended a three-hour inservice training session and observed two demonstration CMC lessons. Procedures The second author informally and intermittentlyin·ter·mit·tent adj. 1. Stopping and starting at intervals. See Synonyms at periodic. 2. Alternately containing and empty of water: an intermittent lake. observed both classrooms a few times during both years. No observational data more formal than anecdotal notes were collected. Because this experiment was designed as a test of curriculum rather than a test of fidelity to a given set of teaching procedures we did not require the teachers to teach in any specific way. In year 1, each teacher spent approximately 45 minutes per day engaged in math instruction, however his or her presentation differed considerably. Teacher A used the scripted presentation in the CMC teacher presentation book. She frequently asked questions to which the whole class responded, but she did not use a signalunisonunison, in music, tones identical in pitch produced by two or more parts or voices. In popular usage a vocal composition is said to be sung in unison even though some of the voices are separated from others by the interval of an octave. responding. If she got a weak response she would ask the question again to part of the class (e.g., to one row or to all the girlsTo All The Girls is the 1st track on Paul's Boutique by American hip hop group the Beastie Boys, released on July 25, 1989. Produced and written by the Beastie Boys & the Dust Brothers. Engineered by Mario Caldato & Allen Abrahamson. ) or ask individuals to raise their hands if they knew the answer. There were high levels of teacher-pupil interaction, but not every student was academically engaged. Generally, one lesson was covered per day and the first 10 minutes were set aside to correct the previous day's homework Then a structured, teacher-guided presentation followed, during which the students responded orally or by writing answers to the teacher's questions. Student answers received immediate feedback and errors were corrected immediately. If there was time, students began their homework during the remaining minutes. During year 1 Teacher B's math period was divided into three 15-minute parts. First, students checked their homework as B gave the answers. Then students told B their scores, which he recorded. Second, B lectured or demonstrated a concept, and some students volunteered to answer questions from time-to-time. The teacher presentation was extemporaneousex·tem·po·ra·ne·ous adj. 1. Carried out or performed with little or no preparation; impromptu: an extemporaneous piano recital. 2. and included explanations, demonstrations, and references to text objectives. Third, students were assigned textbook problems and given time for independent work. During year 2, when both Teacher A and B implemented CMC, their presentations became more similar, but differences remained. Teacher A, who sought additional training in direct instruction presentation techniques during the summer, had a very polished presentation. She now signaled to initiate unison responding, proceeded at apace and engaged all students during the entire lesson. Her was dynamic and enthusiastic. Teacher B followed the script, but deviated somewhat from the CMC delivery procedures. He added his own explanations, asked questions of the whole class, but did not require all students to demonstrate their understanding by responding overtlyo·vert adj. 1. Open and observable; not hidden, concealed, or secret: overt hostility; overt intelligence gathering. 2.. He continued his practice of using the first part of the period to go over homework. Both teachers had emphasized mastery of multiplication facts for several years. They continued to do so both years of the study and assessed progress through timed tests. Teacher A introduced the fact families (e.g., 2x1, 2x2, 2x3, etc.) in the same order in which they were introduced in CMC (9s, 3s, 4s, 7s, 6s, 8s, 5s, 1s, 2s). Students in A's class took a one-minute, 24 item timed test in one fact family and, when they passed, they went on to the next. Parents were encouraged to practice with their children at home, but little class time was allottedal·lot tr.v.al·lot·ted, al·lot·ting, al·lots 1. To parcel out; distribute or apportion: allotting land to homesteaders; allot blame. 2., outside of what was in the textbook, to practice facts. Teacher B did not follow the CMC order for introducing fact families. Instead the facts were given in numerical numerical expressed in numbers, i.e. Arabic numerals of 0 to 9 inclusive. numerical nomenclature a numerical code is used to indicate the words, or other alphabetical signals, intended. order (1s, 2s, 3s, etc.) and the facts were not broken down into smaller units for mastery. Students took a one-minute test of all facts on an irregular basisAdv.1.on an irregular basis - in an irregular manner; "her letters arrived irregularly" irregularly . During year 1, the teachers administered the multiplication facts and curriculum-based pretests to their own classes during the first week and a half of October. During year 2 these tests were given in late August. Both years the NAT was administered as a pretest during district-wide testing in early October. All posttests, including the NAT, were administered during the same two-week period in early May. Teachers A and B switched places in giving the curriculum-based posttests to each other's class to prevent any coaching. The same directions were read to both classes. Results There were two questions that we wanted to answer: (a) Did implementation of the CMC curriculum when taught by A improve achievement when compared to Teacher B in year one and, if so, on which measures' and (b) Did implementation of the CMC curriculum by Teacher B in year 2 improve achievement when compared to B's year 1 achievements and, if so, on which measures? Comparison Between Teachers in Year 1 Based on analysis of varianceThe discrepancy between what a party to a lawsuit alleges will be proved in pleadings and what the party actually proves at trial. In Zoning law, an official permit to use property in a manner that departs from the way in which other property in the same locality, there were no significant pretest differences between students in the two curriculum groups on the computation, concepts and problem solving subtests of the NAT nor on the total test scores. Nor did any significant pretest differences show up on any of the curriculum-based measures (see Table 2). Significant posttest differences in favor of the CMC group were found in mean raw scores on both of the curriculum-based tests as well as on the multiplication facts (see Table 1). The differences on the CMC curriculum posttest were quite large, (CMC = 41 or 74% correct), SF = 15 or 27% correct), with F_(1, 40) = 104.4, [MATHEMATICAL EXPRESSION A group of characters or symbols representing a quantity or an operation. See arithmetic expression. NOT REPRODUCIBLE IN ASCIIASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ] = 0.0001 (see Figure 1). Against typical expectations, the CMC group even outscored the SF group on the test based on the SF curriculum, (19 or 87% vs. 16 or 72%) with F(1, 40) = 11.2, p = 0.002. The CMC group also scored significantly higher on rapid recall of multiplication facts. Of 72 items, the mean correctly answered in 3 minutes for the CMC group was 66 compared to 48 for the SF group with F (1, 40) = 33.3, p = 0.0001 for the multiplication facts posttest. Posttest comparisons on the computation subtest of the NAT, (Table 1), indicated a significant difference in favor of the CMC group, F (1,40) = 8.32, p = 0.006. On the other hand, neither the scores for the concepts and problem-solving portion of the NAT nor the total NAT showed any significant group differences. The total NAT scores put the CMC group at the 51st percentile and the SF group at the 46th percentile, but this difference was not statistically significant. In summary, during year 1 the groups began the year with approximately equivalent scores on the pretests. The slight differences that were apparent favored the SF group. At posttest, statistically significant differences favored the CMC group on the NAT computation subtests, curriculum-based measures and multiplication fact fluency, but not on the NAT concepts and problem-solving subtest nor on the NAT total score. Comparison Before and After Implementation for Teacher B Our second question was, did achievement improve when the CMC curriculum was implemented with B in year 2 relative to the SF outcomes in year 1? Comparing the pretest scores of year 1 and year 2 for Teacher B's students, no significant differences were found on the subtest and total scores of the NAT nor on the pretest scores of the SF and the multiplication facts measures. However, significant pretest differences on the CMC measure occurred, E (1,34) =7.49, p= .009, with the pretest scores lower for year 2 than for year 1. In response to this potential confounding confounding when the effects of two, or more, processes on results cannot be separated, the results are said to be confounded, a cause of bias in disease studies. confounding factor, a two-factor analysis of variance for repeated measures was used rather than doing simple posttest comparisons to evaluate the effect of the curriculum. Because identical forms of each of the tests were used during pre and post testing the raw scores are comparable. For the NAT total score, the main effect for time, (pretest vs. posttest scores) was significant, F (1, 34) = 43.8, p = .0001, but the interaction between type of curriculum and time was not. The students learned each year, but the higher mean in the second year as against the first year on the NAT was not significant. The same pattern held for both the NAT subtests, computation and problem solving. On the other hand, for the CMC measure the curriculum x time interaction was highly reliable, F (1, 34) = 40.5, p = .0001, with the gains greater after the second year than the first year. This finding is not surprising because the CMC measure was based on the CMC curriculum. Before implementation of the CMC, the students taught by B using the SF text began the year with a mean score of 7 (12% correct) on the CMC measure and improved to 15 (27%), a gain of 15 percentage points. After implementation of CMC in year 2, B's students jumped from means scores of 4 to 33 (6% to 60% correct), a gain of 54 percentage points. Table 3 shows pre and posttest means and standard deviations In statistics, the average amount a number varies from the average number in a series of numbers. (statistics) standard deviation - (SD) A measure of the range of values in a set of numbers. for Teacher B's students on all measures for both years. For the SF measure, the curriculum x time interaction was also strong, F (1, 34) = 15.82, p = .0004, with the second year gains higher. In year one, B's students pretested at a mean score of 13 (57% correct) and improved to 16 at posttest (72% correct), a gain of 15 percentage points with the SF program. After implementation of CMC in year 2, B's students mean scores improved from 10 to 18, (47% to 82% correct), a gain of 35 percentage points. It should be remembered that the SF measure was not aligned with the CMC curriculum. Finally, the interaction for the multiplication facts fluency test was also significant, F (1, 34) = 10.5, p = .002, with the second year gains greater. Before implementation of CMC, B's class average pretested at 22 multiplication facts in 3 minutes to and improved on a posttest to 48 facts, a gain of 26 facts due to the SF program. After implementation of CMC, B's students went from 17 multiplication facts in 3 minutes at pretest to 54 facts in 3 minutes, a gain of 37 facts. In summary, improvements on the two curriculum-based measures and the fact fluency measure were much greater after implementation of the Direct Instruction CMC curriculum in year 2 than before its implementation in year 1. The pre and posttest means (raw scores for the NAT, percent correct for curriculum-based measures, and facts completed in 3 minutes for facts fluency) for both years are shown in Figure 2. Crossover Crossover The point on a stock chart when a security and an indicator intersect. Crossovers are used by technical analysts to aid in forecasting the future movements in the price of a stock. In most technical analysis models, a crossover is a signal to either buy or sell. effects occurred for all four test measures, with a steeper slope or increased improvement in year 2. Discussion This study suggests that students learning from CMC perform better than students learning from SF when measured by curriculum-based tests. At the end of year 1, students in Teacher A's CMC classroom performed better on curriculum-based measures than students in the other, SF, fourth grade class. The two classes were not significantly different at pretest which suggests that the differences in achievement were not due to characteristics of the groups, but rather to implementation of a different curricula used by Teacher A. The data for students in Teacher B's classes, comparing year 1 using SF to year 2 using CMC as the math curriculum, suggests that the critical variable in student achievement was the curriculum, not the teacher. The significant curriculum x time interaction on both curriculum-based measures and the multiplication facts test favored CMC over SF. Although the higher achievement of students in Teacher A's group after year 1 could initially be attributed, all or in part to the teacher, the repl ication of higher student achievement in year 2 with Teacher B makes that interpretation less credible. We believe this implementation of CMC was less than optimal because (a) students began the program in fourth grade rather than in first grade and (b) students could not be placed in instructional groups. A unique feature of the CMC program is that it's designed around integrated strands rather than in a spiraling fashion. Each concept is introduced, developed, extended, and systematically reviewed beginning in Level A and culminating in Level F (6th grade). This design sequence means that students who enter the program at the later levels may lack the necessary preskills developed in previous levels of CMC. This study with fourth graders indicated that even when students enter Level D, without the benefit of instruction at previous levels, they could reach higher levels of achievement in certain domains. However, more students could have reached mastery if instruction were begun in the primary grades. Another drawback DRAWBACK, com. law. An allowance made by the government to merchants on the reexportation of certain imported goods liable to duties, which, in some cases, consists of the whole; in others, of a part of the duties which had been paid upon the importation. in this implementation had to do with heterogeneous ability levels of the groups. Heterogeneityhet·er·o·ge·ne·i·ty n. The quality or state of being heterogeneous. heterogeneity the state of being heterogeneous. was an issue for both curricula. However, the emphasis on mastery in CMC created a special challenge for teachers using CMC. To monitor progress CMC tests are given every ten lessons and mastery criteria for each skill tested are provided. Because of the integrated nature of the strands, students who do not master an early skill will have trouble later on. Unlike traditional basals, concepts do not "go away," forcing teachers to continue to reteach until all students master the skills. This emphasis on mastery created a challenge for teachers that was exacerbated in this case by the fact that students had not gone through the previous three levels of CMC. Why didn't the improved learning for students using the CMC program demonstrated on the curriculum-based tests show up on the NAT? Our guess is that a more optimal implementation of CMC would have increased achievement in the CMC group, which may have shown up on the NAT. In general, the tighter focus of curriculum-based measures such as those used in this study makes them more sensitive to the effects of instruction than any published, norm-referenced test A norm-referenced test is a type of test, assessment, or evaluation in which the tested individual is compared to a sample of his or her peers (referred to as a "normative sample"). . Standardized tests have limited usefulness for program evaluation when the sample is small, as it was in this study (Carvercarver /car·ver/ (kahr´ver) a tool for producing anatomic form in artificial teeth and dental restorations. carver (carving instrument), n, 1974; Marston, Fuchs, & Deno, 1985). Nevertheless, we included the NAT as a dependent measure because it is curriculum-neutral. The differences all favored the CMC program. That no significant differences occurred either between teachers or across years on the NAT should be interpreted in the light of several other factors. One, the results do not indicate that the SF curriculum outperformed CMC, only that the NAT did not detect a difference between the groups, despite the differences found in the curriculum-based measures. Two, performance on published norm-referenced tests such as the NAT are more highly reading comprehensionReading comprehension can be defined as the level of understanding of a passage or text. For normal reading rates (around 200-220 words per minute) an acceptable level of comprehension is above 75%. scores than with computation scores (Carver, 1974; Tindal & Marston, 1990). Three, the NAT concepts and problem solving items were not well-aligned with either curriculum. The types of problems on the NAT were complex, unique, non-algorithmic problems for which neither program could provide instruction. Performance on such problems has less to do with instruction than with raw ability. Four, significant differences on the calculation subtest of the NAT favored the CMC program during year 1 (see Snider and Crawford, 1996 for a detailed discu ssion of those results). Because less instructional time is devoted to computation skills after 4th grade, the strong calculation skills displayed by the CMC group would seem to be a worthy outcome. Five, although the NAT showed no differences in problem solving skills between curriculum groups or between program years, another source of data suggests otherwise. During year 1, on the eight word problems on the curriculum-based test, the CMC group outscored the SF group with an overall mean of 56% correct compared to 32%. An analysis of variance found this difference to be significant, with F = 10.8, p = .002. Commonly teachers do not expect the textbook to be a significant assist in teaching math facts to fluency. Teachers learn how to do that on their own. Anecdotally Teacher A told us that Teacher B's students usually "learned their facts better than my students." The fact that Teacher A's class, using CMC, outperformed Teacher B's class is notable. The fact that Teacher B's students, using CMC, significantly outperformed his previous years class is even more interesting. The CMC program works on multiplication facts beginning in lesson 1 and continuing through lesson 68. The multiplication facts are taught in the following order in Level 1:): 5s, 9s, 3s, 4s, 7s, 6s. (Fact teaching begins in Level C.) For each series of facts, students work from a number map that shows a unique pattern for that fact family. As each fact family is introduced, the students use these facts to solve other problems in their classwork and homework. Aside from the motivation and opportunity for students to learn math facts offered by the teachers, the systematic integration and practice of those facts in CMC probably helped the students achieve a higher level of mastery. Both teachers reported anecdotally that the high-performing students seemed to respond most positively to the CMC curricula. One of Teacher A's highest performing students, when asked about the program, wrote, "I wish we'd have math books like this every year.... it's easier to leam in this book because they have that part of a page that explains and that's easier than just having to pick up on whatever. It may be somewhat counter-intuitive that an explicit, structured program would be well received by more able students. We often assume that more capable students benefit most from a less structured approach that gives them the freedom to discover and explore, whereas more didacticdi·dac·tic adj. Of or relating to medical teaching by lectures or textbooks as distinguished from clinical demonstration with patients. approaches ought to be reserved for low-performing students. It could be that high-performing students do well and respond well to highly-structured approaches when they are sufficiently challenging. These reports are interesting enough to bear further investigation after collection of objective data. This study is a model of the kind of small research project that districts should undertake prior to spending thousands of dollars adopting a new textbook. The cost of implementing a new program on a small scale is minimal and the data are easy to collect. After seeing the data from year 1, Teacher B and two first and third grade teachers also volunteered to pilot the program. In the following year, the program was adopted district-wide. Too often in education, important curricular decisions that affect thousands of children are made because of ideology (Dixon & Carnine, 1994) or faddismfad n. A fashion that is taken up with great enthusiasm for a brief period of time; a craze. [Possibly from fidfad, fussy person, fussy, from fiddle-faddle. (Slavin, 1990). This study provides a model for how educators can make data- based decisions. The data from the second year provide evidence that curriculum is a critical factor in student achievement. These data show that this teacher was able to achieve substantially better student outcomes by changing the curriculum that he was using. This is not to say that teacher skill, dedication and compassioncompassion, n a profound awareness of another's suffering coupled with a desire to alleviate that suffering. are not important; but rather that given these qualities, teachers can produce better educational outcomes if they also have access to "tools that work" (Carnine, 1992). This study adds to a growing body of research indicating that CMC is a powerful tool that can enable teachers to help students understand and apply mathematical concepts. Carnine, D. (1991). Curricular interventions for teaching higher order thinking to all students: Introduction to the Special Series. Journal of Learning Disabilities, 24. 261- 269. Carnine, D. (1992). Expanding the notion of teachers' rights: Access to tools that work 25 13-19 Carver, R. P. (1974). Two dimensions of tests: Psychometricpsy·cho·met·rics n.(used with a sing. verb) The branch of psychology that deals with the design, administration, and interpretation of quantitative tests for the measurement of psychological variables such as intelligence, aptitude, and and edumetric. American PsychologistThe American Psychologist is the official journal of the American Psychological Association. It contains archival documents and articles covering current issues in psychology, the science and practice of psychology, and psychology's contribution to public policy. , 29, 512-518. Farr, R., Tulley, M. A., & Powell, D. (1987). The evaluation and selection of readers. Elementary School Journal Published by the University of Chicago Press, The Elementary School Journal is an academic journal which has served researchers, teacher educators, and practitioners in elementary and middle school education for over one hundred years. , 87(3), 267-282. Fiore, T. A., & Cook, R. A. (1994). Adopting textbooks and other instructional materials: Policies and practices that address diverse learners. 15, 333-347. Grossen, B. & Carnine, D. (1996) Consideratecon·sid·er·ate adj. 1. Having or marked by regard for the needs or feelings of others. See Synonyms at thoughtful. 2. Characterized by careful thought; deliberate. instruction helps students with disabilities achieve world class standardsWorld class standards refers to the level of achievement, mainly in math and science, attained by students in the four countries that make up the East Asian Tigers; South Korea, Singapore, Japan, and Taiwan, as well as in Europe. . Teaching Exceptional Children, 28(4) 77- 81. Invitation to Mathematics. (1988). Glenview, IL.: Scott, Foresman, & Co. Stein, M., Carnine, D., & Dixon, R. (1998). Direct Instruction: Integrating curriculum design and effective teaching practice. InterventionA procedure used in a lawsuit by which the court allows a third person who was not originally a party to the suit to become a party, by joining with either the plaintiff or the defendant. in School and Clinic. 33. 227-234. Tarver, S., & Jung, J. (1995), A comparison of mathematics achievement and mathematics attitudes of first and second graders instructed with either a discovery-learning mathematics curriculum or a direct instruction curriculum. Effective School Practices. 14(1), 49-57. the upholding by individuals of the principles, laws, ethics and conventions of their profession. . In D. L. Elliott & A. Woodward (Eds,), Textbooks and schooling89th Yearbook of the National Society for the Study of Education, Part 1, pp. 178-193). Chicago; National Society for the Study of Education.
This is a free online course offered by the Saylor Foundation.'Precalculus II continues the in-depth study of functions... see more This is a free online course offered by the Saylor Foundation.'Precalculus II continues the in-depth study of functions addressed in Precalculus I by adding the trigonometric functions to your function toolkit. In this course, you will cover families of trigonometric functions, as well as their inverses, properties, graphs, and applications. Additionally, you will study trigonometric equations and identities, the laws of sines and cosines, polar coordinates and graphs, parametric equations and elementary vector operations.You might be curious how the study of trigonometry, or "trig," as it is more often referred to, came about and why it is important to your studies still. Trigonometry, from the Greek for "triangle measure," studies the relationships between the angles of a triangle and its sides and defines the trigonometric functions used to describe those relationships. Trigonometric functions are particularly useful when describing cyclical phenomena and have applications in numerous fields, including astronomy, navigation, music theory, physics, chemistry, and—perhaps most importantly, to the mathematics student—calculus.In this course, you will begin by establishing the definitions of the basic trig functions and exploring their properties and then proceed to use the basic definitions of the functions to study the properties of their graphs, including domain and range, and to define the inverses of these functions and establish the properties of these. Through the language of transformation, you will explore the ideas of period and amplitude and learn how these graphical differences relate to algebraic changes in the function formulas. You will also learn to solve equations, prove identities using the trig functions, and study several applications of these functions.' This is a free online course offered by the Saylor Foundation.'Calculus can be thought of as the mathematics of CHANGE.... see more This is a free online course offered by the Saylor Foundation.'Calculus can be thought of as the mathematics of CHANGE. Because everything in the world is changing, calculus helps us track those changes. Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently CONSTANT. Solving an Algebra problem, like Y = 2X + 5, merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate R, such as Y = X0+Rt where t is elapsed time and X0 is the initial deposit. But with compounded interest, now things get complicated for algebra as the rate R is now itself a function of time with Y = X0+ R(t)t. Now we have a rate of change which itself is changing. Calculus "to the rescue," as Isaac Newton introduced the world to mathematics specifically designed to handle "those things that change." Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful, beautiful, and useful set of ideas and techniques. You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences, including physical, biological, social, economic, and engineering. However, calculus is an intellectual step up from your previous mathematics courses. Many of the ideas you will learn in this course are more carefully defined and have both a functional and a graphical meaning. Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use. Calculus offers a huge variety of applications and many of them will be saved for future courses you might take. This course is divided into four learning sections, or units, plus a reference section, or Appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding "limits" could not be more important as that topic really begins the study of calculus. The third unit will introduce and explain derivatives. With derivatives we are now ready to handle all those "things that change" mentioned above. The fourth unit makes "visual sense" of derivatives by discussing derivatives and graphs. Finally, the fifth unit provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over.' This is a free online course offered by the Saylor Foundation.'The main purpose of this course is to bridge the gap between... see more This is a free online course offered by the Saylor Foundation.'The main purpose of this course is to bridge the gap between introductory mathematics courses in algebra, linear algebra, and calculus on one hand and advanced courses like mathematical analysis and abstract algebra, on the other hand, which typically require students to provide proofs of propositions and theorems. Another purpose is to pose interesting problems that require you to learn how to manipulate the fundamental objects of mathematics: sets, functions, sequences, and relations. The topics discussed in this course are the following: mathematical puzzles, propositional logic, predicate logic, elementary set theory, elementary number theory, and principles of counting. The most important aspect of this course is that you will learn what it means to prove a mathematical proposition. We accomplish this by putting you in an environment with mathematical objects whose structure is rich enough to have interesting propositions. The environments we use are propositions and predicates, finite sets and relations, integers, fractions and rational numbers, and infinite sets. Each topic in this course is standard except the first one, puzzles. There are several reasons for including puzzles. First and foremost, a challenging puzzle can be a microcosm of mathematical development. A great puzzle is like a laboratory for proving propositions. The puzzler initially feels the tension that comes from not knowing how to start just as the mathematician feels when first investigating a topic or trying to solve a problem. The mathematician"plays" with the topic or problem, developing conjectures which he/she then tests in some special cases. Similarly, the puzzler "plays" with the puzzle. Sometimes the conjectures turn out to be provable, but often they do not, and the mathematician goes back to playing. At some stage, the puzzler (mathematician) develops sufficient sense of the structure and only then can he begin to build the solution (prove the theorem). This multi-step process is perfectly mirrored in solving the KenKen problems this course presents. Some aspects of the solutions motivate ideas you will encounter later in the course. For example, modular congruence is a standard topic in number theory, and it is also useful in solving some KenKen problems. Another reason for including puzzles is to foster creativity.' This is a free online course offered by the Saylor Foundation.'Numerical analysis is the study of the methods used to solve... see more This is a free online course offered by the Saylor Foundation.'Numerical analysis is the study of the methods used to solve problems involving continuous variables. It is a highly applied branch of mathematics and computer science, wherein abstract ideas and theories become the quantities describing things we can actually touch and see. The real number line is an abstraction where many interesting and useful ideas live, but to actually realize these ideas, we are forced to employ approximations of the real numbers. For example, consider marking a ruler at \sqrt{2}. We know that \sqrt{2} \approx 1.4142, but if we put the mark there, we know we are in error for there is an infinite sequence of nonzero digits following the 2. Even more: a number doesn't have any width, yet any mark we make would have a width, and in that width lives an infinite number of real numbers. You may ask yourself: isn't it sufficient to represent \sqrt{2} with 1.414? This is the kind of question that this course will explore. We have been trying to answer such questions for over 2,000 years (it is said that people have given their lives for the idea of \sqrt{2}, and they certainly wouldn't think 1.414 sufficient). Modern computers can perform billions of arithmetic operations per second and trying to predict the path of a tropical storm can require many trillions of operations. How do we carry out such simulations and how do our approximations affect the result? The answer to the first question is certainly colored by the second!Numerical analysis is a broad and growing discipline with many open questions. This course is designed to be a first look at the discipline. Over the course of this semester, we will survey some of the basic problems and methods needed to simulate the solutions of ordinary differential equations. We will build the methods ourselves, starting with computer arithmetic, so that you will understand all of the pieces and how they fit together in state of the art algorithms. Along the way, we will write programs to solve equations, plot curves, integrate functions, and solve initial value problems. At the end of some chapters we will suggest – in a section called "Of Things Not Covered" – some topics that would have been included if we had more time or other avenues to explore if you are interested in the topics presented in the unit.' This is a free online course offered by the Saylor Foundation.'Real Analysis II is the sequel to Saylor's Real Analysis I,... see more This is a free online course offered by the Saylor Foundation.'This course is an introduction to complex analysis, or the... see more This is a free online course offered by the Saylor Foundation.'This course is an introduction to complex analysis, or the theory of the analytic functions of a complex variable. Put differently, complex analysis is the theory of the differentiation and integration of functions that depend on one complex variable. Such functions, beautiful on their own, are immediately useful in Physics, Engineering, and Signal Processing. Because of the algebraic properties of the complex numbers and the inherently geometric flavor of complex analysis, this course will feel quite different from Real Analysis, although many of the same concepts, such as open sets, metrics, and limits will reappear. Simply put, you will be working with lines and sets and very specific functions on the complex plane—drawing pictures of them and teasing out all of their idiosyncrasies. You will again find yourself calculating line integrals, just as in multivariable calculus. However, the techniques you learn in this course will help you get past many of the seeming dead-ends you ran up against in calculus. Indeed, most of the definite integrals you will learn to evaluate in Unit 7 come directly from problems in physics and cannot be solved except through techniques from complex variables.We will begin by studying the minimal algebraically closed extension of real numbers: the complex numbers. The Fundamental Theorem of Algebra states that any non-constant polynomial with complex coefficients has a zero in the complex numbers. This makes life in the complex plane very interesting. We will also review a bit of the geometry of the complex plane and relevant topological concepts, such as connectedness.In Unit 2, we will study differential calculus in the complex domain. The concept of analytic or holomorphic function will be introduced as complex differentiability in an open subset of the complex numbers. The Cauchy-Riemann equations will establish a connection between analytic functions and differentiable functions depending on two real variables. In Unit 3, we will review power series, which will be the link between holomorphic and analytic functions. In Unit 4, we will introduce certain special functions, including exponentials and trigonometric and logarithmic functions. We will consider the Möbius Transformation in some detail.In Units 5, 6, and 7 we will study Cauchy Theory, as well as its most important applications, including the Residue Theorem. We will compute Laurent series, and we will use the Residue Theorem to evaluate certain integrals on the real line which cannot be dealt with through methods from real variables alone. Our final unit, Unit 8, will discuss harmonic functions of two real variables, which are functions with continuous second partial derivatives that satisfy the Laplace equation, conformal mappings, and the Open Mapping Theorem.' 'Statistical Reasoning introduces students to the basic concepts and logic of statistical reasoning and gives the students... see more 'Statistical Reasoning introduces students to the basic concepts and logic of statistical reasoning and gives the students introductory-level practical ability to choose, generate, and properly interpret appropriate descriptive and inferential methods. In addition, the course helps students gain an appreciation for the diverse applications of statistics and its relevance to their lives and fields of study. The course does not assume any prior knowledge in statistics and its only prerequisite is basic algebra.We offer two versions of statistics, each with a different emphasis: Probability and Statistics and Statistical Reasoning. Each course includes all expository text, simulations, case studies, comprehension tests, interactive learning exercises, and the StatTutor labs. Each course contains all of the instructions for the four statistics packages options we support. To do the activities, you will need your own copy of Microsoft Excel, Minitab, the open source R software, TI calculator, or StatCrunch.One of the main differences between the courses is the path through probability; Statistical Reasoning places less emphasis on probability than does the Probability and Statistics course and takes an empirical approach.'
"... mathematical b ..." mathematical beneficial effect of dispelling the myth that mathematics is literal, is inherent in the structure of the universe, and exists independent of human minds. (Lakoff & Nuez, 1997, p. 85) 8 Abstract mathematical ideas are almost always defined by metaphorical mappings from concrete, familiar domains. Understanding takes place when these concrete domains fit the students' own, individual experience, and frustration and confusion ensues when they are incongruent. English (1997) provides a very good example of what happens if the metaphorical mapping is rooted in an a-priori construction that doesn't fit the students' own individual experience. The example concerns the use of a line metaphor to r... "... calculus t ..." calculus together on additional challenging problems (ibid.). In 1978, with Rose Asera, Leon Henkin, Dick Stanley, and other members of the Professional Development Program (PDP) at UC Berkeley, he created calculus intensive discussion sections for underrepresented students. The sections emphasized groupwork on challenging problems and a community based on shared interest in succeeding in mathematics (Asera, 2001; Fullilove & Treisman, 1990; Eric Hsu personal communication, February 2008; Treisman, 1992). Since then, students in PDP's Intensive Discussion Sections (IDS) and similar programs elsewhere have outperformed comparable students in traditional calculus sections, and been more likely to successfully take additional STEM courses (Alexander, Burda & Millar, 1997; Abstract ..." Abstract and Wilensky 2002 [Abrahamson, D., & Wilensky, U. (2002). ProbLab. Northwestern University,
MATH 240Scientific Computation• 5 Cr. Department Division Description: Introduction to numerical methods used to solve problems in the sciences and engineering. Students will use software to solve problems and communicate the results of calculations. Awareness of appropriate software tools to help analyze a physical problem and the limitations and strengths of these tools will be emphasized. Prerequisite: MATH 208. Recommended: MATH 238. Outcomes: After completing this class, students should be able to: Upon completion of this course, students will be able to: 1. Write and document effective Matlab or Scilab scripts involving logical and iterative flow control and file input and output. 2. Use Matlab or Scilab to write efficient commands to manipulate data and implement numerical solution algorithms. 3. Produce effective plots of numerical data using Matlab or Scilab. 4. Explain the consequences of finite precision and the inherent limits of the numerical methods considered. 5. Select appropriate numerical methods to apply to various types of problems in engineering and science. 6. Demonstrate they understand the mathematics concepts underlying the numerical methods considered. 7. Demonstrate understanding and implementation of numerical solution algorithms applied to the following classes of problems: * Finding roots of equations * Solving systems of algebraic equations * Curve fitting * Interpolation * Numerical differentiation of data and functions * Numerical integration of data and functions * Solutions of ordinary differential equations including Initial value problems, Boundary value problems and Systems of equations * Other numerical methods or classes of problems as chosen by the instructor
Trigonometry This course covers basic concepts of trigonometry, including definitions and properties of trigonometric functions. Topics include solutions of applied problems involving right triangles; graphs of trigonometric functions, including period changes, amplitude changes, and phase shifts; trigonometric identities; trigonometric equation solving; and evaluation of inverse trigonometric functions. Subject:MATH Units:3 Instructor information about this course Learning Management System (LMS) for this course:Blackboard LMS link: Course start page:blackboard.miracosta.edu Course email:agloag@miracosta.edu Office:online Office hours:Fridays 2:00 - 3:00 Phone:(619) 602-5364 Instructor notes:Text and Materials: Trigonometry, Tenth Edition, by Lial, Hornsby, Schneider, and Daniels, ISBN-13: 978-0-321-67177-6. REQUIRED: MyMathLab: In this course you are required to sign up for MyMathLab in order to access homework sets, lecture material and practice problems. You can access the MML site at: An electronic version of the textbook is available to you here. To sign up you need to use the CourseID: gloag68315 and the access code that comes with your textbook.
MathWorks Natick, Massachusetts, who have strong academic records in mathematics and science. To qualify for this scholarship, applicants must commit to pursuing a degree in mathematics, engineering, science, or related program at an accredited four-year college or university
Description By purchasing a value pack, you will save compared to purchasing these two books separately. Target audience Suitable for Year 10 students. Series overview Focus on the fundamentals with Pearson Mathematics Essentials Edition. These streamlined editions of the Pearson Mathematics student books use the same strong pedagogy and up-to-date research to comprehensively cover the requirements of the Australian Curriculum. We've simplified the text to give you the 'nuts and bolts', covering all the theory and all the questions at a more affordable price.
Our Educational Software (FREE with your eBook, unlock software wizard below) titles have been developed over twenty years where many, many thousands of copies are installed in schools and colleges all over the world. They are designed to be used in conjunction with any standard textbook, not just our eBooks. Students can select a topic e.g. Multiplying Fractions from the extensive menu options and change any of the numerator and denominator variables to explore the effect on the answer, even showing all levels of simplification. Where appropriate a graphical image will also reflect those value changes i.e. trigonometric angles redrawn to scale. This is unique for educational software, most just provide a few standard selectable examples. Ours will accept almost any workable value that would be found in a real situation and why its used extensively in industry as a huge reference and calculation resource.. Features of FREE Software to go with your eBook (Incl. Physically Disabled User features): Last published 2010 - All Windows platforms including Windows 8 - Hundreds of color fully interactive images where every value change updates the graphics and calculations - Explanatory text - Related topics are presented together in single windows - Default typical values - Full color printing single page with image for user values, text, calculations and graphs if part of topic - Copy & Paste (a feature that was used to construct all the accompanying eBook content) - Ideal for teachers making student hand-outs and assignments - Calculations and graphing windows open independently to check students calculations - Full screen whiteboard technology for whole class teaching (teachers packs eBooks and School Site Licence) - Self-Assessment questions with random values with multiple choice answers - Electronics and maths Toolbox (electronics and STEM titles) as used by professionals to quickly make all those standard calculations without having to remember the formula - For Business Studies Students there are additional features to interactively explore Break-Even charts and Supply & Demand curves - Drop down menus with topic search - Click forward and back through topics makes revision more enjoyable -Specialist Editors for equations, logic, graphs, statistics and algebra enable calculations and equations from any standard textbook to be inserted and explored changing just one value or variable at a time - BASIC programmer with full instructions to learn in minutes using statement wizards - For physically disabled users software can be operated independently of the keyboard using mouse clicks only or other voice, sight or wind activated pointing devices to choose topics and change values. FREE software is now also available with our physical paperback book titles. Search 'eptsoft' on Amazon. Search TECHNOLOGY and SCIENCE in EDUCATION MAGAZINE: Devoted to the teaching of Science, engineering education and design technology, including art and design, business studies, craft design technology, textiles, food technology and ICT. Buy as eBook for £1.95 ($2.99) and get £700 STEM: Science, Technology, Engineering and Maths unlimited user site licence software for your school FREE! A special thank you to those who give feedback to the eBook retailers it is very much appreciated. Pay by phone, its the same great software! micro mobile phone paymentsbuy software download only for only € 2,00 or equivalent in your own currency. You can even pay with your landline phone, its really easy. Same PC software install, combining download and unlocking together, registering is not required. Ideal for those without PayPal or a Bank account and it will cost you even less. We are almost giving it away! See links below. Search 'eptsoft' on Amazon and check out our Bestsellers. Rank #1 in Computer Software with others in top #10 for technical and educational titles. We sell a great many eBooks and software downloads every day and problems are extremely rare. Just follow the instructions, but we are here to help if you need us. This review is from:Electrical Principles V10 (Kindle Edition) "Easy to read nice diagrams best eBook I have purchased on electronics. Has nice layout if you look at the front cover that is how this books layout is with colour diagrams." This review is from:Mathematics V10 Home Study (Kindle Edition) "Well laid out, clear and easy to use, I use it for planning some of my students course work. Liked the fact that its the electronic version, as I'm running out of shelf space." How to get the FREE Educational software to go with your eBook. The eBook payment receipt is used to unlock the Free software. This method of marketing means we can make our software available worldwide and taking advantage of the hugely powerful marketing of Amazon, Google, Apple, Sony, Samsung etc. Simply select your eBook retailer from the links below make the payment and follow the instructions. You don't need an eBook eReader to download the software just the payment receipt to unlock the Install Release Code. Click here to see William Ashey's YouTube video demonstrating one of our educational software titles. All titles follow the same software format. Here William concentrates mainly on the maths tools whereas the largest part of all the software uses interactive graphics to teach the subject as shown on the STEM Ad below. These are only briefly touched on at the end of the video.
Extend Your Learning This course will provide a participatory professional learning experience that will enable middle school mathematics teachers to understand the essential tools of early algebra. Workshops, readings, online keynote addresses, as well as a vibrant and active online community will help teachers deepen their own knowledge of the mathematics that supports formal algebra. The content is based on the book, Developing Essential Understanding of Expressions, Equations & Functions for Teaching Mathematics in Grades 6–8. This 12-week course can be taken independently or as a supplement to the Interactive Institute. The course is available both Fall 2013 and Spring 2014 semesters for your convenience. Choose the option that best fits your schedule: The Fall 2013 online course begins the week of August 19, 2013 and ends by November 17, 2013. Live online sessions will be on Tuesdays at 5:00 p.m. ET. All online sessions last approximately 75 minutes. The Spring 2014 online course begins the week of January 20, 2014 and ends by April 20, 2014. Live online sessions will be on Wednesdays at 7:00 p.m. ET. All online sessions last approximately 75 minutes. Throughout the course, students will be expected to attend and participate weekly. Participants will join live online sessions, engage in online discussion forums, read the assigned text and additional articles, and analyze student work, emphasizing the critical understandings that support formal algebra. View or download the course syllabus (PDF) for more information. Upon registering, students will have the option to take this course for two college credits. Additional fees for the credit option will apply. If you attended the July workshop in New Orleans, the online course is just $25. To only register for the online course, the cost is $200 for NCTM members, $250 for nonmembers. Visit our Institute Registration page and click the "Register Now" button to register. The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
MATLAB: An Introduction with ApplicationsAn effective way to become MATLAB® proficient! Now updated to reflect MATLAB®, Version 7, this practical guide offers an introduction to understanding and using this powerful program. Starting with basic features, the book covers everything needed to use MATLAB effectively––from simple arithmetic operations with scalars, to creating and using arrays, to three–dimensional plots and solving differential equations. Detailed images of computer screens, tutorials, worked examples, and homework questions in math, science, and engineering provide a thorough and effective means of mastering the program. MATLAB®, An Introduction, Second Edition, is a valuable resource for instructors, students, and practicing engineering, alike. Features of the Second Edition New: Updated coverage reflects MATLAB, Version 7. New: Includes a new chapter (Chapter 11) on symbolic math, providing an introduction to this useful feature of MATLAB. New: A new section in Chapter 4 covers importing data. Examples incorporated throughout the book provide valuable experience running MATLAB. Annotated examples help users learn the program and its commands in an easy–to–use format. Sample programs, applications, and homework problems show how MATLAB is used in science and engineering sorry to say that the 3rd edition is a great disappointment compared to the 2nd. It is unnecessarily prolix, with a great many typos. The copy editing is so bad that in one place several lines of text are repeated identically. It is difficult not to conclude that the 3rd edition was rushed into print mainly to obsolete the second edition and enrich the publisher. It would be a mistake, I think, to reward the publisher for such ill behavior. Although this edition contains some material not in the second edition, the extra content will not make much difference to a beginning student, and my advice to him or her is to purchase the 2nd edition, used. Neither edition treats structures or cell arrays, so I don't think a reader sacrifices much in the way of content by staying with the 2nd edition. Here's my three-year old review of the second edition - I still like it. This book was written for teaching Matlab to freshmen in an introductory engineering course, so most of the examples are from first year physics and engineering. Nevertheless, after looking at all competing texts, I chose it to teach Matlab to sophomore geology majors, most of whom had not yet taken calculus or physics. I was very happy with the results; by the end of the semester the students were well on their way to being competent programmers, and I think they will find calculus and physics much easier because of their experience with this book. I chose this text because it is very well written--you can tell the author has had long experience teaching the subject--and because of its many excellent examples. Most people learn faster by example than by theory, and the examples in this book are easier to follow than those of other texts. Each example shows the command window with a gray background and white insets, or call-outs, containing explanations. The pages are attractive. In the main text, Matlab commands are set in Courier to clearly distinguish them from the discussion itself. Sections are fairly short and easy to follow, and at the end of each chapter there are many problems of gradually increasing difficulty. The solutions to some problems are given at the back of the book. The abundance of complete examples makes it easy to skip around in the book as soon as students are familiar with Matlab syntax. There are astonishingly few typos and none were serious. Cell arrays and structures are used only where needed for particular commands, a wise pedagogical decision. I particularly enjoyed the second edition's new chapter on symbolic math, as I had never used this part of Matlab in my own research. The book is 7.5"x9.25" in size with 343 pages, and so is easy to carry around. It's inexpensive, as textbooks go nowadays. 26 of 26 people found the following review helpful 5.0 out of 5 starsReader22 April 2007 By Parry S - Published on Amazon.com Format:Paperback If you plan to start with Matlab with no prior experience, this book beats most of the other available titles.Since an inside view of the book is not available on Amazon, I will for the benefit of others list out the chapters here.Ch1 begins with the necessary introduction,developing familiarity with the command window,display formats and precedence of operators.It moves on to Ch2 and Ch3 where arrays are introduced and the mathematical operations on them explained.Ch4 is about script files,Ch5 on elementary plotting techniques using in-built functions like plot and fplot.Ch6 introduces functions and Ch7 extends the previous material to formal programming techniques like loops and control structures.Ch8 explains curve fitting and interpolation,Ch9 is about three dimensional plots and special graphics.Ch10, the last one of the book uses Matlab to do symbolic math which cover elementary algebraic equations.The examples contained in the book are from elementary physics and engineering,so if you are looking for more advanced material that has been treated using Matlab,this might be a little less helpful.The numerical techniques again cover simple problems like projectile trajectory,flow of water from a vessel with a small hole punched in its sidewall,RC circuits, viscosity and so on.Relatively advanced topics like Fourier transforms and applications to signal processing are also left out.If you are done with this book or feel that the material isnt of much help, I will suggest that you might try "Numerical Computing with Matlab" by Moler(he is perhaps one of the architects of Matlab).This book(electronic version) is available for free from the mathworks website [...].Overall this book does a good job in explaining details and is also generously sprinkled with figures and screenshots.Please try it if you are first timer to Matlab. 8 of 8 people found the following review helpful 5.0 out of 5 starsGreat for learning the basics of MATLAB.17 Aug 2007 By Brian Mckenzie - Published on Amazon.com Format:Paperback\|Amazon Verified Purchase I purchased this title because I am starting a numerical analysis sequence next year using Matlab and I knew only how to plot in 2D and do simple calculations at the command line. After studying from Gilat's text for the past month or so I feel very comfortable using Matlab for all the basics and I am ready to learn how to exploit the full power of the program. Each chapter gives just enough mathematical background to provide anyone with at least college algebra/trig enough to understand what is going on. Although this book does not cover any topic too deeply, it does cover the fundamentals of many aspects of Matlab in a way that allows the reader to move fairly quickly through the whole book without getting bogged down in any one area. In the end you will know the basics about how Matlab operates: how to work with vectors and matrices, how to write simple programs and function files, how to plot and format data, how to fit data to a curve, and how to differentiate and integrate both numerically and symbolically, and a bunch of other great tools for solving problems. Also, as the other reviewers mentioned, the book makes very good use of graphics to show how input and output should look, as well as what exactly each line means. I would recommend this text to anyone wanting to learn the basics of Matlab.
This book introduces a new αβ math for describing physical laws in science, medicine, and engineering. The αβ math is an extension to the traditional XY math to address the... More > nonlinearity of the continuous numbers. The book starts with introducing the fundamentals of nonlinearity followed by describing the methodology for analyzing the nonlinear phenomena.In the αβ math, the fundamentals of nonlinearity are based on two mathematical axioms and two universal standards for linear and nonlinear measurements. A series of proportionality laws, in conjunction with a Graph-based, true-Value compared, and Proportionality-oriented (GVP) math system, are introduced for assisting in data analyses. The new αβ math is built on the classification of continuous numbers into linear and nonlinear numbers. The linear numbers are defined as the continuous numbers that have no association with any asymptotes; and the nonlinear numbers are the continuous numbers that have association with one or two asymptotes.< Less
More About This Textbook Overview Intended for schools that want a single text covering the standard topics from Beginning and Intermediate Algebra. Topics are organized by using the principles of the AMATYC standards as a guide, giving strong support to teachers using the text. The book's organization and pedagogy are designed to work for students with a variety of learning styles and for teachers with varied experiences and backgrounds. The inclusion of multiple perspectives -- verbal, numerical, algebraic, and graphical -- has proven popular with a broad cross section of students. Use of a graphing calculator is assumed. BEGINNING AND INTERMEDIATE ALGEBRA: THE LANGUAGE AND SYMBOLISM OF MATHEMATICS is a reform-oriented book. Related Subjects Meet the Author More by this Author James Hall JAMES W. HALL is an Edgar and Shamus Award–winning author whose books have been translated into a dozen languages. He has written four books of poetry, a collection of short fiction, and a collection of essays. This is his fifteenth novel. He and his wife, Evelyn, divide their time between South Florida and
master booklist 2010-2011 please note: all books coded as u0022newu0022 and highlighted in yellow are new for this year u0026 can purchase used updated 8/9/10 if you are ... Notes to the Teacher Objectives Correlation Presents the North Carolina objectives for Geometry and lists the items related to each objective that appear in the Pre-Course ... State the postulate or theorem you would use to prove the triangles are congruent. (4.3, 4.4, 4.6) PDFs/12CumulativeReview.pdf ii The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to ... 11 B. MODERN APPROACHES Letu0027s look at differences in how countries diagnose autism. United States. A psychologist in the United States first described the symptoms of autism 60 ... Helpful Hints for Pre-AP Math Betsy King Central High School 1. Tutorials: If you have questions, go to your teacheru0027s tutorials. You will know the tutorial schedule on day ... Hints Pre-AP Math.pdf anchorage school district anchorage, alaska asd memorandum #319 (2008-2009) may 4, 2009 to: school board from: office of the superintendent subject: adoption of new ...
books.google.com - The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises throughout to aid the reader's understanding.This edition includes substantial new material in areas that include: tensor products,... algebra Review: Abstract Algebra User Review - John Lee - Goodreads My first algebra book, and definitely a good one. The exercises are a little too straightforward at times, and a little too tricky at times, but with a bit of guidance, all of them are very doable ...Read full review Review: Abstract Algebra User Review - Waffles - Goodreads It's a math text, so I didn't enjoy reading it, but it is a good comprehensive overview of algebra. I'm glad this was the text for my algebra sequence.Read full review Review: Abstract Algebra Review: Abstract Algebra User Review - Dan - Goodreads This book is dense and huge. So you know it has a ton of information. I don't know if it is the best treatment of the material, but it is thorough (maybe even TOO thorough.) But all in all it was the ...Read full review
Discrete Mathematics Mathematical Reasoning and Proof with Puzzles, Patterns, and Games 9780471476023 ISBN: 0471476021 Pub Date: 2005 Publisher: John Wiley & Sons Inc Summary: Did you know that games and puzzles have given birth to many of today's deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley's Introduction to Discrete Mathematics, you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through games, puzzles, patterns, magic tricks, and real-world problems. You will discover how new mathematical topics can ...be applied to everyday situations, learn how to work with proofs, and develop your problem-solving skills along the way. Online applications help improve your mathematical reasoning. Highly intriguing, interactive Flash-based applications illustrate key mathematical concepts and help you develop your ability to reason mathematically, solve problems, and work with proofs. Explore More icons in the text direct you to online activities at Improve your grade with the Student Solutions Manual. A supplementary Student Solutions Manual contains more detailed solutions to selected exercises in the text. Ensley, Douglas E. is the author of Discrete Mathematics Mathematical Reasoning and Proof with Puzzles, Patterns, and Games, published 2005 under ISBN 9780471476023 and 0471476021. Five hundred six Discrete Mathematics Mathematical Reasoning and Proof with Puzzles, Patterns, and Games textbooks are available for sale on ValoreBooks.com, one hundred six used from the cheapest price of $75.37, or buy new starting at $142.41.[read more] Ships From:Dayton, OHShipping:Standard, ExpeditedComments:Book is in overall good condition!! Cover shows some edge wear and corners are lightly worn. Page... [more]Book is in overall good condition!! Cover shows some edge wear and corners are lightly worn. Pages have a minimal to moderate amount of markings. FAST SHIPPING W/USPS TRACKING9780471476023 ISBN:0471476021 Pub Date:2005 Publisher:John Wiley & Sons Inc Valore Books is the best place for cheap Discrete Mathematics Mathematical Reasoning and Proof with Puzzles, Patterns, and Games rentals, or used and new condition books that can be mailed to you in no time.
Study Guides Introduction to Coordinates in One Dimension We envision the real numbers as laid out on a line, and we locate real numbers from left to right on this line. If a < b are real numbers then a will lie to the left of b on this line. See ... Introduction to The Derivative as a Rate of Change If f(t) represents the position of a moving body, or the amount of a changing quantity, at time t , then the derivative f′(t) (equivalently, ( d/dt)f(t)) denotes the rate ... Introduction to Graphing of Functions We know that the value of the derivative of a function f at a point x represents the slope of the tangent line to the graph of f at the point ( x , f(x) ). If that slope is ... Introduction to Maximum/Minimum Problems One of the great classical applications of the calculus is to determine the maxima and minima of functions. Look at Fig. 3.9. It shows some (local) maxima and (local) minima of the function f . Introduction to Related Rates If a tree is growing in a forest, then both its height and its radius will be increasing. These two growths will depend in turn on (i) the amount of sunlight that hits the tree, (ii) the amount of nutrients in the soil, (iii) the ... Introduction to Antiderivatives Many processes, both in mathematics and in nature, involve addition. You are familiar with the discrete process of addition, in which you add finitely many numbers to obtain a sum or aggregate. But there are ... Introduction to Area Under a Curve Consider the curve shown in Fig. 4.1. The curve is the graph of y = f ( x ). We set for ourselves the task of calculating the area A that is (i) under the curve, (ii) above ...
Calculus Help In this section you'll find study materials for calculus help. Use the links below to find the area of calculus you're looking for help with. Each study guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn calculus. Study Guides Introduction Compound Interest Yet a third illustration of exponential growth is in the compounding of interest. If principal P is put in the bank at p percent simple interest per year then after one year the account has Introduction to The Method of Cylindrical Shells Our philosophy will now change. When we divide our region up into vertical strips, we will now rotate each strip about the y -axis instead of the x -axis. Thus, instead of generating a disk with ... Introduction to Surface Area Let f ( x ) be a non-negative function on the interval [ a, b ]. Imagine rotating the graph of f about the x -axis. This procedure will generate a surface of revolution, as shown in Fig. ... Introduction to Simpson's Rule Simpson's Rule takes our philosophy another step: If rectangles are good, and trapezoids better, then why not approximate by curves? In Simpson's Rule, we approximate by parabolas. Calculus Properties of the Exponential Now we want to learn some "calculus properties" of our new function exp( x ). These are derived from the standard formula for the derivative of an inverse, as in Section 2.5.1. ... Before you begin studying calculus, you may want to get an idea of what you know and what you need to learn. The test will answer some of these questions for you. The test is 50 multiple-choice questions covering the topics in this book. While 50 questions can't cover every concept, skill, or ... Introduction Calculus is the study of change. It is often important to know when something is increasing, when it is decreasing, and when it hits a high or low point. Much of the business of finance depends on predicting the high and low points for prices. In ...
Download Next: Variable Expressions Chapter 1: Equations and Functions Chapter Outline Loading Contents Chapter Summary Image Attributions Description This chapter covers evaluating algebraic expressions, order of operations, using verbal models to write equations, solving problems using equations, inequalities, identifying the domain and range of a function, and graphs of functions.
Multivariable Calculus is an expansion of Single-Variable Calculus in that it extends single variable calculus to higher... see more Multivariable Calculus is an expansion of Single-Variable Calculus in that it extends single variable calculus to higher dimensions. This course begins with a fresh look at limits and continuity, moves to derivatives and the process of generalizing them to higher dimensions, and finally examines multiple integrals (integration over regions of space as opposed to intervals). This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 103) This course introduces the student to the study of linear algebra. Practically every modern technology relies on linear... see more This course introduces the student to the study of linear algebra. Practically every modern technology relies on linear algebra to simplify the computations required for internet searches, 3-D animation, coordination of safety systems, financial trading, air traffic control, and everything in between. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Computer Science 105, Mathematics 211) Linear Algebra is both rich in theory and full of interesting applications (from simplifying internet search algorithms to... see more Linear Algebra is both rich in theory and full of interesting applications (from simplifying internet search algorithms to managing air traffic); in this course the student will try to balance both. This course includes a review of topics learned in Linear Algebra I. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 212Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to... see more Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. A very large fraction of solvable PDEs are either linear first- or second-order PDEs, or are related to such PDEs by transformation or perturbation theory. Fortunately, these PDEs also make up the language for much of the mathematical description of nature. Most of this class will concentrate on those equations that have proven to be of great importance to real-world applications. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 222) The study of "abstract algebra" grew out of an interest in knowing how attributes of sets of mathematical objects behave when... see more The study of "abstract algebra" grew out of an interest in knowing how attributes of sets of mathematical objects behave when one or more properties we associate with real numbers are restricted. The student will begin this course by reviewing basic set theory, integers, and functions in order to understand how algebraic operations arise and are used. The student then will proceed to the heart of the course, which is an exploration of the fundamentals of groups, rings, and fields. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 231) This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as... see more This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later, this course presents more advanced topics, such as Galois theory—one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 232) This course is designed to introduce the student to the rigorous examination of the real number system and the foundations of... see more This course is designed to introduce the student to the rigorous examination of the real number system and the foundations of calculus. Analysis lies at the heart of the trinity of higher mathematics—algebra, analysis, and topology—because it is where the other two fields meet. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 241)This course examines how numerical methods are used by engineers to translate the language of mathematics and physics into... see more This course examines how numerical methods are used by engineers to translate the language of mathematics and physics into information that may be used to make engineering decisions. Often, this translation is implemented so that calculations may be done by machines (computers). This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mechanical Engineering 205)
several areas in classical and modern geometry: analytic geometry, conic sections, Platonic solids and polyhedra, tessellations of the plane, projective, hyperbolic, and differential geometry. Students will see how symmetry groups serve as a unifying theme in geometry. This course will introduce students to the skill of writing formal mathematical proofs.

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.