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Nuffield National Curriculum Mathematics Nuffield National Curriculum Mathematics was written to provide comprehensive coverage of the 1996 National Curriculum for mathematics. Each student's book in the series offers focused coverage of mathematical topics identified in the National Curriculum level descriptions. Used together the books in the series provide a straightforward and motivating route through National Curriculum mathematics for students. The series structure of separate books for Number and algebra, Shape, space and measures and Handling data reflected the structure of the National Curriculum, with a students' book for each NC level and content attainment target up to NC Level 7. Level 8 and above are treated in one longer student's book. Using and applying mathematics is not treated separately but is an integral part of each book. Up to stage four, every student's book is presented as a series of units, each designed to provide about two weeks' work. Each book builds on the previous level and anticipates the next level. There are also some enrichment activities which are essential to a balanced mathematical education. A strength of this series is that students may work on the book which is most appropriate to their current needs as it was believed that students would not progress through National Curriculum levels uniformly and that some students are better at topics which interest them or which they meet in other contexts. To help teachers plan their teaching, each students' book includes a chart showing where the statements in the National Curriculum level descriptions are covered in the book. This chart is also shown in the assessment packs as is a Programme of Study matching chart. In addition to this, detailed content descriptions are provided at the top of each students' book .Stage one of Nuffield National Curriculum Mathematics consists of three books one each for Number and algebra, Shape space and measures and Handling data. They are all at level four of the National Curriculum. Each students' book is accompanied by an Assessment and Resource pack offering the following materials: •… Stage two of Nuffield National Curriculum Mathematics consists of three books at level five, one each for Number and algebra, Shape, space and measures and Handling data. They are all at level four of the National Curriculum. These students books were suitable for a foundation GCSE course. Each students' book is accompanied… These level six books from Nuffield National Curriculum Mathematics, on Number and algebra, Shape, space and measures, and Handling data, were all suitable for a foundation GCSE course. Each students' book is accompanied by an assessment and resource pack offering the following materials: • Teaching notes - brief… Nuffield National Curriculum Mathematics stage four books were intended for those students working at level seven and followed an intermediate GCSE course. As with previous stages, there are three books, each one covering an attainment target but also incorporating using and applying mathematics. The assessment and resource… The Nuffield National Curriculum Mathematics stage five book, for those students following an higher GCSE course, was split into the same three sections as the previous stages' books. Each section was divided into chapters giving relevant information and presented activities to do and questions to answer.
exponential and logarithmic functions and their graphs; properties of logarithms. Although it does not specifically cover calculus, Math Readiness provides the necessary background for university calculus courses. Each short lesson will be given as a lecture, followed by a problem session. During the problem session, you will work on exercises with other students in small groups with the guidance of senior class assistants. Math Readiness Summer Camp: A two-week intensive program held on the U of S Campus in late summer (includes lectures and small group tutorials). Math Readiness Fall and Winter Term Evening classes: 40 hours of class time with an instructor and pre-arranged tutorial time. The Math Readiness Summer Camp also helps you get comfortable with the university environment. In addition to classes, tours are arranged to help familiarise you with the University of Saskatchewan. Plus, you will have enough free time to get to know the city before you start your fall classes. Questions? Math Readiness is offered through partnership by the Department of Mathematics & Statistics and the Centre for Continuing & Distance Education. Visit the Department of Mathematics and Statisticswebsite for more information.
Functions:Algebra to Calculus will weave procedural and conceptual elements of differential calculus and integral calculus into a rigorous study of linear,quadratic, polynomial, exponential, logarithmic, and rational functions. Each function family will be explored algebraically, numerically, graphically and verbally. The classroom will be student-centered with a strong emphasis on collaborative learning. Students will be expected to engage in a rigorous study of the mathematics and participate fully in reflective practices centered on teaching and learning. This course is intended for students who want a rigorous survey of the first-year of college mathematics or who plan on teaching middle school mathematics. Students who plan to teach high school mathematics are also encouraged to take this course, and additional course work in pre-calculus and calculus may be necessary to complete your mathematical preparation to teach high school math.
This revised edition of Pre-Algebra links all the activities to the NCTM Standards. The activities were designed to provide students with practice in the skill areas necessary to master the concepts introduced in a course of pre-algebra. Reinforcing operations skills with both decimals and fractions plus activities involving ratios, integers, proportions, percents, rational numbers, simple equations, plotting coordinates, and graphing linear equations are all part of this new edition. Examples of solution methods are presented at the top of each page. New puzzles and riddles have been added to gauge the success of skills learned. Contains complete answer key Pre-algebra Revision Of If8761 online from Wayfair, we make it as easy as possible for you to find out when your product will be delivered. You can check on a delivery estimate for the Carson Dellosa Publications Part #: IF-G99033 here. If you have any questions about your purchase or any other Teacher Resources product for sale our customer service representatives are available to help. Whether you just want to buy a Carson Dellosa Publications Pre-algebra Revision Of If8761 or shop for your entire home, Wayfair has a zillion things home.
Internal Revenue Investigator Mathematics is more than just algebra, geometry and calculus. It is the primary tool of science, the language of modern technology and the structure of creativity. In the broadest sense, mathematics is the study of patterns, relationships and logical structures. Regardless of the area of mathematics, the common goal is not only to understand the objects under study but to relate them and form connections to other phenomena.
Hi! I'm looking for a book about the relation betweenI've noticed that my collection of books is sorely lacking in books related to Maths, and I've always been interested in the history, and practical applications of Maths. I don't suppose anyone here has recommendations for the history of Maths, or even practical applications? I realise that this is bit general, but still, help would be appreciated. I'm in my last year of high-school, and I'm looking for a math book to use in addition to the one we use in class. I also have a suggestion: Arthur Benjamin's "Secrets of Mental Math" ... 984&sr=8-1 It improves your mental addition, subtraction, multiplication and division skills to amazing levels, and also teaches you other things like memorizing numbers better. How much calculus do you know? If you haven't taken it yet, or don't otherwise know it, I would recommend finding a basic calculus textbook. If your school offer calculus, you might be able to borrow one, but it will almost certainly not be very proof-oriented (which, if it's your first introduction to calculus, is probably a good thing). If you are comfortable with the concepts of basic calculus (differentiation and integration of one variable- you probably won't need series that much, but they can't hurt),you might want to try a multivariable calculus book- see this thread for recommendations. If you want to find out what real algebra is, you could try group theory (or more advanced abstract algebra), but you've most likely not seen those concepts before if you haven't read outside of the standard math curriculum, and there's a good chance that your math teacher won't have either. Finally, linear algebra is useful and greatly generalizes the idea of "vector" outside of how you learn them in precalculus/physics. This is a textbook that I've recently worked through, and it seems to be well-written. It also has the advantages of including answers, being free, and being proof-based. Most of the proofs are pretty simple, so they're a good introduction to mathematical rigor and induction. I'm looking for a good book on the algebraic developments that occured within the last half-century or so, particularly the classification of finite simple groups, mosterous moonshine, and all the rest of the stuff that is used in string theory. I know the basics--undergraduate level classes, introductory graduate classes in algebra (Dummit & Foote), analysis (Royden), topology (Munkres), Number theory (professor's own lecture notes), and convexity theory (I don't remember the book offhand). I also know a decent amount about representation theory and differential geometry from my class in Quantum Field Theory, but certainly not as much as I'd like. I'm pretty confident I'd be able to read any book recommended, given the time. I have tried reading the original papers, but these aren't in a convenient format for reading and doing independent study. I'm not so much interested in a full proof of the enormous theorem; more like a book that covers things like the Leech lattice or the monsterous moonshine conjecture in somewhat seperate sections, for some light reading. I decided to stay as an undergraduate for an extra year next year, and my university doesn't have anyone whose research is in this particular area. I'm looking for something to keep myself busy in an independent study for a semester or a year before I go to grad school. The classification of finite groupsLE4dGOLEM: What's a Doug? Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood. I just finished reading the book ------------ John Derbyshire's Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics ------------ and really liked it. It's set up so that anyone could get a good grasp on the Riemann Hypothesis, even people without any knowledge of calculus. Every even chapter is a brief history of a famous mathematician, and every odd chapter is about the math. I'd strongly recommend it to anyone interested in math or math history, at basically any level above high school. Okay, so the book Complex Variables by Robert B. Ash is giving me a super hard time. I think I've only managed to complete four problems out of the 13 I've attempted and have resorted to looking up solutions, it may be that I'm giving up too easily. As a fourth semester undergrad this book shouldn't be too tough for me. But for some reason it's giving me trouble. Does anyone have any other recommendations for books on complex analysis that aren't going to beat me up and make me sad? Should I just give up on Complex Analysis? I'm preparing for an upcoming differential geometry course, which I'll take for the second time. The book that the course is using is not very enlightening and I'm having a lot of trouble getting my head around the concepts. I have to learn about manifolds, equivalent definitions of manifolds, transformations between manifolds, one forms, k-forms, etc. etc. Everything is discussed in the context of R^n. Can someone recommend me some books that will help me make sense of the subject? Thanks in advance! Bravemuta wrote:Hi! I'm looking for a book about the relation bewteenThe Pythagoreans might be of historical interest to you. Their pseudo-religion of number found its strongest evidence in the mathematical ratios of music. One of my professors gave me a book that had been sitting in his closet, The Magic of Numbers by Eric Bell, which he said was all about the Pythagoreans. I still haven't read it (for shame!), but I imagine it has more depth than the average pop math book on patterns found in nature. teseract wrote:i'm searching a good book about "Discrete maths", for semi-begginers (i had that assignature in the college, but i want to know more about Graphs, Groups, and the talky...word thing Theory!). What could you recommend me? My apologies for being two years late in replying, but for anyone else still looking, Discrete Mathematics with Applications by Susanna Epp is an excellent introduction that can be fully self-taught if necessary. I came here to read a cool post, a witty dialogue, a fresh joke, but stumbled upon a "bump"... Way to go, jerk...~CordlessPen I'm really enjoying _The Princeton Companion to Mathematics_, edited by Timothy Gowers (ISBN 978-0-691-11880-2). It's a bit less than the price of a textbook (US$90 list; more typically around $60) and in its thousand pages it covers a heck of a lot. I got it because working on a MS in CS, I keep finding references to concepts I haven't encountered before in the papers I'm reading. Usually, these articles give me enough more than Wikipedia to keep going. doogly wrote:The classification of finite groupsThanks. I've picked up a few books on Vertex Operator Algebras, which our library has a surprisingly good selection for despite no one researching them here. I wasn't so much interested as string theory in particular as any kind of modern algebra that is currently being researched. Vertex Operator Algebras should keep me occupied for a while though; at least over the summer, and hopefully into next year . equivalent definitions of manifolds What, exactly, do you mean here? Like how the circle S1 is diffeomorphic to the space R / Z? Or do you actually mean some kind of alternate definition of the concept of a manifold that is somehow equivalent? If you mean the first, any decent book will have that kind of thing in it. If you mean the second, no book I've read defined manifolds significantly differently. Regarding your question, I learned differential geometry from "Tensor Analysis on Manifolds" by Bishop and the Spivak volumes 1 and 2. Spivak is nothing short of amazing, but it doesn't seem to match everyone's tastes. Similarly, the Bishop book is sort of abstract at times and can be dense compared to some other undergraduate texts. If you're really having trouble, try looking up some "Differential Geometry for Physicists" books--it's hit and miss whether they'll help, but the concepts they do cover tend to be done in a way that isn't prohibitively abstract. You may need to know some basic physics to use them, though. For a couple of summers now I've worked through a book on a topic that interested me, but I didn't have the time to focus on during the year. This year I'm looking at set theory. So now I need a book. It should be fairly extensive. It shouldn't be too elementary, as I'm not completely new to set theory (for example Halmos' Naive Set Theory isn't what I'm looking for). If there are exercises included, all the better. And it should serve as a good reference sort of thing, to quickly find some fact in, in the future. As a concrete example, if I were looking for something in category theory, MacLane's CTFTWM would fit perfectly, while Awodey's Category Theory would be a bit on the simplistic/long-winded side. A quick check on amazon found this and this. Based on the preview pages both of these seem promising. I've looked at Just's and Weese's book before and found it very enjoyable, but I didn't have the time needed to put into it. So what do you think? Do you recommend either of these two? Or something else? Well, I have Basic Set Theory by Azriel Levy sitting at my desk right now. It looks quite good; it definitely doesn't waste time (it's crammed with proofs and exercises). I've put it to limited use for a logic course I had, and it served its purpose well, for whatever that's worth. It's probably terrible for someone starting out with set theory, but as your post said, that's not the case for you. I'm unfamiliar with both of the books you linked to, so I can't offer my opinion there. Yakk wrote:hey look, the algorithm is a FSM. Thus, by his noodly appendage, QED I've looked through the topic and I'm still a touch unsure - I'm looking for a text in abstract algebra, and I don't know what to choose at all. I don't have any real problem with formal rigor - I've taken a few proof-intensive courses. I'm just coming at it from kind of an odd angle - It's been a few years since I had an elementary linear algebra course. I'm not a math major (I'm CS), so I've mainly been taking things like theory of computation and combinatorics, rather than the standard "proof-intensive advanced calculus/analysis and linear algebra" sequence that most universities seem to use as a bridge to upper-level courses. I was thinking about Dummit and Foote, but one professor I spoke with recommended Gallian, Herstein, or Isaacs. I really have no idea what to go with. Isaacs is admittedly a graduate text, but he said that it provided a rather complete coverage, and didn't really presuppose any prior knowledge of the material. I really have no idea what to do - it seems like everyone loves at least one text from the set of undergraduate texts and hates at least one other. I really just want to learn abstract algebra to broaden my mathematical horizons and brush up on my proof writing. Should I just jump in on one and see how it goes? I want to try the graduate text, but I'm slightly worried about getting in over my head. What makes a text a graduate text, when it doesn't presuppose prior knowledge? Does it just tend to mean the author presumes extensive experience in proof reading/writing, and therefore adjusts the style accordingly (e.g. if the audience has lots of experience with reading proofs, the author might be a bit more laconic)? "Only on XKCD do we try to figure out which tessellating shape for burgers results in the least waste-meat." -aleflamedyud I also want to give Artin's Algebra a shout out. I really liked this one, definitely worth giving a peek to if you have a chance. He takes a more geometric view, spends time with more some special problems, and gets into some topics often not done in a first course, like representation. I liked it much better than Gallian as an undergrad book, though Artin is harder. (They are both undergrad in that they assume the same level of preparation, but Gallian didn't require as much from the reader). In a more satisfying way, I thought. The only other one I have used is D&F, which is probably best left to a second romp through algebra also. LE4dGOLEM: What's a Doug? Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood. I completed up to vector calculus my first year at university, but haven't taken math since then. Next year, I am going to be concentrating on formal epistemology, and would like a good primer on model theory for studying formal languages. Any suggestions? The book would preferably be geared towards non-mathematics majors, and focus on logic applications. If the request is basically impossible, some course of books moving from algebra to model theory would be better, I suppose. I will be starting college in fall 2010 and want to use the summer to prepare for a linear algebra course. I have a pretty good background in AB and BC Calc(calc 1 and 2) but their was a prerequesite course for linear algebra I was allowed to skip. Apparently, it was a bit of a proof course that taught things such as proof by induction and introductory topics before linear algebra. So, can anyone suggest me a good book to bridge the gap between calculus 1+2 and linear algebra? Izawwlgood wrote:I for one would happily live on an island as a fuzzy seal-human. mmmcannibalism wrote:So, can anyone suggest me a good book to bridge the gap between calculus 1+2 and linear algebra? If you are willing to learn to think about proofs (and it sounds like you are), Lax's Linear Algebra is decent. Or are you looking for basic proof practice before linear algebra? I can try to think of something, but at the end of the day I think these things are best learned by simply reading books which require them. More to the point, there isn't really a gap between calc and linear algebra, they are not really connected so tightly at this level. Any one have any recommendations for Coding Theory? Maybe something with some Algebra tossed in too? This seems like a field where there should be a "standard" text or two, but I'm not finding much on my own. I've had a lot of success applying basic geometry to problems which can be expressed that way over the years. I have a PhD in engineering, but I reckon most of the geometry I know comes from secondary (high) school. I've always compensated with a strong faculty for spatial relations. Recently, I´ve found myself struggling with the limitations of that - I'm working on generalising a very useful 2D result to 4D, and my lack of formal geometry has slowed me down a lot. Even something as simple as co-ordinate transformation of a line in 4D space - I've had to look up how to write the line (I quickly realised that l w + m x + n y + o z + c = 0 defines a volume!), and my intuition struggles with the transformations (it's not easy to picture 4D!) Can anyone recommend a geometry textbook or books which would suit me? I think something which is simple but rigourous, or which compiles a lot of ideas and tricks for intuitive work would be appropriate (both would be ideal!). I took Linear Algebra last semester and I was into the abstract stuff (once I understood it and wrapped my head around it of course) enough to even try to do some work on my work on whatever class is after Linear Algebra. So I was wondering what is after Linear Algebra and what are some good books that cover that subject? Or if some book recommendations for the subject have already been given in this thread you can just name the subject and I can just look through the thread for the books. Talith wrote:Thank you very much! There are some recommendations for abstract algebra even on this page (or the previous page if this post starts a new page) so that makes it quite easy for me. romulox wrote:hope this helps -romulox What book would you recommend if I wanted to try to learn Abstract Algebra on my own, or would you advise against that idea entirely and just wait until I can take an Abstract Algebra class? I made it through Linear Algebra all right, but I'm no genius. I can usually pick out stuff from a decent undergrad text without a teacher's help though.
This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems... see more This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems regarding abstract algebra. Included is a Table of Contents that lists the topics such as Integers, Functions, Groups, Polynomials, Galois Theory, Unique Factorization, etc. There is also a link to an online study guide for the topic. This is a recording of a webinar by the authors of the material, "Demos with Positive Impact" ("... see more This is a recording of a webinar by the authors of the material, "Demos with Positive Impact" (" target=״_blank״ as part of the MERLOT Classics Series on Elluminate. It is a good opportunity to explore the site from the authors' eyes and to gain insight into how they use it in classes.It would be good for a faculty development workshop or for individual enjoyment. This video was created by a student for a graduate class in digital storytelling. The author decided to use this format to... see more This video was created by a student for a graduate class in digital storytelling. The author decided to use this format to illustrate functional relationships in math. The student claimed that "The idea of functions is very difficult for most of my students to understand because it's usually taught very abstractly." This is a humorous way to get the point across to which students can relate. This site provides links to 109 podcasts.'The Math Dude makes understanding math easier and more fun than your teachers ever... see more This site provides links to 109 podcasts.'The Math Dude makes understanding math easier and more fun than your teachers ever led you to believe was possible. Host Jason Marshall provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most mathphobic people looking forward to working out whatever math problem comes their way. If you're getting ready to take the SAT, GRE, or any of the other standardized tests; or if you're going back to school and need to brush up on the basics, the Math Dude's Quick and Dirty Tips to Make Math Easier will strengthen your fundamental skills, help you better understand the language of math, and succeed when it comes to taking a test. And if you just want to calculate the tip without using your iPhone and impress all your friends, his tips and tricks are for you too.'According to one user, 'I find this series very useful for students who need a different way to think about Math. The visual that is described and repetition of examples during the podcast are extremely helpful and go beyond memorization.'
COLLEGE ALGEBRA Course Outline This syllabus gives a detailed explanation of the course procedures and policies. You are responsible for all of this information, and should ask your instructor if anything is unclear. PREREQUISITES This is not a beginning algebra course . The course presumes that the student has attained a B or better in Intermediate Algebra, or has an ACT math score of 22 or better, or has an equivalent level of preparation. Units 1 and 2 review the prerequisite material. MATERIALS The course materials packet College Algebra Units 1-5 (Hawkinson) is available through Varney's Bookstore. Course Info, Syllabus, Lectures, Textbook, Sample Quizzes, and Software are accessed through the Course Home Page here. CALCULATOR You will need a calculator with exponential and logarithmic capabilities, typically designated as "scientific" and having some combination of y x , ^ , ln x and LN keys. A TI-30X IIB(S) is suggested. A graphing calculator is acceptable, but not required . STUDY View the lecture online for each lesson. A Lecture Outline for each lecture's notes can be found in the course packet. The text for the course is online as well, and is designed to be read carefully by the student after the corresponding lecture. These are then reinforced by the homework assignment. If you need assistance, please feel free to contact me in my office, by phone or by e-mail. HOMEWORK The homework questions for each lesson are located in the course packet; these should be done in the space provided in a neat, organized manner that is consistent with the methods discussed in the lectures and the text. All lessons for a unit will be turned in for a grade when the quiz for the unit is given. Each lesson Exercises set is worth 6 points. The homework for each lesson includes an Investigation, which is an extension of the lesson designed to help the student think independently about a selected topic. Each Investigation is worth 4 points. SHOW WORK - no credit will be given for answers only. NOTE that the homework comprises 46% of the final course grade. COMPUTER WORK You will need to have access to a computer with a modern web browser having both Javascript and Java enabled to view the lectures and complete the readings/applications for the course. A graphing utility is also included online to show the impact of current technology on the study of mathematics. QUIZZES You will take a quiz over each unit as listed in the course schedule. Ask your proctor to request a quiz about one week before you plan take it. All questions are to be worked out in a manner consistent with the lectures and course text. Each quiz is worth 30 points toward your final course grade. You may choose the pace at which you take the quizzes, with the following restrictions.  No more than two quizzes may be requested and taken at a time.  All quizzes, and the Final exam, must be completed by the course closing date. SAMPLE QUIZZES A sample quiz for each unit is available in an interactive computer format online. The help files are particularly useful in reviewing the unit material. Note that these samples are meant only for practice, not an iron clad representation of a Unit Quiz. GRADING The total points possible for the course are as follows. Quizzes (5@30 points) 150 points Homework (23@6 points) 138 points Investigations (23 @ 4 points) 92 points Final Exam 120 points 500 points Total A final course grade will be assigned according to the scale below. A 450 to 500 points B 400 to 449 points C 350 to 399 points D 300 to 349 points F less than 300 points TIME REQUIREMENTS Any 16 week course in a quantitative subject such as this requires a great deal of time investment on your part. Please be prepared to spend at least 8 hours per week studying for this course. COURSE WEB PAGE Resources / Announcements / Info / Frequently Asked Questions (FAQ) POLICY NOTES  If you have any condition (e.g. physical or learning disability) which will require academic accommodations, please notify the instructor.  Plagiarism and cheating are serious offenses and may be punished by failure on the exam, paper, or project, failure in the course and/or expulsion from the University. Dale P. Hawkinson dph@math.ksu.edu KSU - Holton 101E (785)532-5386 office Manhattan, KS 66506 (785)539-3377 home COLLEGE ALGEBRA Course Outline LEC. UNIT LES. TOPIC 1 1 1 Polynomials 2 1 2 Factoring 3 1 3 Algebraic Fractions 4 1 4 Linear Equations & Inequalities 5 1 5 Linear Graphs and Systems Quiz 1 6 2 1 Roots and Fractional Exponents 7 2 2 Quadratic Equations 8 2 3 Polynomial Equations 9 2 4 Root and Fractional Equations 10 2 5 Solving Equations Using Graphing Technology Quiz 2 11 3 1 Functions 12 3 2 Functions & Word Problems 13 3 3 Functions & Variable Inputs 14 3 4 Functions & Graphs 15 3 5 Interpreting Graphs Quiz 3 16 4 1 Linear Functions & Models 17 4 2 Quadratic Functions & Models 18 4 3 Polynomial Functions & Models 19 4 4 Rational Functions & Models Quiz 4 20 5 1 Exponential Functions 21 5 2 Logarithmic Functions 22 5 3 Exponential & Logarithmic Equations 23 5 4 Exponential & Logarithmic Models Quiz 5 Final Exam Outline – see Course web page Final
Middle School Math Grade 6 covers the fundamentals of fractions, decimals, and geometry. Also explored are units of measurement, graphing concepts, and strategies for utilizing the book's content in practical situations. Volume 1 includes the first 6 chapters Geometry FlexBook is a clear presentation of the essentials of geometry for the high school student. Topics include: Proof, Congruent Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations Trigonometry FlexBook is an introduction to trigonometry for the high school student. Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex Numbers.' proportions
Essentials of College Algebra With Modeling and Visualization - 3rd edition Summary: Today's algebra students want to know the why behind what they are learning and it is this that motivates them to succeed in the course. By focusing on algebra in a real-world context, Gary Rockswold gracefully and succinctly answers this need. As many topics taught in today's college algebra course aren't as crucial to students as they once were, Gary has developed this streamlined text, covering linear, quadratic, nonlinear, exponential, and logarithmic functions a...show morend systems of equations and inequalities, to get to the heart of what students need from this course. By answering the why and streamlining the how, Rockswold has created a text to serve today's students and help them to truly succeed. ...show less 6.1 Functions and Equations in Two Variables 6.2 Systems of Equations and Inequalities in Two Variables 6.3 Systems of Linear Equations in Three Variables 6.4 Solutions to Linear Systems Using Matrices 6.5 Properties and Applications of Matrices 6.6 Inverses of Matrices 6.7 Determinants SOME WATER DAMAGE
״Designed for people of all ages, Math Flash Cards Addition is an app that allows the user to practice simple basic addition... see more ״Designed for people of all ages, Math Flash Cards Addition is an app that allows the user to practice simple basic addition facts or extend the users ability to work out complex addition problems up to three digit numbers. Users can control the number of digits used to generate the problems. From one digit to three digits can be seclected by the user. Users also can control the number of questions given during one session. If a wrong answer is given by the user, the correct answer is shown before the next problem is given. Sound feedback is provided to the user for correct and incorrect answers. If you are looking for a program to help improve your addition skills, this just might be the app for you.*Features* - Over 1,000,000 math problems to solve! - Customizable timer (can be turned on or off) - The max number can be set as low as 1 or as high as 999 - You can set a minimum number(0 - 999, it has to be lower than your maximum number) - Supports negative numbers(Turned off by default) - Negative numbers can be generated randomly or you can control which numbers are negative! - Users can set one of the numbers to a specific number - Provides sound affects (can be turned on or off) - Users can decide how many questions to complete - Support the new iPad's Retina Display״This is a free app "•The Instructors should note that this book probably contains more information than you will be able to cover in a single school year." should note that this book probably contains more information than you will be able to cover in a single school year." According to The Orange Grove, "This book is based on an honors Calculus course given in the 1960s. The book contains more... see more According to The Orange Grove, "This book is based on an honors Calculus course given in the 1960s. The book contains more material than was normally covered in any one year. It can be used (with omissions) for a year's course in Advanced Calculus, or as a text for a 3-semester introduction to analysis. There are exercises spread throughout the book.״ This is a free textbook offered by BookBoon.'Advanced Maths for Chemists teaches Maths from a "chemical" perspective and is... see more This is a free textbook offered by BookBoon.'Advanced Maths for Chemists teaches Maths from a "chemical" perspective and is the third of a three part series of texts designed for a first-year university course. It is the Maths required by a Chemist, Chemical Engineer, Chemical Physicist, Molecular Biologist, Biochemist or Biologist. Tutorial questions with fully worked solutions are used and structured on a weekly basis to help the students to self-pace themselves. Coloured molecular structures, graphs and diagrams bring the text alive. Navigation between questions and their solutions is by page numbers for use with your PDF reader.' This is a free textbook offered by BookBoon.'In this book, which is basically self-contained, the following topics are... see more This is a free textbook offered by BookBoon.'In this book, which is basically self-contained, the following topics are treated thoroughly: Brownian motion as a Gaussian process, Brownian motion as a Markov process, and Brownian motion as a martingale. Brownian motion can also be considered as a functional limit of symmetric random walks, which is, to some extent, also discussed. Related topics which are treated include Markov chains, renewal theory, the martingale problem, Itô calculus, cylindrical measures, and ergodic theory. Convergence of measures, stochastic differential equations, Feynman-Kac semigroups, and the Doob-Meyer decomposition theorem theorem are discussed in the second part of the book.' This is a collection of learning resources for the K-12 area. Special features include: Teacher Web Resources (by category... see more This is a collection of learning resources for the K-12 area. Special features include: Teacher Web Resources (by category of subject), Administrator Web Resources, and Student Web Resources. One can find lesson plans and podcasts as well as links to other resources. One can also search for a particular topic, and suggest other resources.ALEX is a partner of thinkfinity. In addition to funding, Thinkfinity.org shares its 55,000+ resources with Alabama to link directly from the Alabama Courses of Study from Alabama's partnership web portal, ALEX. ״Created by a high school math teacher with over 25 years of experience in the classroom. Develop your algebraic equation... see more ״Created by a high school math teacher with over 25 years of experience in the classroom. Develop your algebraic equation solving skills through playing a Bingo game. This game will take you step by step through the process of learning how to solve the most basic equation up through multiple-step equations by way of 13 different levels and it will allow you to choose from a variety of Bingo games from straight-line Bingo through multiple patterns of Bingo all the way up to Black-out Bingo if you choose. The game will keep track of your time and points to be able to compete with others as well as yourself.״״This game is great for Pre-Algebra and Algebra I students who are just learning how to solve equations as well as for Algebra II and even Precalculus students needing to review their equation solving skills. It can also be used an Algebra tutorial for anyone preparing for a standardized test such as the S.A.T. or A.C.T.״This app costs $.99 This is a free online course offered by the Saylor Foundation.'This introductory mathematics course is for you if you have a... see more This is a free online course offered by the Saylor Foundation.'This introductory mathematics course is for you if you have a solid foundation in arithmetic (that is, you know how to perform operations with real numbers, including negative numbers, fractions, and decimals). Numbers and basic arithmetic are used often in everyday life in both simple situations, like estimating how much change you will get when making a purchase in a store, as well as in more complicated ones, like figuring out how much time it would take to pay off a loan under interest.The subject of algebra focuses on generalizing these procedures. For example, algebra will enable you to describe how to calculate change without specifying how much money is to be spent on a purchase–it will teach you the basic formulas and steps you need to take no matter what the specific details of the situation are. Likewise, accountants use algebraic formulas to calculate the monthly loan payments for a loan of any size under any interest rate. In this course, you will learn how to work with formulas that are already known from science or business to calculate a given quantity, and you will also learn how to set up your own formulas to describe various situations by translating verbal descriptions to mathematical language. In the later units of this course, you will discover another tool used in mathematics to describe numbers and analyze relationships: graphing. You will learn that any pair of numbers can be represented by a point on a coordinate plane and that a relationship between two quantities can be represented by a line or a curve.Units 6, 7, and 8 may seem more abstract than the earlier ones, as you will deal with expressions that contain mostly variables and not too many numbers. While the procedures you will master in these units might seem to have little practical application, you have to keep in mind that they result in formulas that describe very real situations in business, accounting, and science. Knowing how to perform various operations with algebraic expressions will eventually enable you to solve quadratic and even more complex equations. You will explore a variety of real-world scenarios that can be described by these kinds of equations. For example, if a ball is thrown up in the air, solving a quadratic equation will help you find out when it will hit the ground. As another example, if you know the area of a rectangular garden, then you can use a quadratic equation to find the length of each side.'
More About This Textbook Overview Porter and Hill is the first completely interactive linear algebra course. Developed by the authors and class-tested at Penn, Temple and Duke University, Interactive Linear Algebra runs in Mathcad (Windows environment). The subject is taught in a laboratory setting, with or without additional lectures, and students realize that through this technology-centered approach, mathematics becomes an experimental science. Using the interactive approach, students become active participants in the learning process, which leads to a deeper understanding of the concepts, and at the same time the approach develops confidence in their ability to read, use and write about linear algebra. The electronic text guides students through the standard topics in linear algebra, with a carefully planned series of computer-based discussions, examples, questions, and projects. With its graphics, symbolics, numerics and editing capabilities, Mathcad provides the digital tools needed for developing, visualizing, connecting and applying important
Mathematics This summer, the political scientist Andrew Hacker's New York Times Op-Ed essay "Is Algebra Necessary?" set off a national debate on mathematics education. Here is how the essay begins: A typical American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I've found myself moving toward the strong view that we shouldn't. The debate inspired us to suggest several algebraic opportunities right here in the pages of The Times. After considering them, and reading Mr. Hacker's essay in full, we invite you to tell us what you think. Is algebra necessary? In this lesson, students explore the fundamental characteristics of currency by reading and researching about the bitcoin, the upstart digital commodity that has grabbed the attention of speculators, investors, bankers and regulators worldwide.
The Cruncher 2.0 is a beginner's full-featured spreadsheet tool. Use fun design elements to turn an ordinary information-gathering and reporting assignment into an exciting adventure. Included projects guide your child through the organization and charting of information across all areas of current classroom curriculum, including math, science, social studies, language arts, and geography. Then, easily analyze the collected information, create colorful graphical and linear representations, and develop simple mathematical conclusions. Six step-by-step tutorials will guide your child through the process. Grade Builder Algebra 1 covers an entire year of Algebra in an easy-to-follow format that includes 60 lesson topics, tutoring on specific problem areas, and games intended to reinforce the lessons and test the user's understanding and retentionHigh Achiever Trigonometry for Grades 10-12 is curriculum based software foracademic success. For high school students currently enrolled inTrigonometry, and a great study aid for anyone preparing for his or her collegeentrance examinations Skills Learned Addition and subtraction, money, time, fractions, decimals, percents, weight, measurement&patterns Math, strategy, and critical thinking are exercised in Numberball. First, discover how to operate the intriguing Numberball machine. Use gadgets, blowers, and fireballs to direct numbers and symbols through the pipe system and place them to complete an equation. Start at easy levels and work your way to more challenging problems. There is never just one solution to a problem. Great for Collegiate Entrance Exam PrepProduct InformationHigh Achiever Algebra 2 for Grades 9-12 is curriculum based software foracademic success. It is for high school students currently enrolled inAlgebra 2 and is a great study aid for anyone preparing for his or her collegeentrance examinations.Skills Learned Absolute Value Intersection of Lines Linear Inequalities Factoring Polynomials Second Degree Equations Second Degree Inequalities conic Sections Exponential Functions Logarithmic Functions Exponential Equations Logarithmic Equaitons Product Features Study Aid Provides assistance in preparing for college entrance exams. Great for Collegiate Entrance Exam PrepProduct InformationHigh Achiever Geometry for Grades 10-12 is curriculum based software foracademic success. For high school students currently enrolled in Geometryand is a great study aid for anyone preparing for his or her college entranceexaminations.Skills Learned Circles Triangles and Quadrilaterals Parallel and Perpendicular Lines Coordinate and Space Geometry Angle Measurement and Vectors Points Area Circumference Plane Reasoning Equality and Similarity Non-Euclidean GeometryProduct Features Study Aid College entrance exam preparation Covers topics commonly taught in 7th grade math and some pre-algebra concepts. Also suitable for high school students and adult learners who need to brush up on their basic math skills. Features include 28 standards-based lessons, over 200 interactive quiz questions, 26 skill-building animations, and a searchable database of over 500 key basic math terms. Covers topics commonly taught in 8th grade math and some pre-algebra concepts. Also suitable for high school students and adult learners who need to brush up on their basic math skills. Features include 25 standards-based lessons, over 300 interactive quiz questions, 25 skill-building animations, and a searchable database of over 500 key basic math terms. Explore the virtual village of Mathville, where everything from work to sport is filled with math and fun! In Mathville Middle School version 3, you'll work, shop, and play -- and hone your math skills along the way.As you try out careers ranging from chef to webmaster, you'll solve real-world math problems you'd face in these professions.You'll also do the math needed to keep yourself fed, clothed and housed. And you'll use your mathematical know-how in sports ranging from hockey to basketball.While reinforcing the math skills learned in school, Mathville MS is designed to empower learners to develop creative problem-solving skills and a real sense of math confidence.
Linear Algebra With Applications - 4th edition Summary: Linear Algebra with Applications is a flexible blend of theory, important computational techniques, and interesting applications. Instructors can select the topics that give the course their desired perspective. The text provides a solid foundation in the mathematics of linear algebra, while introducing some of the important computational aspects of the field, such as algorithms. The presentation of interesting applications has been one of the most compelling feature...show mores of this book provides students a well balanced coverage of standard linear algebra topics that apply mathematics by examining real-life applications, making for a enlightening learning experience13 +$3.99 s/h Good Greener Books London, 07/21/2000 Hardcover 4th
and Intermediate Algebra for College Students The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated ...Show synopsisThe Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process16287561628756Hardcover. Instructor Edition: Same as student edition with...Hardcover. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 9780321628756This book is a good book to start off with if you don't really understand math that well. the only problem with the book i reviced was the teacher edition and i asked for the student. but everything else
Description This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other coursesane and Solid Geometry (Universitext
Quick Overview In this NCEA Level 2 Textbook, Neil Marshall provides a solid foundation of Mathematics for entry into the workplace, to a Level 3 Statistics and Modelling course, or to a degree requiring Level 2 Mathematics. Some topics will already be familiar, whilst others cover intriguing new areas of practical mathematics. The use of graphical calculators in integrated into the units, taking out much of the donkey-work, and other technology is introduced as necessary to smooth the path of learning. This course has been taught successfully, in a variety of guises, to a middle-ability Year 12 students, many of whom would have found a curriculum assessed through the Level 2 Achievement Standards too challenging, and it has equipped them with a good grounding to proceed with the next step along the way. This book contains: -Clear instructions with plenty if practical examples -Advice on use of technology in solving maths problems -Lots of exercises for practice, so the skills become automatic -Unit Standard practice assessments it aid final preparation for assessment Unit standards covered: -5244: Demonstrate calculus skills -5247: Make and evaluate statements about populations based on sample data -5249: Use networks to find optimal solutions to problems in geometry -5250: Use probability techniques to solve problems -5260: Find and use derivatives to solves problems involving rates of change -5261: Find and use integrals to solve problems -7564: Plan, carry out and report on a statistical investigation into a given area -12318: Use surveying techniques and maths to solve problems relating to maps or plans -12332: Demonstrate knowledge of measures and displays used to compare data sets -12333: Demonstrate understanding of, and use, questionnaire design
It probably helps if the format is in a construct that you use. I got really jazzed about the quadratic equation and figuring out multiple unknowns, but a bunch of letters w/o meaningful context leaves me cold.
Real World Math: Engaging Students through Global Issues promotes student engagement by providing real-world data on global issues with a focus on practical solutions. The student workbook and corresponding teacher's guide concentrate on foundational algebra and geometry concepts. All lessons are aligned with National Council of Teachers of Mathematics Standards and Expectations. Topics range from climate change to financial literacy and build both mathematical knowledge and global perspective. Complementary datasets are also available to download for free. Learn more about Real World Math
Concepts Through Functions, a Unit Circle Approach to Trigonometry This new text embodies Sullivan/Sullivan's hallmarks - accuracy, precision, depth, strong student support, and abundant exercises while exposing ...Show synopsisThis new text embodies Sullivan/Sullivan's hallmarks - accuracy, precision, depth, strong student support, and abundant exercises while exposing students early (Chapter One) to the study of functions and taking a unit circle approach to trigonometry. "IT WORKS" for instructors and students because it focuses students on the fundamentals: "preparing "for class, "practicing "their homework, and "reviewing." After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus and will have a solid understanding of the concept of a function
GrafEq Free To Try GrafEq (pronounced 'graphic') is an intuitive, flexible, precise and robust program for producing graphs of implicit relations. GrafEq is designed to foster a strong visual understanding of mathematics by providing reliable graphing technology. Tess Free To Try While you draw, Tess will maintain the symmetry group you have chosen- 24 rosette (circular), all 7 frieze (strip), and all 17 wallpaper groups are included. Illustrations may be printed from Tess or exported to GIF,JIF,PCX,DXF,SVG,and other formats. Easy Math Free To Try Do you think your kids may benefit from more math practice? If so, here's a simple program that will help! Includes Multiplication, Division, Subtraction, Addition, Fractions and more. Rt-Plot Free To Try Simplexety Free Simplexety is used to get the most out of Formula Parsing and Scientific Calculation. With it, you can evaluate mathematical formulas, draw graphs and program with very simple VBScript. Simplexety is a sophisticated calculation application. A-Converter Free To Try A-Converter is a handy utility, that can handle unit conversions in number of categories. Just enter the value, select category with the source units and you will get the list of converted values, ready to be copied into the clipboard Infinity Free To Try These days, there are many things that require mathematical modeling: from exchange rates prediction to engineering and financial planning. Infinity is the unique math application that brings actual mathematical modeling results! Download FREE trial! Galactic Geometry 3D Free To Try Calculate volume and surface area to blast away rocks and save your space ship! Galactic Geometry is an engaging 3D environment for learning about geometric figures and their equations. Students practice math with vivid animation and sound. The automata which are modeled in this application are composed of a set of spheres whose size and axis are relative to one another, and where each sphere is rolling upon the surface of one other sphere in a fully deterministic pattern in space and in time. The paths through space taken by one or more points within each sphere can also be visualized as the automaton carries out is choreographed movements. This application is a laboratory for the synthesis of the automata
Elementary/Intermediate Algebra: Combined Approach 9780495553458 ISBN: 049555345X Edition: 5 Pub Date: 2008 Publisher: Cengage Learning Summary: Master algebraic fundamentals with Kaufmann/Schwitters ELEMENTARY AND INTERMEDIATE ALGEBRA 5e. Learn from clear and concise explanations, multiple examples and numerous problem sets in an easy-to-read format. The text's 'learn, use & apply' formula helps you learn a skill, use the skill to solve equations, then apply it to solve application problems. With this simple, straightforward approach, you will grasp and appl...y key problem-solving skills necessary for success in future mathematics courses. Kaufmann, Jerome E. (Jerome E. Kaufmann) is the author of Elementary/Intermediate Algebra: Combined Approach, published 2008 under ISBN 9780495553458 and 049555345X. One hundred thirty seven Elementary/Intermediate Algebra: Combined Approach textbooks are available for sale on ValoreBooks.com, twenty five used from the cheapest price of $4.59, or buy new starting at $28ewn binding. Cloth over boards. 933 p. Contains: Illustrations. Audience: General/trade. I have for sale a VERY GOOD CONDITION hardbound textbook of 933 pages titled " ELEMENTARY AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH " Fifth Edition, written by Kaufmann an Schwitters with a copyright year of 2009 by Brooks/Cole ( ISBN 0-495-55345-X ) (27764) This textbook DOES NOT include the packet titled " STUDENT ACCESS FOR McKeague's Interactive Elementary Algebra ". This textbook has very minor cover, corner and edge wear. The cover corners are slightly worn or split. Fanning
You are here Loci Browse Articles This site features three simple-to-use applets: contour diagrams, curve families, and surface of revolution. The applets are written in Java and exploit Sun Microsystems' Java OpenGL technology so they will run on Apple OS X, Microsoft Windows 2000 or above, Solaris and many common configurations of Linux. We highlight five pages written in XHTML with links to SVG files that produce animations illustrating calculus concepts such as the sign of the derivative, inflection points, conic sections, area between two curves, and multivariable functions. This suite of five interactive applets (written with GeoGebra) allows exploration of definitions and theorems commonly presented in first-year analysis courses. Topics include sequence convergence, continuity at a point, the Mean Value theorem, Taylor series, and Riemann sums. Included with each applet is a pair of activities: one for becoming comfortable using the applet, and one for using the applet to explore the associated topic in depth.
Math 9 is the first step in preparing students for the study of calculus by providing important skills in algebraic manipulation and interpretation at the college level. Topics will include a review of basic algebraic concepts; lines; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions, identities, inverse functions and equations; applications of trigonometry; systems of equations and matrices; conic sections; sequences, series and combinatorics. Hand-held graphing calculators will be used extensively to highlight their strengths and their limitations as a problem-solving tool. Real world applications will be numerous. Math 10 prepares students for the study of calculus by providing important critical thinking and problem solving skills. The central theme of the course is the analysis of mathematical functions as models of change. Families of functions - linear, exponential, logarithmic, power, periodic, polynomial, rational - will be introduced, compared and contrasted. Course content will include an introduction to functions and functional notation; transformation of functions; composite, inverse and combinations of functions; vectors and polar coordinates; series; parametric equations; complex numbers. Hand-held graphing calculators will be used extensively to highlight their strengths and their limitations as a problem-solving tool. Real world applications will be numerous. Prerequisite: Mathematics 9 and proficiency with the TI-83 graphing calculator as gained from, for instance, Math 209. This course is intended for students preparing for a career in elementary school teaching. Emphasis will be on the structure of the real number system, numeration systems, elementary number theory, and problem solving techniques. Technology will be integrated throughout the course. Prerequisite: Mathematics 208, or successful completion of a high school geometry course and Mathematics 233. Operations with signed numbers, evaluation of expression containing numbers and letters, simplifying algebraic expressions, equations, word problems, exponents, polynomials, factoring and special products, fractions, graphing, systems of equations, radicals, and quadratic equations. Mathematics 205, 205A, 205B and 206 have similar course content. This course may not be taken by students who have completed Mathematics 205B or 206 with a grade of "C" or better. This course may be taken for Mathematics 205B credit (2.5 units) by those students who have successfully completed Mathematics 205A with a grade of "C" or better. The course contains the material covered in the first half of the Mathematics 205 course. It will cover signed numbers, evaluation of expressions, solving linear equations and inequalities, and applications. Graphing of lines, the slope of a line, graphing linear equations, solving systems of equations, basic rules of exponents, and operations on polynomials will be covered. Mathematics 205, 205A, 205B and 206 have similar course content. This course may not be taken by students who have completed Mathematics 205 or 206 with a grade of "C" or better. Advisory: Completion of Mathematics 402. Concurrent enrollment in Guidance 563A is advised. Students who were previously unsuccessful in Mathematics 205 are encouraged to attend.
Melissa A. Benedict C & I 301 Math Biography 2 The student that I interviewed is a 21 year-old female who attends the University of Illinois. She will be receiving her bachelor's degree in finance in the spring of 2004. In my interview with her, we discussed her mathematics schooling experiences in Glen Ellyn, Illinois, an affluent suburb of Chicago. Her parents specifically chose to reside in the district when she was young, because of its reputation for high-quality schools. The high school she attended served approximately 1,300 students, almost all of whom where white and middle-upper-class. She comes from a family with mathematical background: Her dad is the Math Department Chairman at Proviso East, and her mother teaches math at Proviso West. Perhaps not surprisingly, the first thought that comes to mind when she thinks of math is her Dad. Her definition of mathematics is the use of numbers to solve problems and make things logical. Throughout her schooling, she has done particularly well in math. In elementary school, she was enrolled in challenge classes, and then honors classes in junior high. In high school, she took Advanced Placement courses, where she always received A's and B's. Her highest subscore on the ACT was in math. When asked what she enjoys most about math, her response was getting a solution and knowing that it is correct. This seems to be a common theme for all math students, including myself. Obviously, she considers herself good at mathematics, as she has had much success in it. She first began to think of herself as good at math at a very young age. Her parents would often create extra worksheets and activities for her in order to polish her math skills. Her favorite math teacher was Mrs. Ellenbaum, whom she had for Intermediate Algebra and AP Calculus. She said Mrs. Ellenbaum made class enjoyable and knew just the right balance for letting students goof around and have a good time, and also get the work done. When asked if she used math outside of school, she immediately responded yes. She uses math at her job where she works as a teller at a bank, and also for paying bills. When confronted with everyday problems, she often thinks about them mathematically, and tries to solve them accordingly. Her math facts are excellent, and she knew some before even entering kindergarten. She was often ahead of the rest of the class, because of the extra practice she received at home. She has not had many bad math experiences, but the worst event that she can think of was taking the AP Calculus test. She had been doing very well all year in the class, but she found the test to be especially difficult and quite stressful. There was a considerable amount of material covered and on top of that, pressure to perform well in order to get credit. She did not get the college credit as she had hoped, and took two semesters of calculus at the University. She did very well in both courses, noting that seeing the material for the second time made it much easier. Consequently, her best math experience was during her first semester of calculus at the University when she received a 100% on an exam. She said that she understood the underlying principles of calculus much better than the first time she learned it, and receiving such high marks was a confidence builder for her. The element that she least enjoys about mathematics is the frustration that often comes with solving a difficult problem. She dislikes working on a problem for a long time and trying several methods when none of them seem to be giving her a correct solution. In general, math had always been easy for her until high school when the material became more complex and required a deeper understanding of concepts. For the most part, though, she has had positive experiences in math throughout her life. Her definition of algebra is understanding math with formulas, theories, and more general cases, instead of just numbers. She mentions that she uses algebra in order to figure out the rent for her apartment. With seven people and five bedrooms, she came up with a formula to figure out how much everyone should pay each month to make it fair. She has a tendency to take situations and put them in to mathematical contexts. Interestingly, she thinks being good at math means not only having a good understanding of the subject, but also being persistent and asking for help when you don't clearly understand a concept. Math is one of her favorite subjects because she has met it with great success. To conclude our interview, I inquired about how important she thought math was for the general population. She answered that it is possible to get by without anything but basic math skills like adding and subtracting, but at some point you will probably need to rely on other people to help you with more complex mathematical situations that you are bound to run into. She believes that you are clearly at an advantage in life when you have good mathematical skills. It's refreshing to know that there are students like her who realize the value of a mathematics education, and who put their mathematical knowledge to use. I also think that parental support is a key for the most successful students. The challenge then, is to prepare all students with a high-quality mathematics education, regardless of their educational background. Hopefully, though, students like the one I interviewed will be an inspiration for us that this challenge, although enormous, must be taken
Our Best-Sellers All Computer Graphic Titles An ideal course book for mathematics undergraduates and graduates alike, this is a complete introduction to vector analysis/ Each topic covered is given a practical application within computer graphics. Transformations and Projections in Computer Graphics provides a thorough background, discussing the mathematics of perspective in a detailed, yet accessible style. It also reviews nonlinear projections in depth, including fisheye, panorama, and map projections frequently used to enhance digital images. This book focuses on five hot research directions in 3D model analysis and processing in computer science: compression, feature extraction, content-based retrieval, irreversible watermarking and reversible watermarking. This book presents a broad overview of computer graphics (CG), its history, and the hardware tools it employs. Covering a substantial number of concepts and algorithms, the text describes the techniques, approaches, and algorithms at the core of this field. This practical and illustrated book looks at how to generate advanced virtual reality worlds. It covers principles, techniques, devices and mathematical foundations. It begins with basic definitions, and then moves on to the latest results from current research. This book provides a comprehensive description of mathematical techniques for rotating points and frames in 2D and 3D computer graphics. Such transforms are notoriously difficult to visualize, which is why the book includes a large number of illustrations. Research into the 3D Physiological Human is a very active field focusing on the creation of patient-specific computer models for personalized healthcare. This book details recent advances in this increasingly important area. This book reveals the software architecture of the modern real-time 3D graphics rendering engine and the relevant technologies. The book is based on the authors' experience developing this high-performance, real-time system.
Breadcrumb navigation: Mathematica at BC 11/09/11 Mathematica is a computational software program used in scientific, engineering, and mathematical disciplines and other areas of technical computing. It was conceived about twenty-five years ago by Stephen Wolfram of Wolfram Research ( ). The name "Mathematica" was suggested to Stephen Wolfram by Steve Jobs. Mathematica started as a symbolic programming tool, and over the years, it expanded to a computing system able to cover a wide range of applications. Mathematica is used at institutions of higher education around the world, with hundreds of courses based on it. Boston College has a site license, making this software available to the BC community. It is also available through a web interface at apps.bc.edu. Mathematica is used by students, faculty, and staff in various departments, including Mathematics, Physics, Chemistry, Economics, and Finance. The system provides a versatile and easy-to-learn platform. It can be used for a wide range of tasks and projects from learning Calculus to solving Physics, Economics, and Finance problems, to research projects, and helping to develop scientific papers. "This summer, I received an Undergraduate Research Fellowship to study a topological problem. The computation is not just large, it involves organizing information in geometric forms and working with numerous algorithms and concepts from linear algebra, topology, and graph theory. I found Mathematica language instinctive and smooth, and I was able to write routines which executed complex mathematical algorithms." Justin Butler, PhD student, Physics Department: "As a doctoral student in Physics, Mathematica has been an invaluable tool in my research involving quantum transport in opto-electronic device simulation. Having a program that can quickly and accurately calculate eigenvalues and complex integrals is very useful. Additionally, Mathematica's ease of use, makes it particularly attractive as a tool in computational research."
Math For Nurses - 8th edition Summary: Compact and easy-to-use, Math for Nurses is a pocket-sized guide/reference to dosage calculation and drug administration. It includes a review of basic math skills, measurement systems, and drug calculations/preparations. Math for Nurses helps students to calculate dosages accurately and improve the accuracy of drug delivery. The author uses a step-by-step approach with frequent examples to illustrate problem-solving and practical applications. Readers will find it great for use in the clinical ...show moresetting or as a study aid. Practice problems throughout the text and end-of-chapter and end-of-unit review questions will aid students' application and recall of material. A handy pull-out card contains basic equivalents, conversion factors, and math formulas. ...show less 1609136
Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.
This course integrates the learning of calculus concepts with precalculus. A study of functions, particularly polynomial and rational functions, exponential and logarithmic functions and their graphical representations and algebraic manipulation are covered. Limits of functions, one-sided limits, continuity, and derivatives, including basic rules of differentiation, chain rule and implicit differentiation of polynomials, rational functions and exponential functions are also part of this course. (Two years of high school mathematics and a score between 35% and 55% on the School of Mathematical Sciences Placement Exam) Class 3, Workshop 1, Credit 4 (F, W, S
algebra 1 and algebra 2...'m algebra 1 and 1 and
Advanced Mathematics This sequence is our version of Algebra II/ Trigonometry/ Pre-Calculus, and is for those students who have completed geometry. Algebra and Geometry combine into an amazing mathematical dance that these courses beautifully demonstrate. Despite the high level of mathematics that these courses represent, students continue to work in within the QED™ framework that is focused on context, concept, discovery, and application. Through the study of: conic sections polynomial theory trigonometry transcendental functions Students have the opportunity to not just memorize the "formula" but to actually understand its very existence through the activities they do in class. Sequence The Conics™ Through an exploration of the methods of conic section construction, students will learn polynomial theory and advanced function theory. This will help students gain full mastery of these crucial Algebra II standards. This is our version of trigonometry. This course, however, covers a wider range of functions that are collectively referred to as the transcendental functions, which include the trigonometric and exponential functions and are unified by theory of complex numbers.
Book summary Polynomials, functions, and trig, oh my! From the author of two bestselling Complete Idiots Guides comes a book aimed at high school and college students who need course help or a brush-up. It follows a standard precalculus curriculum, includes sample problems, and will help students make sense of their textbooks. Difficult topics, such as quadratic equations, logarithms, graphing trig functions, and matrix operations are presented with W. Michael Kelleys signature wit and wisdom. " College enrollment is projected to increase 23% between 2000 and 2013 " According to figures released by ACT Inc., nearly 75% of all college-bound students take precalculus or calculus in high school " Author is an award-winning math teacher recognized for his ability to make intimidating math topics approachable for even the most terrified students [via]
Recommended for These Courses Description The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas. About the Author Professor Robert L. Devaney received his A.B. from Holy Cross College and his Ph.D. from the University of California at Berkeley in 1973. He taught at Northwestern University, Tufts University, and the University of Maryland before coming to Boston University in 1980. He served there as chairman of the Department of Mathematics from 1983 to 1986. His main area of research is dynamical systems, including Hamiltonian systems, complex analytic dynamics, and computer experiments in dynamics. He is the author of An Introduction to Chaotic Dynamical Systems, and Chaos, Fractals, and Dynamics: Computer Experiments in Modern Mathematics, which aims to explain the beauty of chaotic dynamics to high school students and teachers.
Elementary Numerical Analysis (McGraw-Hill (1965) Tools "... Optical veloc ..." Optical velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image. "... It wha ..." It what the objectives mean before you have finished the course; but at that stage, you should come back here and check that they do make sense. If they don't, you may have missed something important. Aims The overall aim of the course is to present modern computer programming techniques in the context of mathematical computation and numerical analysis and to foster the independence needed to use these techniques as appropriate in subsequent work. Learning Objectives By the end of the course the student should: • be aware of the background of computing within mathematics, and of possible choices of programming language; • be able to analyse appropriate mathematical problems in a form suitable for programming; • be able to construct programs in a modern object-oriented programming language, using the available facilities appropriately; • be able to describe, analyse, program and contrast a number of methods for investigating problems in symbolic computation and numerical analysis. These problems will include at least three topics from the following: – root finding; – numerical integration; – the solution of ordinary differential equations; – digital signatures; – Monte Carlo methods; iii iv • be able to write programs to assist investigations in subsequent mathematics courses; and • have improved analytic skills.
Math Programming Techniques This page contains links to documents describing how some popular decomposition schemes, solution techniques and modeling paradigms can be implemented in a high level modeling language. Some of the techniques and algorithms described require familiarity with advanced topics in mathematical programming. In general just enough theory is touched upon so that the notation used becomes clear. For more information use an advanced text book.
MATH 0830 MATH 0830 - Pre-Algebra Fall 2013 (Section #7392) Course Information Page A basic mathematics course designed to provide skill development in operations with whole numbers, fractions, decimals, percents, and signed numbers. Algebra concepts including solving linear equations, geometry topics, and measurement are also presented. This class uses material that is available through Etudes. If you have questions about this class, please e-mail the instructor, Shirley Louie .
View Thread It seems bizarre to a lot of people that I have chosen to study Statistics in college, to me though statistics, or at least how I see it, is so different from mathematics. It is the difference I guess between theory and application. Granted occasionally I will have to struggle through a bit of application that requires theory but it is never a complete wall. Unfortunately to get a degree in Statistics you have to take a lot of theoretical mathematics, the stuff driven by abstract notation and language. I am in a very strange position because the typical accommodation is to simply not take math classes in college if you have dyscalculia. I want to take those classes but without any accommodation I am doomed to fail them. Right now I get to take my exams in a quiet room with extra time and a four function calculator but when I am trying to recall the formula for a Poisson distribution or how to calculate the integral of the inverse of tan(x) that calculator and extra time don't do much. I have asked in the past for a formula sheet when I was taking multivariate calculus but was turned down because supposedly having one would give me an unfair advantage and would mean I didn't bother to learn or understand the concepts. Does anyone have ideas for what would be considered reasonable accommodation for someone with dyscalculia in higher level mathematics? I know some will say that you can't be in higher level mathematics with dyscalculia but to me that's like telling someone you can't possibly read a novel if you are dyslexic. I have always found different ways to learn mathematics that are usually time consuming and non traditional which has worked up to a point but the farther up I get it seems the more resistance I encounter to finding those different ways. twistedxkiss wrote:Yes, you required to get expert advice from your coordinator. Make it practical and get benefited from the same.
Research shows that algebra helps you think logically, and in a complex way. In another way, it shows that the student can meet and conquer a challenge on their own. Algebra is considered the basis for all maths. Anytime you cook by a recipe but need to make more or less then what the recipe serves, when you adjust it, you will use algebra. Figuring out a sale price you use algebra. It comes into play in real life more than you will ever realize.
Mathematics Course Descriptions This course is designed to provide entering freshmen and new students with an orientation to the university, its traditions, its program offerings, and its academic requirements and regulations. The focus is on adaptation to college life, problem solving skills, and critical thinking skills including effective study and test taking methods. This course will also provide an orientation to the Department of Mathematics, its various degree paths, and the nature of mathematical reasoning. MAT 1306 Basic Algebra Credit: 3 hrs. This course is designed for students with limited proficiency in elementary algebra. Topics include signed number operations, simplifying algebraic expressions, exponents, polynomials, equations and inequalities, word problems, and factoring. Requirements: All students scoring below a given level on the mathematics placement examination must enroll in this course. Students enrolled in this course receive a grade of P or F. Credit for this course is not counted towards the total hours needed for graduation. MAT 1311 College Algebra Credit: 3 hrs. This course covers topics in applied algebra. Topics include a review of factoring, algebraic fractions, rational exponents, radicals, first-degree linear equations and graphs, quadratic equations, first-degree inequalities, and linear systems of equations. Prerequisite: MAT 1306 or a satisfactory score on the mathematics placement examination given by the university. This course may not be used as an approved elective by mathematics majors. MAT 1312 Precalculus I Credit: 3 hrs. This course introduces techniques for solving inequalities involving absolute value, polynomials, and rational expressions. Included are discussions of functions and their graphs for linear, quadratic, and general polynomials, rational functions, exponentials, and logarithms. General graphing techniques and the conics are also discussed. Prerequisite: MAT 1311 or a satisfactory score on the mathematics placement test. MAT 1313 Precalculus II Credit: 3 hrs. This course, a continuation of MAT 1312, helps to prepare a student for Calculus I. The following are among the topics studied: trigonometric functions and identities, solutions of trigonometric equations and triangles, graphs of the trigonometric functions, and verbal problems involving applications of trigonometric functions. Also included are sequences, series and mathematical induction. Prerequisite: MAT 1312 or a satisfactory score on the mathematics placement test. MAT 1323 Fundamentals of Mathematics Credit: 3 hrs. This course serves as the core requirement for those students whose departments do not require any more mathematics courses, with the exception of MAT 2326 (Elementary Statistics). Topics include basic algebraic concepts, sets, statistics, probability, mathematics of finance, and problem solving. Prerequisite: MAT 1306 or a satisfactory score on the mathematics placement examination given by the university. This course may not be used as an approved elective for mathematics majors. MAT 2260 Precalculus Review Seminar Credit: 2-6 hrs. This course includes a review of topics covered in precalculus coursesrequisite: MAT 1313 or approval from the instructor. Grade: Pass/Fail. MAT 2301 Introduction to Computer Algebra Systems Credit: 3 hrs. This course presents a brief introduction to the software and hardware being used. Included will be work with one or more computer algebra systems, such as Maple, Derive or Mathematica. Time will be spent not only learning to use the software, but using experimentation and discovery to better understand mathematical concepts. Some topics addressed are solutions of equations and inequalities, functions and their graphs, and other pre-calculus and calculus topics. Prerequisite: MAT 2317 or 2333. MAT 2303 Principles of Mathematics I Credit: 3 hrs The first of two semesters in a fundamental of mathematics sequence for education majors with the exception of Secondary Mathematics Education and Comprehensive Science. Problem solving, real numbers, numbers theory, decimals, rational numbers, percents, and numeration systems are the mathematics concepts of focus for this course. Prerequisite: Place above MAT 1306 or completion of college math course. MAT 2304 Principles of Mathematics II Credit: 3 hrs The second of two semesters in a fundamental of mathematics sequence for education majors except Secondary Mathematics Education and Comprehensive Science. Probability, statistics, algebra, measurement, geometry, and logic are the mathematics concepts of focus for this course. Prerequisite: MAT 2303 This course is the first of four sequential semester courses which addresses calculus for mathematics, science and engineering majors. The course examines functions, graphs, limits and derivatives, and rules of differentiation. This includes differentiation of polynomial, rational, trigonometric, logarithmic, exponential functions, application of differentiation and the use of computational tools. Prerequisite: MAT 1313 or advanced placement. This course will not count with MAT 2333. MAT 2318 Calculus II Credit: 3hrs This course is the second of four sequential semester courses which addresses calculus for mathematics, science and engineering majors. The course examines techniques and applications of integral calculus, improper integrals, elementary differential equations, and the use of computational tools. Prerequisite: MAT 2317. MAT 2321 Foundations of Modern Mathematics Credit: 3hrs This course is designed for mathematics and mathematics education majors as an introduction to mathematical principles and reasoning. It gives an introduction to the discipline of mathematics emphasizing deductive arguments and the development of analytical skills needed in understanding and building mathematical arguments. The content will include an introduction to logic and methods of proof and takes a look at functions and the " #! definition of continuity. The course also examines the algebraic and topological properties of R and introduces metric spaces. Prerequisite: MAT 2317. MAT 2326 Elementary Statistics Credit: 3 hrs. The major emphasis of this course is on the use of statistics as a tool in the decision-making process. The following are among the topics to be developed: common statistical measures, graphing techniques, probability, the binomial distribution, the standard normal distribution, t-tests, correlations and prediction, chi-square, and analysis of variance. (Cross-listed with SOC 2326 and PSY 2326). MAT 2333 Calculus for Business Majors Credit: 3 hrs. This course includes a brief review of the concepts of functions and combinations of functions. It also covers the basic concepts of differential and integral calculus and its applications. Special attention is given to problems in business and economics. Prerequisite: MAT 1312 or approval from instructor. This course includes a review of topics covered in core mathematics courses for majorsrequisites: MAT 2316, MAT 3412, MAT 3341, or approval from the instructor. Grade: Pass/Fail. MAT 3310 Probability and Statistics I Credit: 3 hrs. This course is designed to give an introduction to set theory and probability theory and to the concept of random variables, both discrete and continuous. Consideration is given to a discussion of several standard types of distributions. Prerequisites: MAT 2318. MAT 3311 Probability and Statistics II Credit: 3 hrs. This course is a continuation of MAT 3310. Treatment is given to random sampling and classical statistical inference, especially point and interval estimation, tests of hypotheses, general linear models, Bayesian methods, and an introduction to least squares. Prerequisite: MAT 3310, MAT 3317. MAT 3312 Biostatistics Credit: 3 hrs This course covers topics in both probability and statistics including: probability function and its properties, discrete and continuous random variables and their probability distributions, data description and their presentation, hypothesis testing, decision making and experimental design. Data will be used from the areas of biology, psychology and neuroscience with appropriate software. Use of computer is a requirement. This course is for sophomore/junior level students with major or minor in an area of life science. Prerequisite: MAT 1312 and Bio 1315 (Introduction to Biotechnology). MAT 3316 Calculus III Credit: 3 hrs This course is the third of four sequential semester courses which addresses calculus for mathematics, science and engineering majors. Course includes sequences, infinite series, power series, Taylor's Theorem, conics and parametric equations, polar coordinate system, vectors and geometry of space, vector-valued functions and the use of computational tools. Prerequisite: MAT 2318. MAT 3317 Calculus IV Credit: 3 hrs This course is the fourth of four sequential semester courses which addresses calculus for mathematics, science and engineering majors. Course examines the functions of several variables, partial derivatives, gradients, directional derivatives, maxima and minima, multiple integration, line and surface integrals, Green's Theorem, Divergence Theorems, Stokes' Theorem, applications and the use of computational tools. This course presents Euclidean and non-Euclidean geometry from a modern perspective. Topics include congruence, parallelism, similarity, measurements, constructions, solid geometry, ratio, proportion, the parallel postulate, and an overview of non-Euclidean geometries. Direct and indirect proofs will also be studied. Prerequisite: MAT 2337. This course develops the techniques used in linear programming such as the simplex method and the duality method. Linear programming techniques will be applied in the solution of transportation problems, industrial problems and problems in economic theory. Prerequisites: MAT 2316 and CSC 1311. MAT 3356 Independent Study Credit: 1-6 hrs. This course provides an opportunity for mathematics majors at the junior and senior level to work on an independent project with the guidance of a faculty member. The project may consist of a combination of review of research, a research project, or a research paper. Topics covered in this course are not offered in formal courses. This course may be repeated if a student has not earned the maximum of six semester hours. This course is limited to junior and senior mathematics majors and subject to the approval of the instructor and chair. MAT 3391 Mathematics Co-Op Credit: 3 hrs. (See the course description for the Cooperative Education course number 3391 in the Undergraduate Catalog.) MAT 3691 Mathematics Co-Op Credit: 6 hrs. (See the course description for the Cooperative Education course number 3691 in the Undergraduate Catalog.) MAT 4301 Differential Equations I Credit: 3 hrs. This course develops techniques for solving differential equations, presents theory to support those techniques, and includes applications of differential equations. The course includes the study of equations of order one, linear differential equations, non-homogeneous equations, the Laplace transform, and systems of equations. Prerequisite: MAT 2318. MAT 4302 Differential Equations II Credit: 3 hrs. This course covers some methods for finding solutions of differential equations not considered in MAT 4301. It includes non-linear differential equations, power series solutions of differential equations, Fourier series, and an introduction to methods of solutions of partial differential equations of mathematical physics: heat and wave equations. Prerequisite: MAT 4301 and MAT 3317. MAT 4304 History of Mathematics Credit: 3 hrs. This course is a chronological study of the development of mathematics. It includes those mathematicians and periods in which the study of certain areas of mathematics prevailed. Prerequisite: MAT 2317. MAT 4311 Real Variables I Credit: 3 hrs. This course presents the real numbers, least upper bound and greatest lower bound, sequences and series of real numbers, monotone and Cauchy sequences, limit superior and limit inferior, metric spaces, connected, complete and compact metric spaces, continuous functions on metric spaces, sequences and series of functions, and the three famous theoremsâ??Weierstrass Approximation Theorem, Picard Existence Theorem, and the Ascoli-Arzela Theorem. Prerequisite: MAT 3317. MAT 4312 Topology Credit: 3 hrs. This course will cover operations on sets, properties of functions, topology of the real line, metric spaces, topological spaces, connectedness, compactness, and product and quotient spaces. Prerequisite: MAT 3317 or permission of instructor. MAT 4313 Real Variables II Credit 3 hrs. This course is a continuation of MAT 4311, Real Variables I. This course extends the study to include the topology of Euclidean spaces, differentiability in Euclidean Spaces, and metric spaces. Sequences of functions, uniform convergence, convergence of series, and power series will also be covered. Prerequisite: MAT 4311. MAT 4315 Advanced Calculus Credit: 3 hrs. This course presents differential and integral calculus of functions with domain and range in Euclidean nspace. Topics include geometry of n-space, sequences and series in n-space and of functions, uniform convergence, improper integrals with parameters, Fourier series, extrema, differentiation of transformations, implicit function theorems, transformations of multiple integrals, differential forms, and Green, Gauss, and Stokes Theorems in a general set up. Prerequisite: MAT 3317. MAT 4330 Directed Study Seminar Credit: 3 hrs. Students may enroll for study of an area of mathematics not given in a formal course. Approval must be given by the department chair and the instructor. All parties must agree on the course format and content. This course is limited to senior mathematics majors. MAT 4331 Mathematical Modeling Credit: 3 hrs. Mathematical model building in both discrete and continuous cases will be developed. A variety of mathematical problems in physical, biological, social, and behavioral sciences will be discussed. Specific problems will be given in applied dynamical systems, differential and integral equations and some statistical processes. In every topic, the emphasis will be on construction, interpretation, analysis, simulation, and testing of models. Prerequisites: MAT 3317, MAT 4301, MAT 3310, and CSC 1311. This course includes simple and multiple regression, model selection procedures, analysis of variance, simultaneous inference, and the design and analysis of experiments. Applications include the use of a statistical computer package. Prerequisite: MAT 4332. MAT 4352 Principles of Teaching Mathematics Credit: 3 hrs. This course is designed for students preparing to teach secondary school mathematics. Innovative techniques to be used in the teaching of mathematics and assessment procedures will be discussed and developed. No credit is allowed for work of less than C quality. (The course is three periods per week.) Prerequisite: Admission to teacher education program. (Cross-listed with EDU 4352) This course is a continuation of MAT 4356; Mathematical Statistics I. Topics include estimation and hypothesis testing, applications of statistical inference, introduction to regression, and correlation. Prerequisite: 4356. MAT 4386 Automata, Formal Languages and Computability Credit: 3 hrs. This course studies computer science theory and the mathematical foundations of digital computers. Its topics include the family of computing machines (finite-state, push-down and Turing), the Chomsky hierarchy of languages, decidability, unsolvable problems, and applications of automata to areas of syntactic analysis, modeling, and artificial intelligence. Prerequisites: CSC 4340 and MAT 2316, or consent of instructor. (Cross-listed with CSC 4386) MAT 4387 Senior Seminar I Credit 3 hrs. This course contains lectures, dialogues, and readings in mathematical topics in order to reinforce the knowledge and skills learned in core courses thus far. This course provides the opportunity for students to look at applications and problems in order to prepare for proficiency and licensure exams such as the GRE or first actu exam. The students will be asked to read journal articles and give summary presentations in class. Prerequisite: MAT 4311. MAT 4388 Senior Seminar II Credit 3 hrs This course includes readings and weekly student lectures or student-led discussions on a variety of mathematical topics determined by the interest of the students and the instructor. Emphasis will be placed on independent research and clear exposition. A paper is required. Prerequisite: MAT 4387. MAT 4391 Mathematics Co-Op Credit: 3 hrs. (See the course description for the Cooperative Education course number 4391 in the Undergraduate Catalog.) MAT 4691 Mathematics Co-Op Credit: 6 hrs. (See the course description for the Cooperative Education course 4691 in the Undergraduate Catalog.) MAT 4981 Observation, Student Teaching and Practicum Credit: 9 hrs. This course deals with the application of theory to teaching situations in the secondary schools. During the first six weeks, students spend one-half day in a classroom setting, engaging in directed observation, small group tutoring and part-time classroom teaching. The final ten-week period is devoted to full-time student teaching in the same classroom setting. Proficiency in training and handling typical classroom situations is developed. This course is required for secondary education majors. Prerequisite: Approval by the Teacher Education Committee and the major department. (Cross-listed with EDU 4981)
Tag Archive for 'math' By Jakayla Mullin and his team Source: Best College Reviews The relationship between Core Curriculum and college preparedness Most educational experts agree that common core curriculum is not the solution to closing the achievement gap. Too bad politicians are the ones with a final say. Common Core Curriculum is meant to be an equalizing force… Read More › by Staff Writers of OnlineUniversities.com : 100 Time-Saving Search Engines for Serious Scholars (Revised) Back in 2010, we shared with you 100 awesome search engines and research resources in our post: 100 Time-Saving Search Engines for Serious Scholars. It's been an incredible resource, but now, it's time for an update. Some services have moved on, others have been… Read More › Symbolab is a semantic web search engine for math and science. It allows users to search for equations, formulas and expressions using mathematical symbols and scientific notations as well as full text search. This tool works great with math tutors to ensure high level learning. The stated goal of the site is to provide the most relevant search results… Read More › by Jane Moorman, New Mexico State University An easy, last-minute Christmas gift could be as simple as downloading an app. An estimated 2.4 billion apps are expected to be downloaded during the holidays. Thanks to app developers at New Mexico State University, new mobile device owners have access to free apps on a variety of research-based… Read More › Wolfram Alpha introduces a fundamentally new way to get knowledge and answers — not by searching the web, but by doing dynamic computations based on a vast collection of built-in data, algorithms, and methods. It aims to collect and curate all objective data; implement every known model, method, and algorithm; and make it possible to compute… Read More › CK-12 is a leader of open educational resource(OER) provider for k-12 education. Beginning this month, CK-12 foundation launched the new, multi-modality platform, available for the majority of the expanding STEM concepts. Now CK-12 will surprise you with the quality, flexibility and depth that the open educational resources can offer. Some of the features of Multi-Modality… Read More › From press release of Learning Games Network (LGN) : NewSchools Venture Fund today announced a $200,000 investment in Learning Games Network (LGN), the leading game-based learning research and development studio. The investment will support LGN in building the market for high-quality learning games through the design and development of games and related tools; and help LGN… Read More › By Kim Jones, CEO, Curriki Curriki has launched a free Algebra 1 course that addresses each of the Common Core State Standards. This algebra course was sponsored and funded by AT&T and developed by Curriki. The online project-based modular course pulls in students through real-world examples, engaging projects, interactive Web 2.0 tools, videos and targeted feedback. With… Read More › STEM education, which stands for Science, Technology, Engineering and Mathematics was an initiative recently brought about in an effort to encourage education in fields that currently lack the experts to fill job vacancies. This particular initiative has taken these much needed specialties and further integrated them into regular curriculum in an effort to avoid simply… Read More ›
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Student Solutions Manual for Larson/Hostetler/Edwards' Algebra and Trigonometry: A Graphing Approach and Precalculus: A Graphing Approach Summary This manual offers step-by-step solutions for odd-numbered text exercises and for all items in the Chapter and Cumulative Tests, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. It also provides practice tests with answers.
Edexcel GCSE 2012 Maths Linked Pair Pilot reforms The Edexcel GCSE 2012 linear Maths Linked Pair Pilot specification is now available to download for first teaching in September 2012 (for two-year courses) and first assessment in June 2014. The main changes are: No content change to the specification Linear assessment structure: all units are taken at the end of the course* *Please see the FAQs with specific details to how linear rules operate with the linked pair. Background to the Linked Pair Pilot The 'linked pair' pilot began in September 2010, and consists of two GCSEs: Methods which looks at the pure aspects of mathematics Applications, which includes using mathematics in everyday contexts including "financial applications" and problem-solving in real-life scenarios The 'linked pair' pilot is worth two GCSEs and is being piloted at the same time as our single Edexcel GCSE Mathematics specifications. Jointly, the linked pair GCSEs cover the rigorous core national curriculum programme of study, which is also assessed by the single GCSE. The pair, in addition, give a broader grounding in both methods in mathematics and applications of mathematics.
Chapter 3 Study Guide Math 101 1. Make time in your schedule to learn; you cannot take shortcuts. 2. Read each section in your textbook and answer the questions in ... Destination Math Aligned to Florida Go Math! Third Grade *Destination Math does not align to all standards. Those standards are not shown on this document. DATE EVENT August 2 Professional Development Day August 3 - 6 Teacher Workdays August 9 Students Report August 12 - September 3 Chapter 1 August 30 CBAT - Citrus ... Timelines/2nd Grade/Back of Instructional Calendar for Second Grade.pdf - 1 - New York Integrated Algebra Exam Brief Review New York Integrated Algebra Guide This resource helps to prepare students for the New York Regents Exam. MATH 104 Precalculus Chapter 2 2.1: Quadratic Functions The degree of a polynomial: The highest power of the variable General Form of a quadratic: f ! 2.pdf
Free Online Math Classes The Degree Finder in 3 easy steps The topics covered in this course include real numbers, set theory, intervals and inequalities, Lines, functions and graphs, limits and continuity, differentiation, integration, and sequence and series. This course offers an introduction to computationally intensive statistics. Topics of study include the organization and use of statistical learning and data mining, model validation procedures, databases, and graphics. UC - Irvine's CSET Mathematics III course prepares students to take the California Subject Examinations for Teachers. This course includes study in trigonometry, limits and continuity, integrals and applications, and sequences and series.
Basic Algebra Course Description Provides the basic mathematical skills necessary to enter MATH 099. Topics include operations of whole numbers and signed numbers, fractions and decimals, as well as ratio, proportions, and percents. Introduces equations, geometric applications, the laws of exponents, operations with polynomials, and basic factoring. Three class hours weekly.
This course describes discrete mathematics, which involves processes that consist of sequences of individual steps (as... see more This course describes discrete mathematics, which involves processes that consist of sequences of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Computer Science 202) A series of applets for teaching Fractal Geometry. Includes: L-Systems; Box-Counting Fractal Dimension; Cellular Automata;... see more A series of applets for teaching Fractal Geometry. Includes: L-Systems; Box-Counting Fractal Dimension; Cellular Automata; Iterated Function Systems (deterministic, random, data-driven, and with memory); Pascal's Triangle; Circle Inversion; Limit Sets of Circle Inversion. The online course materials that go with this applet series is at . This course is taught to high school math teachers as well as university students. This award-winning site is billed as a resource for educators and students of game theory. It contains online lecture notes,... see more This award-winning site is billed as a resource for educators and students of game theory. It contains online lecture notes, book reviews, a large number of interactive materials in various categories, quizzes, and more.
Welcome MATHS AT YOUR FINGER TIPS! ARE YOU STRUGGLING WITH MATHS? HERE IS THE SOLUTION TO ALL YOUR TROUBLES! MASTER THE TOPIC BEFORE YOUR FRIENDS! Mathematics has been for years a thorn in the lives of many students - a bulky syllabus, teachers who have to limit themselves to curricula due to time constraints, inability of shy students to ask for further explanation, students who feel forced to have recourse to several coaching classes after school hours to keep pace with their friends in this competitive world. It is now time for change! It is time for you to realise that THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE. The website provides you with reliable online tutorials working towards a complete coverage of school syllabus for Forms III, IV, V and VI. Our target group range from students of lower secondary to students sitting for the Cambridge School Certificate and Higher School Certificate Examinations as well as those competing for National scholarships. Our aim is to make Mathematics accessible to all, while making it pleasurable for the secondary school student to master all aspects of the topics they have to study, with the aim to achieve the brightest results at different points of their secondary school career. Each maths lesson from this site is presented in a clear, simple and logical way, and is meticulously designed to promote quick understanding and enhance absorption and retention during exam time. Bright results are now a click away! Getting Started Register Apply Pay Start Create your account to become a member. It will take less than one minute. Select the course you wish to be enrolled and click on "Request Course"
This course is a detailed technical and historical exploration of the Apollo project to "fly humans to the moon and return... see more This course is a detailed technical and historical exploration of the Apollo project to "fly humans to the moon and return them safely to earth" as an example of a complex engineering system. Emphasis is on how the systems worked, the technical and social processes that produced them, mission operations, and historical significance. Guest lectures are featured by MIT-affiliated engineers who contributed to and participated in the Apollo missions. Students work in teams on a final project analyzing an aspect of the historical project to articulate and synthesize ideas in engineering systems. An interesting collection of readings on technology – mainly the development of aviation. Ranging from the construction of... see more An interesting collection of readings on technology – mainly the development of aviation. Ranging from the construction of the Boeing 777 to Lockheed skunkworks to Xerox PARC. Very useful if you love airplanes and technology as I do! VectorPad is a Tablet PC application to visually introduce students to Vector MathUsers draw vectors with electornic ink and... see more VectorPad is a Tablet PC application to visually introduce students to Vector MathUsers draw vectors with electornic ink and the computer performs the following operations: vector addition, vector subtraction, dot product, cross product, vector projections and shows the result graphically.
Description This introduction presents the mathematical theory of probability for readers in the fields of engineering and the sciences who possess knowledge of elementary calculus. Presents new examples and exercises throughout. Offers a new section that presents an elegant way of computing the moments of random variables defined as the number of events that occur. Gives applications to binomial, hypergeometric, and negative hypergeometric random variables, as well as random variables resulting from coupon collecting and match models. Provides additional results on inclusion-exclusion identity, Poisson paradigm, multinomial distribution, and bivariate normal distribution A useful reference for engineering and science professionals First Course in Probability: SOLUTIONS MANUAL (7th Edition
A First Course in Calculus (Undergraduate Texts in Mathematics) This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions. This is an introductory course book that teaches C++ programming. The book concentrates on the procedural paradigm. It is intended for students who possibly have not programmed before and wish to go ... This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives ... Oggi in Italia is a successful, market-leading introductory Italian program featuring a balanced four-skills approach to language learning and varied perspectives of Italian culture, ranging from its ... The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, ...
What quantitative research methods are appropriate for mathematics education research? How can you incorporate appropriate quantitative methods into your own studies? What procedures and tools can you use to analyze data sets? How can you interpret results from quantitative research studies? How are potential research studies changing and what are the implications for mathematics education research in the future? MATH 744 will explore these questions as well as expose you to quantitative techniques designed to answer specific questions related to mathematics education research. This course will provide an overview of research methods and designs in mathematics education and related statistical procedures. Based on calls for more scientific research in education, this course will provide you with an opportunity to analyze data sets and answer pressing research questions using SPSS, SAS, Excel, and Tinker Plots. You will gain an understanding of what it takes to conduct quality research in mathematics education and how you can connect research to practice to improve policy and teaching. While prior exposure to statistical techniques is recommended, ELRS 821 is not a required prerequisite. The instructor will make an effort to differentiate course material based on students' experiences. MATH 744 fulfills an elective requirement for students in the EdD in Mathematics Education program.
I'm having great difficulty knowing the logic behind the problem about clep calculator model. Can someone please assist me to know how to come up with a detailed answer and explanation regarding clep calculator model specifically in topic of exponential equations? I was told how to do this before but now I forgot and confused how to solve it. I find it complicated to understand it on my own so I believe I need assistance since I believe I can't do this on my own. If someone knows about clep calculator model can you please help me? Thank you! Hey. I think I can lend you a hand. Can you elaborate some more on what your problems are? What precisely are your troubles with clep calculator model? Getting a first class teacher would have been the greatest thing. But do not be anxious. I think there is a way out. I have come across a number of algebra programs. I have tried them out myself. They are pretty smart and good. These might just be what you need. They also do not cost a lot. I believe that what you require is Algebrator. Why not try this out? It could be just be the thing for your problems. That's true, a good program can do miracles . I tried a few but Algebrator is the best. It doesn't matter what class you are in, I myself used it in Remedial Algebra and Basic Math too, so you don't have to be concerned that it's not on your level. If you never used a program before I can tell you it's not complicated, you don't have to know anything about the computer to use it. You just have to type in the keywords of the exercise, and then the software solves it step by step, so you get more than just the answer. Thank you, I will check out the suggested software. I have never studied with any software before, I didn't even know that they exist. But it sure sounds cool! Where did you find the software? I want to get it right away, so I have time to prepare for the exam. I remember having often faced problems with dividing fractions, function domain and proportions. A truly great piece of math program is Algebrator software. By simply typing in a problem from workbook a step by step solution would appear by a click on Solve. I have used it through many algebra classes – College Algebra, Intermediate algebra and Pre Algebra. I greatly recommend the program.
College Algebra : Graphing Approach - Text Only - 4th edition Summary: As part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, College Algebra: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help students succeed in mathematics. This new edition, intended for ...show morealgebra courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills
National. "With the exception of a few standards in trigonometry, the math standards end after Algebra II," said James Milgram, professor of mathematics emeritus at Stanford University. "They include no precalculus or calculus." U.S. government data show that only one out of every 50 prospective STEM majors who begin their undergraduate math coursework at the precalculus level or lower will earn a bachelor's degree in a STEM area.
More About This Textbook Overview Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincaré, Clebsch, Jacobi and other outstanding mathematicians of the last century, was mainly an analytical theory. In our century the methods and ideas of topology, commutative algebra and Grothendieck's schemes enriched it and seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This classic book, written in 1897, covers the whole of algebraic geometry and associated theories. Baker discusses the subject in terms of transcendental functions, and theta functions in particular. Many of the ideas put forward are of continuing relevance today, and some of the most exciting ideas from theoretical physics draw on work presented here. Editorial Reviews Booknews A reissue of the 1897 classic that despite its modest title, in fact covers the whole of algebraic geometry and associated theories. Some of the topics are the infinities of rational functions, specification of a general form of Riemann's integral, Jacobi's inversion problem, radical and factorial functions, the transformation of theta functions, and degenerate Abelian integrals. An added forward provides a historical context and suggests the continuing importance of the methods
Polynomial Vocabulary - Definition of a Polynomial Before adding and subtracting polynomials or multiplying polynomials, it is important to know the definition of a polynomial and polynomial vocabulary. This video describes important polynomial definitions and terms including monomial, the degree of a monomial, polynomial degree and standard form. (7:15) Author(s): No creator set Market Comparison A comparison of the two markets, perfect competition and monopoly, considering the similarities and differences Author(s): No creator set License information Related content No related items provided in this feed The Language of Algebra This site provides a brief review of many aspects of algebraic language and use, from symbol sets and fractions to exponents and factoring. Intended as a reference for students already familiar with algebra, it is the first section of the online text Introductory Statistics: Concepts, Models, and Applications. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. Author(s): No creator set Greenough's Greeno UMass Amherst's Greeno Sub Shop, located in the Central Residence Area, is "just one of the manifestations of awesomeness that is student-run collectivism" on campus (says Adam Schultz, co-manager). Find out what Greeno has to offer! Author(s): No creator set License information Related content Rights not set No related items provided in this feed
... Show More to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. Pre-Calculus Workbook For Dummies is the perfect tool for anyone who wants or needs more review before jumping into a calculus class. You'll get guidance and practical exercises designed to help you acquire the skills needed to excel in pre-calculus and conquer the next contender-calculus.Serves as a course guide to help you master pre-calculus conceptsCovers the inside scoop on quadratic equations, graphing functions, polynomials, and moreCovers the types of problems you'll encounter in your courseworkWith the help of Pre-Calculus Workbook For Dummies you'll learn how to solve a range of mathematical problems as well as sharpen your skills and improve your
This scientific calculator contains all the classicals mathematicals functions : ln, log, exp, cos, arccos, etc. It permits to work with constants as Pi and e. The Ans function gives the possibility to calculate the first terms of recursive sequences. Randoms numbers can be used, and associated...
The Math Forum is the comprehensive resource for math education on the Internet. Some features include a K-12 math expert help service, an extensive database of math sites, online resources for teaching and learning math, plus much more. Wolfram\|Alpha is more than a search engine. It gives you access to the world's facts and data and calculates answers across a range of topics, including science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, musicApplication Developer Network Hawkee provides a platform for developers to share their ideas, code, screenshots, applications and projects. Our goal is to give developers a social outlet where technical jargon is not only understood, but embraced. code Snippets Statistics Monitor your pageviews t...
Children's MinistryAlgebra 2 Student Text (2nd ed) focuses on developing thinking and reasoning skills through the discussions of algebra concepts such as quadratic equations, polynomials, complex numbers, and trigonometry. Relevant applications and examples are presented in the feature sectio"I was able to use this book to teach a Sunday night class with a wide age-range. Everyone's attention was kept. The kids love the activites and were able to understand the message so well. They wanted to start it all over when we were finished. I hig..." Read More
An Edge in Education: Advancing Math Courses with Mathematica (Spanish) Dana Vazzana This video features Dana Vazzana, an associate professor of mathematics at Truman State University, who explains why integrating Mathematica into her university-level math classes helps students gain deeper understanding of concepts and insights into real-world applications. Includes Spanish audio.
... Show More students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. This text is ideal for an undergraduate course in axiomatic geometry for future high school geometry teachers, or for any student who has not yet encountered upper-level math, such as real analysis or abstract algebra. It assumes calculus and linear algebra as prerequisites
Mathematical Methods Units 1 & 2 Mathematical Methods incorporates a range of skill areas including, but not limited to, algebra, trigonometry, probability and calculus. Skills developed in Mathematical Methods are applied to a range of practical contexts. The motion of a pendulum can be modeled using periodic functions. The relationship between the pendulum's position and speed can be understood through a study of calculus. Radioactive decay can be modeled using exponential functions, rates of decay understood through a study of calculus. Games of chance, including those found in gaming venues are examined from a theoretical probability perspective. Students studying Mathematical Methods need to have a strong mathematical background and a commitment to study. Structure It is expected that students will have successfully completed 'Advanced Mathematics' in year 10 and study General Mathematics (Methods) Units 1 & 2 concurrently with Mathematical Methods Units 1 and 2. Students that do not study General Mathematics (Methods) may be required to undertake additional course work as prescribed by their teacher. Students attempting Mathematical Methods are expected to have a sound background in number, algebra, function, and probability. Mathematical Methods Units 1 and 2 contain assumed knowledge and skills for Mathematical Methods Units 3 and 4. Unit 1 The areas of study for Unit 1 are 'Functions and graphs', 'Algebra', 'Rates of change and calculus' and 'Probability'. At the end of Unit 1, students will be expected to have covered the material outlined in each area of study, with the exception of 'Algebra' which should be seen as extending across Units 1 and 2. Students are expected to be able to apply techniques, routines and processes involving arithmetic, algebraic manipulation, equation solving, graph sketching, differentiation and integration with and without the use of technology, as applicable. Students should have facility with relevant mental and by hand approaches in simple cases. Students are encouraged to use graphics calculators, spreadsheets, statistical software, graphing packages or computer algebra systems as applicable across the areas of study, both in the learning of new material and the application of this material in a variety of different contexts. Familiarity with determining the equation of a straight line from combinations of sufficient information about points on the line or the gradient of the line and familiarity with Pythagoras theorem and its application to finding the distance between two points is assumed. Students should also be familiar with quadratic and exponential functions, algebra and graphs, and basic concepts of probability. Unit 2 The areas of study for Unit 2 are 'Functions and graphs', 'Algebra', 'Rates of change and calculus', and 'Probability'. At the end of Unit 2, students will be expected to have covered the material outlined in each area of study. Students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, algebraic manipulation, equation solving, graph sketching, differentiation and integration with and without the use of technology, as applicable. Students should be familiar with relevant mental and by hand approaches in simple cases. Students are encouraged to use graphics calculators, spreadsheets, statistical software, graphing packages or computer algebra systems as applicable across the areas of study both in the learning of new material and the application of this material in a variety of different contexts. Assessment Outcome 1 On completion of each unit the student should be able to define and explain key concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures. Outcome 2 On completion of each unit the student should be able to apply mathematical processes in non-routine contexts, and analyse and discuss these applications of mathematics. Outcome 3 On completion of each unit the student should be able to use technology to produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches. Note: Students undertaking Mathematical Methods Units 1 and 2 in 2008 will be expected to have access to a TI-84Plus graphics calculator. From 2009 students will be expected to have access to a TI-Nspire(CAS+) calculator. These calculators will be available for purchase through the school as applicable. Pathways VCE Further Mathematics (Units 3 and 4) VCE Mathematical Methods (Units 3 and 4) VCE Specialist Mathematics (Units 3 and 4) Students successfully completing both year 11 General Mathematics (Methods) and Mathematical Methods are recommended to study any one of the following combinations:
Calculus is the study of functional relationships and how related quantities change witheach other. In your first exposure to calculus, the primary focus of your attention wason functions involving a single independent variable and a single dependent variable. Forsuch a function f , a single real number input x determines a unique single output value f ( x ). However, many of the functions of importance both within mathematics itself aswell as in the application of mathematics to the rest of the world involve many variablessimultaneously. For example, frequently in physics the function which describes the forceacting on an object moving in space depends on three variables, the three coordinateswhich describe the location of the object. If the force function also varies with time,then the force depends on four variables. Moreover, the output of the force function willitself involve three variables, the three coordinate components of the force. Hence theforce function is such that it takes three, or four, variables for input and outputs threevariables. Far more complicated functions are easy to imagine: the gross national productof a country is a function of thousands of variables with a single variable as output, anairline schedule is a function with thousands of inputs (cities, planes, and people to bescheduled, as well as other variables like fuel costs and the schedules of competing airlines)and perhaps hundreds of outputs (the particular routes flown, along with their times).Although such functions may at first appear to be far more difficult to work with thanthe functions of single variable calculus, we shall see that we will often be able to reduceproblems involving functions of several variables to related problems involving only singlevariable functions, problems which we may then handle using already familiar techniques.By definition, a function takes a single input value and associates it with a singleoutput value. Hence, even though in this book the inputs to our functions will ofteninvolve several variables, as will the outputs, we will nevertheless want to regard the inputand output of a function as single points in some multidimensional space. This is naturalin the case of, for example, the force function described above, where the input is a pointin three dimensional space, four if we need to use time, but requires some mathematicalabstraction if we want to consider the input to the gross national product function as apoint in some space of many thousands of dimensions. Because even the geometry of two-and three-dimensional space may be in some respects new to you, we will use this chapterto study the geometry of multidimensional space before proceeding to the study of calculusproper in Chapter 2.Throughout the book we will let R denote the set of real numbers. Definition By n -dimensional Euclidean space we mean the set R n = { ( x 1 ,x 2 ,...,x n ) : x i ∈ R ,i = 1 , 2 ,...,n } . (1.1.1)1 Copyrightc  by Dan Sloughter 2001 2 Introduction to R n Section 1.1 x x x 123 x 1 ( , , ) x 2 x 3 Figure 1.1.1 A point in R 3 That is, R n is the space of all ordered n -tuples of real numbers. We will denote a point inthis space by x = ( x 1 ,x 2 ,...,x n ) , (1.1.2)and, for i = 1 , 2 ,...,n , we call x i the i th coordinate of x . Example When n = 2, we have R 2 = { ( x 1 ,x 2 ) : x 1 ,x 2 ∈ R } , which is our familiar representation for points in the Cartesian plane. As usual, we willin this case frequently label the coordinates as x and y , or something similar, instead of numbering them as x 1 and x 2 . Example When n = 3, we have R 3 = { ( x 1 ,x 2 ,x 3 ) : x 1 ,x 2 ,x 3 ∈ R } . Just as we can think of R 2 as a way of assigning coordinates to points in the Euclideanplane, we can think of R 3 as assigning coordinates to three-dimensional Euclidean space. Topicture this space, we must imagine three mutually perpendicular axes with the coordinatesmarked off along the axes as in Figure 1.1.1. Again, we will frequently label the coordinatesof a point in R 3 as, for example, x , y , and z , or u , v , and w , rather than using numberedcoordinates. Example If an object moves through space, its location may be specified with fourcoordinates, three spatial coordinate, say, x , y , and z , and one time coordinate, say t .Thus its location is specified by a point p = ( x,y,z,t ) in R 4 . Of course, we cannot drawa picture of such a point.Before beginning our geometric study of R n , we first need a few basic algebraic defini-tions. Section 1.1 Introduction to R n 3 Definition Let x = ( x 1 ,x 2 ,...,x n ) and y = ( y 1 ,y 2 ,...,y n ) be points in R n and let a be a real number. Then we define x + y = ( x 1 + y 1 ,x 2 + y 2 ,...,x n + y n ) , (1.1.3) x − y = ( x 1 − y 1 ,x 2 − y 2 ,...,x n − y n ) , (1.1.4)and a x = ( ax 1 ,ax 2 ,...,ax n ) . (1.1.5) Example If x = (2 , − 3 , 1) and y = ( − 4 , 1 , − 2) are two points in R 3 , then x + y = ( − 2 , − 2 , − 1) , x − y = (6 , − 4 , 3) , y − x = ( − 6 , 4 , − 3) , 3 x = (6 , − 9 , 3) , and − 2 y = (8 , − 2 , 4) . Notice that we defined addition and subtraction for points in R n , but we did not definemultiplication. In general there is no form of multiplication for such points that is usefulfor our purpose. Of course, multiplication is defined in the special case n = 1 and for thespecial case n = 2 if we consider the points in R 2 as points in the complex plane. Weshall see in Section 1.3 that there is also an interesting and useful type of multiplicationin R 3 . Also note that (1.1.5) does provide a method for multiplying a point in R n by aa real number, the result being another point in R n . In such cases we often refer to thereal number as a scalar and this multiplication as scalar multiplication . We shall providea geometric interpretation of this form of multiplication shortly. Geometry of R n Recall that if x = ( x 1 ,x 2 ) and y = ( y 1 ,y 2 ) are two points in R 2 , then, using thePythagorean theorem, the distance from x to y is  ( y 1 − x 1 ) 2 + ( y 2 − x 2 ) 2 . (1.1.6)This formula is easily generalized to R 3 : Suppose x = ( x 1 ,x 2 ,x 3 ) and y = ( y 1 ,y 2 ,y 3 ) aretwo points in R 3 . Let z = ( y 1 ,y 2 ,x 3 ). Since the first two coordinates of y and z are thesame, y and z lie on the same vertical line, and so the distance between them is simply \| y 3 − x 3 \| . (1.1.7)Moreover, x and z have the same third coordinate, and so lie in the same horizontal plane.Hence the distance between
If you are an undergraduate engineering or science major, then you need to get a copy of this old classic and become good friends with it. If you are a graduate student or a professional in some branch of engineering or science, and you have not already read this book, then sneak out and get a copy before anybody finds out. (You can pretend that you really knew this stuff all along.) Seriously, this book should be considered Math 101 for scientists and engineers. You simply cannot get by without knowing the basics of vector calculus, curvilinear coordinates, Gauss' law, Stokes' theorem, and of course, the protagonists Divergence, Gradient, and Curl, known to their friends as Div, Grad, and Curl. This is about as tame a book on vector calculus as you could ever hope to meet, which is part of the reason it's been so popular for so long. It's very easy to read (as far as math texts go), it has many simple but effective illustrations, it has ample exercises (most of which have solutions in the back), and it avoids excessive formalism, instead focusing on the nuts-and-bolts of vector calculus as it most commonly arises in electrostatics, for example. Math majors will not be so enamored of this book, simply because of its heuristic approach (hence the word "informal" in the subtitle) and its close ties with applications, which it uses as motivation. Moreover, Schey does not develop differential forms or exterior calculus, which logically subsume and extend the material in this book (at the expense of far greater abstraction, which the majority of engineering and science students will prefer to avoid or at least delay). Instructors, if you teach electrostatics or fluid dynamics, you may wish to consider having this as a supplementary text for your students. It's such a clear and helpful little book your students will really appreciate it. (But, you already knew that.) Bottom line for engineering and science students: You need to know this material, and it simply won't get any easier than this. Don't wait for the audio edition! It's been over two decades since I first studied vector calculus from my old textbook on electromagnetic fields and waves (Lorrain and Corson, Freeman, 1970). I really enjoyed that class, and remain fascinated by the beautiful mathematics involved in the classical field equations of electromagnetism. When I saw Schey's book on the shelf in Boulder, Co., I immediately picked it up and flipped through the pages. This wasn't the book I'd set out to find (I wanted a good book on Photonics, to commemorate the conference I was attending at NIST on fiber-optic measurements) but I decided it would be fun to read it as a refresher course. My first impression of Schey's book is that it would make a great first course in vector calculus. In fact, I recommend it for that purpose. It will also be very useful for the student enrolled in a class on vector calculus, who wants a secondary reference text to help expand concepts. Schey's approach will appeal to physicists and engineers, with it's intuitive, visual style. Schey uses electric fields as the motivating challenge for developing equations that use the divergence, gradient, and curl, and he uses chapter 1 to develop virtually all the physical concepts needed to follow the derivations. For prerequisites, you should have at least one semester of calculus, and it will help to have a little understanding about electromagnetism, as well (a high school level will be more than adequate for this purpose). Schey's book also makes a great refresher text (that's why I bought it). If you've had vector calculus in college, you'll be able to read this book in a week or so. It's nicely illustrated, and has problems at the end of each chapter that are strategically designed to extend concepts brought out in the text (solutions to most of the problems appear at the end of the text). The book's organization is pretty simple, with four sections/chapters. The first is a basic introduction that describes the notion of a vector field and some basic concepts in electrostatics. True to the overall theme throughout the text, Schey uses simple, intuitive explanations and drawings that are especially applicable for beginning students. The second section introduces surface integrals and divergence. As he does in the remaining chapters, Schey develops equations in Cartesian, spherical, and cylindrical coordinate systems (though he sometimes leaves some of these as exercises for the student). He also summarizes them at the end of the book. In addition to giving the functional, coordinate-dependent form, Schey also shows how the operators are limits that exist as physical entities, independent of any particular coordinate system. For example, Schey summarizes divergence as the limit, as the volume goes to zero, of the flux of the vector field through a surface, divided by the volume enclosed by the surface (see page 37). Beginning texts don't always make this clear, resulting in some students failing to understand divergence (for example) as anything more than the equation that describes it in Cartesian coordinates. But Schey artfully incorporates this more general understanding as part of his clear and intuitive style of teaching. The third section is about line integrals, the Curl, and Stokes' theorem. The approach is intuitive, with a minimum of formal mathematics, and abundant, clear, diagrams that greatly help to illustrate principles. As with divergence, Schey provides the mathematical form for Curl in three different coordinate systems, as well as the general description (independent of coordinate system): curl is the limit of circulation to area, in the limit, as the area tends to zero. The fourth, and final section deals with the Gradient. In keeping with the general theme of deriving the mathematical tools to calculate the electric field, Schey summarizes the relationship between the Curl of the vector field, the vector field as the gradient of a scalar function, and the line integral around a closed path of the dot product between the tangent and the vector field. He also extends the notion of the gradient operator to that of the Laplacian, and discusses Poisson's and Laplace's equations. As with the other chapters, Schey makes a point of endowing his explanations with intuitive and visual explanations, explaining that "the gradient of a scalar function F(x,y,z) is a vector that is in the direction in which [the scalar function] F undergoes the greatest rate of increase and that has magnitude equal to the rate of increase in that direction." I really enjoyed reading this book. Having graduated from university over 20 years ago, I'm not as quick to recall this stuff, so I value a concise book with visual, intuitive, and ready explanations. This text provides a systematic introduction to vector calculus in a very readable, informal format. Key concepts like divergence, curl, gradient, line integrals, surface integrals, Divergence Theorem, and Stokes Theorem are introduced in the context of investigating solutions to electrostatics problems without requiring the reader to be especially familiar with physics. I particularly enjoyed the humor that is woven into the text. ("Thus, the anguish of remembering the form of curl F in Cartesian coordinates can be replaced by the pain of remembering how to expand a three-by-three determinant.") I would highly recommend this concise book to students of physics, engineering, and mathematics. It is particularly suitable for self-instruction. I first checked this book out of a library, and was so pleased I decided to buy it. I am enrolled in a graduate level fluid mechanics class after being out of school for a few years and I needed to brush up on my vector calculus. This book was great for that job. It explains the concepts of divergence, gradient, curl, directional derivatives, line integrals, surface integrals, Stoke's Theorem, and Divergence Theorem with good mathematical rigor and notation, yet also with the "words between the lines" that most math texts leave out. In other words, accompanying each equation you will find a sentence or even a paragraph describing what exactly took place between steps. Additionally, the author makes a point to describe the concepts behind the jargon and equations. When you took vector calculus the first time (if you ever did), could you explain in words what a "curl" is, or a "divergence"? This book attempts to do so, and does so fairly well (as well as one could given that these concepts don't have the easiest translation into words). Furthermore, the author even has a sense of humor and made me laugh a few times. When was the last time you laughed out loud at a math book? Finally, this book also includes applications to physics such as electrostatics (the recurring thematic problem of the book is Gauss's Law), fluid dynamics, and work. Not only was it a great refresher, I wanted to own this clear and simple book as a reference.
Practical Foundations of Mathematics explains the basis of mathematical reasoning both in pure mathematics itself (algebra and topology in particular) and in computer science. In addition to the formal logic, this volume examines the relationship between computer languages and plain English Author: Taylor, Paul/ Paul, Taylor/ Bollobas, Bela Series Title: Cambridge Studies in Advanced Mathematics (Hardcover) Series Number: 59 Binding Type: Hardcover Number of Pages: 588 Publication Date: 1999/05/13 Language: English Dimensions: 9.36 x 5.92 x 1.71 inches From the Publisher: Practical Foundations of Mathematics explains the basis of mathematical reasoning both in pure mathematics itself (algebra and topology in particular) and in computer science. In addition to the formal logic, this volume examines the relationship between computer languages and "plain English" Description: This Computer Algebra Handbook gives a comprehensive snapshot of this field at the intersection of mathematics and computer science with applications in physics, engineering and education. It contains both theory, systems and practice of the discipline of symbolic computation ... Description: This book introduces stochastic processes and their applications for students in engineering, industrial statistics, science, operations research, business, and finance. It provides the theoretical foundations for modeling time dependent random phenomena encountered in these disciplines. Through numerous science ...
Buy Used Textbook Buy New Textbook eTextbook Instant Online Access 180 day digital rental $81.25 More New and Used from Private Sellers Starting at $54 Problem Solving Approach to Mathematics for Elementary School Teachers A Problem Solving Approach to Mathematics for Elementary School Teachers E-Manipulatives CD for Future Elementary School Teachers, Version 2. 1 PACKAGE: PROB SOLV APPR MTH&IA CD Problem Solving Approach to Mathematics for Elementary School Teachers Problem Solving Approach to Mathematics for Elementary School Teachers, A Problem Solving Approach to Mathematics, A (Recover) Problem Solving Approach to Mathematics, A (Recover) Student Solutions Manual for A Problem Solving Approach to Mathematics for Elementary School Teachers Technology Manual : Using Spreadsheets, Graphing Calculators, and a Geometry Drawing Utility for a Problem Solving Approach to Mathematics for Elementary School Teachers Videos on DVD with Optional Subtitles for A Problem Solving Approach to Mathematics for Elementary School Teachers Summary More than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teacherssince its first edition, and it remains the gold standard today. This text not only helps students learn the material by promoting active learning and developing skills and concepts-it also provides an invaluable reference to future teachers by including professional development features and discussions of today's standards. The Eleventh Editionis streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS)have been integrated into the book to keep current with educational developments. The Annotated Instructor's Editionoffers new Integrating Mathematics and Pedagogy (IMAP)video annotations, in addition to activity manual and e-manipulative CD annotations, to make it easier to incorporate active learning into your course. MyMathLab®is available to offer auto-graded exercises, course management, and classroom resources for future teachers. To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit Author Biography Rick Billstein is a Professor of Mathematics at the University of Montana. He has worked in mathematics teacher education at this university for over 40 years and his current research is in the areas of curriculum development and mathematics teacher education. He teaches courses for future teachers in the Mathematics Department. He served as the site director for the Show-Me Project, an NSF-funded project supporting the dissemination and implementation of standards-based middle grades mathematics curricula. He worked on the NSF grant Tinker Plots to develop new data analysis software and he serves on the Advisory Boards for several other national projects. From 1992-1997, he directed the NSF-funded Six Through Eight Mathematics (STEM) middle school mathematics curriculum project and is now directing the Middle Grades MATHThematics Phase II Project. Dr. Billstein has published articles in over 20 different journals, and has co-authored over 40 books, including ten editions of A Problem Solving Approach to Mathematics for Elementary Teachers. He typically does about 25 regional and national presentations per year and has worked in mathematics education at the international level. He presently serves on the Editorial Board of NCTM's Mathematics Teaching in the Middle School. Dr. Billstein was recently awarded the George M. Dennison Presidential Faculty Award for Distinguished Accomplishment at the University of Montana. Shlomo Libeskind is a professor in the mathematics department at the University of Oregon in Eugene, Oregon, and has been responsible there for the mathematics teaching major since 1986. In addition to teaching and advising pre-service and in-service teachers, Dr. Libeskind has extensive writing experience (books, articles, and workshop materials) as well as in directing mathematics education projects. In teaching and in writing, Dr. Libeskind uses a heuristic approach to problem solving and proof; in this approach the reasonableness of each step in a solution or proof is emphasized along with a discussion on why one direction might be more promising than another. As part of his focus on the improvement of the teaching of mathematics, Dr. Libeskind is also involved at many levels locally, nationally, and worldwide in the evaluation of mathematics teacher preparation programs. In his home state, he is actively involved in schools and councils, as well as in reviewing materials for the state standards for college admission. Most recently (spring 2008) he visited teacher colleges in Israel as a Fulbright Fellow. During this visit he conducted observations and critiques of the preparation of mathematics teachers at several colleges in Northern Israel. Dr. Libeskind received his Bachelor's and Master's Degrees in Mathematics at the Technion (Israel Institute of Technology) and his PhD in Mathematics at the University of Wisconsin, Madison. Johnny W. Lott began his teaching career in the public schools of DeKalb County, Georgia, outside Atlanta. There he taught mathematics in grades 8-12. He also taught one year at the Westminster Schools, grades 9-12, and one year in the Pelican, Alaska, school, grades 6-12. Johnny is the co-author of several books and has written numerous articles and other essays in the "Arithmetic Teacher", "Teaching Children Mathematics", "The Mathematics Teacher", "School Science and Mathematics", "Student Math Notes", and "Mathematics Education Dialogues". He was the Project Manager for the "Figure This!" publications and website developed by the National Council of Teachers of Mathematics (NCTM) and was project co-director of the State Systemic Initiative for Montana Mathematics and Science (SIMMS) Project. He has served on many NCTM committees, has been a member of its Board of Directors, and was its president from April 2002-April 2004. Dr. Lott is Professor Emeritus from the Department of Mathematical Sciences at The University of Montana, having been a full professor. He is currently the Director of the Center for Excellence in Teaching and Learning, Professor of Mathematics, and Professor of Education at the University of Mississippi. Additionally, he is on the Steering Committee of the Park City Mathematics Institute, works with the International Seminar, the Designing and Delivering Professional Development Seminar, and is editor for its high school publications. His doctorate is in mathematics education from Georgia State University.
Introduction to Real Analysis: An Educational Approach English \| PDF \| 262 Pages \| 10.1 Mb An accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach presents a comprehensive introduction to real analysis while also offering a survey of the field. With its balance of historical background, key calculus methods, and hands-on applications, this book provides readers with a solid foundation and fundamental understanding of real analysis. ELEMENTARY SCIENCE METHODS: A CONSTRUCTIVIST APPROACH, Fifth Edition, is based on two fundamental and complementary ideas: it is more important for children to learn how to do science than to learn about science, and elementary science teachers do not need to know a great deal of science but rather should be co- inquirers with their students.
Math 9 is the first step in preparing students for the study of calculus by providing important skills in algebraic manipulation and interpretation at the college level. Topics will include a review of basic algebraic concepts; lines; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions, identities, inverse functions and equations; applications of trigonometry; systems of equations and matrices; conic sections; sequences, series and combinatorics. Hand-held graphing calculators will be used extensively to highlight their strengths and their limitations as a problem-solving tool. Real world applications will be numerous. Math 10 prepares students for the study of calculus by providing important critical thinking and problem solving skills. The central theme of the course is the analysis of mathematical functions as models of change. Families of functions - linear, exponential, logarithmic, power, periodic, polynomial, rational - will be introduced, compared and contrasted. Course content will include an introduction to functions and functional notation; transformation of functions; composite, inverse and combinations of functions; vectors and polar coordinates; series; parametric equations; complex numbers. Hand-held graphing calculators will be used extensively to highlight their strengths and their limitations as a problem-solving tool. Real world applications will be numerous. Prerequisite: Mathematics 9 and proficiency with the TI-83 graphing calculator as gained from, for instance, Math 209. This course is intended for students preparing for a career in elementary school teaching. Emphasis will be on the structure of the real number system, numeration systems, elementary number theory, and problem solving techniques. Technology will be integrated throughout the course. Prerequisite: Mathematics 208, or successful completion of a high school geometry course and Mathematics 233. Survey of selected topics from contempory mathematics to introduce the student to mathematical thinking for the nonspecialist. Topics include systems of numeration, algebraic modeling, linear programming, trigonometry, math of finance, probability and statistics, and an introduction to calculus. Operations with signed numbers, evaluation of expression containing numbers and letters, simplifying algebraic expressions, equations, word problems, exponents, polynomials, factoring and special products, fractions, graphing, systems of equations, radicals, and quadratic equations. Mathematics 205, 205A, 205B and 206 have similar course content. This course may not be taken by students who have completed Mathematics 205B or 206 with a grade of "C" or better. This course may be taken for Mathematics 205B credit (2.5 units) by those students who have successfully completed Mathematics 205A with a grade of "C" or better. The course contains the material covered in the first half of the Mathematics 205 course. It will cover signed numbers, evaluation of expressions, solving linear equations and inequalities, and applications. Graphing of lines, the slope of a line, graphing linear equations, solving systems of equations, basic rules of exponents, and operations on polynomials will be covered. Mathematics 205, 205A, 205B and 206 have similar course content. This course may not be taken by students who have completed Mathematics 205 or 206 with a grade of "C" or better. Advisory: Completion of Mathematics 402. Concurrent enrollment in Guidance 563A is advised. Students who were previously unsuccessful in Mathematics 205 are encouraged to attend. A survey of practical geometry with an emphasis on applications to other disciplines and everyday life. Parallel lines, triangles, circles, polygons, three dimensional figures, vectors, and right triangle trigonometry will be covered. There will be a weekly lab. This course is a remedial, modular, self-paced course. Application and critical thinking skills are developed in each module. Module A covers operations with whole numbers, equivalent fractions, multyplying self
Mathematica by Example, 4e is designed to introduce the Mathematica programming language to a wide audience. This is the ideal text for all scientific students, researchers, and programmers wishing to learn or deepen their understanding of Mathematica. The program is used to help professionals, researchers, scientists, students and instructors solve... more... This third edition of Mathematica by Example is completely compatible with recent Mathematica versions. Highly readable and informative, this volume is geared toward the beginning Mathematica user, and focuses on the most often used features of this powerful tool. The book covers popular applications of mathematics within different areas including... more... Maple by Example, Third Edition ,... more... Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical... more... Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content... more... This work reports critical analyses on complexity issues in the continuum setting and on generalization to new examples, which are two basic milestones in learning from examples in connectionist models. It also covers up-to-date developments in computational mathematics. more...
Summary: For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics. Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics the...show morey will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more. Features Two semesters worth of material. Gives instructors a wide variety of material from which to choose. Serves as a reference book to students throughout their career. Independent chapters. Allows instructors to tailor the course to students' specific needs and backgrounds. Allows students to start the book at any point they choose. In-depth coverage of core concepts. Gives students an in-depth understanding of the important concepts that are taught in high school mathematics. Provides the instructor with a generalized approach to treat problems. Gives students a much deeper understanding of problems they will be teaching, and gives them an approach to teach their students. Detailed concept analyses--Including historical and conceptual development of mathematical concepts, and alternate language, notation, and characterizations of ideas. Gives the instructor choices in the selection of notation and provides historical and conceptual perspective. Gives students a flexibility that is critical to making choices about what they teach; provides multiple approaches to teaching; and includes information helpful in responding to high school student questions. Connections between concepts, between different areas of mathematics, among various uses of ideas. Helps students understand that mathematics is a unified whole and provides multiple perspectives for looking at mathematical ideas. Allows the instructor to relate the material in the course to almost any other
Intermediate Algebra: Graphs and Functions 3e offers proven pedagogy, innovative features, real-life applications and flexible technology with comprehensive coverage for a solid course in intermediate algebra. In general, Larson's early functions approach along with early polynomials makes the topical organisation very appealing, and highly effective method of teaching / learning for teacher and pupil alike. Highlights of this third edition include: New! Side-by-side Algebraic, Graphical, and Numerical Solutions New! Chapter Opener - each chapter now opens with an objective based overview of the chapter concepts and Key Terms, a list of the mathematical vocabulary New Collaborate! Appearing at the end of selected sections these activities can be assigned for small group work or for whole class discussions Revised Exercise Sets -now grouped into four categories: Developing Skills, Solving Problems, Explaining Concepts, and Ongoing Review they offer computational, applied, and conceptual problems
Math, 17th Edition BUSINESS MATH, 17E provides comprehensive coverage of personal and business-related mathematics. In addition to reviewing the basic operations of arithmetic, this text prepares you to understand and manage your personal finances, as well as grasp the fundamentals of business finances. BUSINESS MATH, 17E prepares you to be smart shoppers, informed taxpayers, and valued employees. Basic math skills are covered in a step-by-step manner, building confidence in users before they try it alone. Spreadsheet applications are available on the Data Activities CD, and a simulation activity begins every chapter. Chapters are organized into short lessons for ease of instruction and include algebra connections, group and class activities, communication skills, and career spotlights107.95 Purchase Options Hardcover $85.99 $85.99 Save $2126.49 from$26.49 Save up to $81.46! Rent thru 06/09/14 for $26.49 $26.49 Save $81.46! Rent thru 12/06/14 for $29.99 $29.99 Save $77.96! Rent thru 12/01/15 for $32.99 $32.99 Save $74.96! Rent thru 11/20/17 for $36.99 $36.99 Save $70 include
ALEX Lesson Plans Title: Predict the Future? Description: Students will use data collected and a "best-fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression. Standard(s): 7: Utilize advanced features of database software, including merging data, sorting, filtering, querying, and creating reports. Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Predict the Future? Description: Students will use data collected and a "best-fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression. Title: Show Me The Money - Saving and Investing Description: Students will learn how to analyze several savings products from various financial institutions. They will also demonstrate the ability to discuss the role of saving and investment products. This a Commerce and Information Technology lesson plan AL1 (9-12) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [F-LE1 Information Literacy (K - 12), or Mathematics (7 - 12) Title: Show Me The Money - Saving and Investing Description: Students will learn how to analyze several savings products from various financial institutions. They will also demonstrate the ability to discuss the role of saving and investment products. This a Commerce and Information Technology lesson plan. domain Exponential Growth and Decay Description: ThisStandard(s): [MA2010] AL1 (9-12) 7: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] ALC (9-12) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2010] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama) Subject: Mathematics (9 - 12) Title: Exponential Growth and Decay Description: This Title: Density Description: DStandard(s): [S1] (8) 1: Identify steps within the scientific process. [S1] CHE (9-12) 1: Differentiate among pure substances, mixtures, elements, and compounds. [S1] ENV (9-12) 1: Identify the influence of human population, technology, and cultural and industrial changes on the environment 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4] [MA2010] AL1 (9-12) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI ALC (9-12) 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) Subject: Mathematics (9 - 12), or Science (8 - 12) Title: Density Description: D Title: What is the slope of the stairs in front of the school? Description: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8-EE6 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5] Subject: Mathematics (8 - 12) Title: What is the slope of the stairs in front of the school? Description: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally. Title: Finding the Slope of a Line Description: ThisStandard(s): (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5] Subject: Mathematics (8 - 12) Title: Finding the Slope of a Line Description: This Title: Math is Functional Description: This ( ALC (9-12) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) AL1 (9-12) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Math is Functional Description: This Thinkfinity Lesson Plans Title: Apple Pie Recording Chart Description: This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects. Standard(s): [MA2010] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP1] 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7-SP1] [MA2010] (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7-SP Apple Pie Recording Chart Description: This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects. Thinkfinity Partner: Illuminations Grade Span: 6,7,8 Title: Building Bridges Description: In 28: Understand that patterns of association can also be seen Subject: Mathematics,Professional Development Title: Building Bridges Description: In Thinkfinity Partner: Illuminations Grade Span: 6,7,8 Title: Gallery Walk Description: In coordinate Gallery Walk Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Automobile Mileage: Age vs. Mileage Description: In Subject: Mathematics Title: Automobile Mileage: Age vs. Mileage Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: The Centroid and the Regression Line Standard(s): 44: AL2 (9-12) 21: Create equations in two or more variables to represent relationships Subject: Mathematics Title: The Centroid and the Regression Line Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Graphing What Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs. Standard(s): [MA2010] (6) 17: Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6-EE6] 10: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7-EE4 Graphing What Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Least Squares Regression Description: In Least Squares Regression Title: Graph Chart Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Standard(s): 2: Recognize and represent proportional relationships between quantities. [7-RP2 of 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2010] AL2 (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 Graph Chart Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Bathtub Water Levels Description: In table Bathtub Water Levels Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: The Effects of Outliers 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3 Subject: Mathematics Title: The Effects of Outliers Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Exploring Linear Data Description: In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit. Standard(s): [S1] (8) 1: Identify steps within the scientific process. 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation Exploring Linear Data Description: In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12 Title: Traveling Distances Description: In Traveling Distances Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Linear Alignment Description: In Standard(s): Linear Alignment Description: In Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12 Title: Make a Conjecture Description: In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart. Standard(s): 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [S-ID2 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2010] AL2 (9-12) 38: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] [MA2010] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1T (9-12) 37: [S-ID4 ALT (9-12) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2010] ALT (9-12) 42: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7 Health,Mathematics Title: Make a ConjectureTitle: Exact Ratio Description: This Standard(s): [MA2010] AL1 (9-12) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [N-RN 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9 Mathematics Title: Exact Ratio Description: This Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Web Resources Interactives/Games where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11] Learning ActivitiesThinkfinity Learning Activities Title: Tube Viewer Simulation Description: This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change. Standard(s): Tube Viewer Simulation Description: This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Flowing Through Mathematics Description: This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Standard(s): cases GEO (9-12) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3 Subject: Mathematics Title: Flowing Through Mathematics Description: This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Math 150 - Lecture 22 Math 150 - Lecture 22 Welcome to lecture 22 of math 150 - mathematics for the contemporary world. In this lecture we go over a quiz given in class as a review for the last test. The topics included in this lecture... From: Jhev1000 Views: 1 0 ratings Time: 22:58 More in Education
Personal tools Views Mathematics Standards From APEC HRDWG Wiki Mathematics standards specify the type of mathematics education that students should receive during the course of their schooling. Mathematics standards are typically organized into five mathematical content areas including: numbers and operations, data and probability, measurement, geometry, and algebra. Standards may also develop desired mathematical abilities such as conceptual understanding, computation, and reasoning skills. Standards help frame mathematics instruction in the classroom and mathematics assessments that check for learning outcomes or results. To search the APEC Wiki for more topics related to mathematics standards, please follow the links below: The APEC publication on informing mathematics standards development compares the content standards context in the United States with similar structures in Hong Kong, Korea, and Singapore, with suggestions for replicating promising practices from the higher-performing economies. This publication was referenced in the US common core standards. On behalf of APEC and the U. S. Department of Education, Achieve, Inc., the organization active in developing the U.S. Common Core State Standards, conducted an analysis of APEC mathematics and science standards, aiming to qualify how standards are organized and to identify common content and performance expectations of APEC member economies' standards. A related report on standards development among high-performing APEC members is also available.
This guide is designed as a teaching tool, aimed at both teachers and student teachers. Its main purpose is to enhance the value of "The Mathematical Experience" as a textbook. It includes a sample syllabus, outlines for group work, sample exams and hints for grading essays. [via] More editions of The Companion Guide to the Mathematical Experience: Study Edition: [via]
Combining scientific inquiry with advanced mathematics, SC1117 is a stimulating, two-semester course for high-school students that will challenge learners to understand and explain how energy, matter, and motion are all related. Engaging lessons introduce theories and experiments and encourage students to develop the knowledge and understanding necessary to support conclusions with numerical results.
Extra Examples shows you additional worked-out examples that mimic the ones in your book. These requirements include the benchmarks from the Sunshine State Standards that are most relevant to this course. The benchmarks printed in regular type are required for this course. The portions printed in italic type are not required for this course. After successfully completing this course, the student will: Demonstrate understanding of the different ways numbers are represented and used in the real world. Demonstrate understanding of number systems. Demonstrate understanding of the effects of operations on numbers and the relationships among these operations, select appropriate operations, and compute for problem solving. Use estimation in problem solving and computation. Demonstrate understanding and apply theories related to numbers. Measure quantities in the real world and use the measures to solve problems. Compare, contrast, and convert within systems of measurement (both standard/nonstandard and metric/customary). Estimate measurements in real world problem situations. Visualize and illustrate ways in which shapes can be combined, subdivided, and changed. Use coordinate geometry to locate objects in two dimensions and to describe objects algebraically. Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system. Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x - b)2 + c. Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.
Calculator2.0 Calculator is used for advanced calculations. Just paste the entire math expression and Calculator will provide you with a result. In ordinary calculators you have to split complicated expressions into simple o... Downloads: 3,683 Calculator Prompter2.2 Calculator Prompter is a math expression calculator. Calcualtor Prompter has a built-in error recognition system that helps you get correct results. With Calculator Prompter you can enter the whole expression, ... Downloads: 7,162
It provides a full set of commonly used scientific calculation functions and supports the following unique features: - Check history results for re-editing purposes; - Draw graphs corresponding to the math equations you input, such as Cartesian y(x) and x(y), parametric x(t), y(t) and polar r(θ)equations; - Allow users to choose from the variable bounds and background color to give a vivid display for a deeper understanding of the equations. Still hesitate? Try the lite version to verify whether it meets your needs fully. Kindly take note that the lite version has some restrictions, such as complicated scientific functions like sin, log are not supported. 1. Added sound effect, which can be disabled in the Settings 2. Optimized translation algorithm, allowing the graph to move and zoom in/out more fluently 3. Changed coordinate calculation algorithm, making the coordinate easily readable (Coordinate is marked via the multiples of 5.) 4. Fixed the bug that a tiny coordinate would be displayed at the origin under some circumstances 5. Operating system requirement: Android 2.2 and above Comments and ratings for Scientific Graphing Calculator (43 stars) by Danny Kezar on 04/06/2013 Difficult to use... (43 stars) by dan driggers on 29/01/2013 It doesn't zoom x and y axis independently (43 stars) by A Google User (43 stars) by Melanie
Articles, chapters, and reviewed essays from subject encyclopedias and handbooks are particularly helpful for providing a snapshot of a specific topic or if you need clarity on one you have already studied. These resources are a good starting point if you are new to a particular subject area. Some of these resources are accessible online by providing your CSUDH username and password, others are available as print, and need to be requested by their call numbers, while other resources are publicly accessible. The Torofind Catalog, available at the University Library's homepage, allows you to search the library's collection of over 450,000 items. The Simple Search screen allows searching by Keyword, Title, Author, Subject, ISBN/ISSNN, or Library of Congress call number by using the dropdown feature in the search bar. The Advanced Searchtab allows you to combine multiple search fields and to restrict the results in different ways. Not all currently available e-books are accessible from the online catalog, therefore, try searching directly through the e-book vendor. E-book databases are available on the library home page under Databases by Subject. The library's online catalog is also used to managerenewals, save and e-mail searches, and more. Below are some subject headings used to describe specialized materials in Mathematics available in our catalog. The hyperlinks will take you to the result list. Otherwise, select the Subject field from the drop down menu of the Torofind Catalog and type the predefined heading. The CSUDH Library holds several mathematics and applied mathematics textbooks. Some are available in our Reserves Room, others can be searched in our online catalog and are located at the stacks, and others may also be available electronically. The following series titles may be either on a broad or specialized subject area. To access further information click on the hyperlinks. Be aware that additional textbooks and books on the same topic may be available at the stacks when searching for these textbooks. Some electronic textbooks are available in the Affordable Learning Solutions Program's page and can be searched under title, instructor's name, or course number. Useful peer-reviewed learning materials, including textbooks, are available in MERLOT under Mathematics and Statistics. Browsing Books and Other Materials The University Library houses books and other relevant materials arranged according to the Library of Congress system pertaining to the discipline of Mathematics. Below is a chart with some call number ranges and locations: Subject Call Number Location Algebra QA154; QA266 4th Floor South Algorithms QA76.6 4th Floor South Calculus QA300 4th Floor South Combinatorial Analysis QA164 4th Floor South Differential equations QA371-373 4th Floor South Diff. equations, Partial QA374-377 4th Floor South Geometry, Algebraic; QA564 4th Floor South Geometry, Differential QA641-660 4th Floor South Number Theory QA241 4th Floor South Checking Out Materials Currently enrolled CSUDH students and staff members may check out up to 30 items from the general collection for 28 days. Faculty members are entitled to check out a maximum of 100 items from the general collection for 6 months. It is a requirement to present a current CSUDH Identification card at the Circulation Desk, located on the second floor of the library. Privileges are also extended to access materials placed on reserve and Interlibrary Loan services. Be aware that the loan periods vary for materials either on reserves or requested through Interlibrary Loan. For more information on renewals, holds, overdue fines, etc. contact the Circulation Desk at (310) 243-3712. Searching Other Library Collections The Catalog of the CSU Libraries allows for searching the collections for all 23 CSU campuses and for finding materials that are not available at your CSUDH Library. These materials may be requested through Interlibrary Loan online at no cost. WorldCatlets you search the collections of libraries in your community, state, country, and around the world. WorldCat locates the nearest libraries to our campus that list your request as available. These items available for loan may be borrowed online and include: books, journal articles, and some dissertations and theses. For additional information on policies contact the Interlibrary-Loan Services at (310) 243-3716. Databases The University Library subscribes to a number of databases that index magazine and journal articles, and other materials many of which specialized in the field of mathematics that may be available full text. Access to electronic databases is available through the library's main webpage via Databases by Title. Databases are also arranged by topics underDatabases by Subject. Full-text access and date coverage varies by individual periodical titles as well as from one database to another; therefore you may find it necessary to search in multiple databases. The Journals by Titleallows you to identify and locate specific journal titles, their availability, whether they are accessible electronically or in print, and their coverage dates. If you are accessing the databases from off-campus, you will be prompted to login with your CSUDH username and password. Core Database MathSciNet is a comprehensive database of mathematical literature by the American Mathematical Society. MathSciNet provides access to reviews and abstracts of mathematical publications and bibliographic information of books, book chapters, and proceedings, as well as specialized Ph.D. theses from theProQuest Dissertations Database. Other Useful Databases MERLOT is a CSU system program that provides peer-reviewed online teaching and learning materials on diverse disciplines, including Mathematics. Oxford Journalsincludes full and optional open access to more than 100 journals from every subject area including Mathematics. Science Directis a full-text scientific database offering peer-reviewed journal articles as well as book chapters on diverse disciplines pertaining to the worlds of Physical Sciences and Engineering, Life Sciences, Health Sciences, and Social Sciences and Humanities. Springer LinkSpringer Link is a full text database specialized in diverse disciplines including Arts, Humanities, Social Sciences, but with a particular expertise in Science, Technology, and Medicine. e-Books Databases e-Books on Algebra, Geometry, Trigonometry, Topology, Arithmetic, and Probabilities among other Mathematic-related topics are available from any of the following databases: Wolfram Alpha. Mathematics is an engine for computing answers and providing knowledge in diverse subject fields, one of which is Mathematics. It provides definitions, computations with special functions, vector analysis computations, derivative calculations and more. Videos Khan Academy. This non-profit organization provides access to their video collection, interactive challenges, and assessments from any computer with access to the Internet.
Summary: CONTEMPORARY MATHEMATICS FOR BUSINESS AND CONSUMERS, BRIEF is a 14-chapter educational adventure into today's business world and its associated mathematical procedures. The book is designed to provide solid mathematical preparation and foundation for students going on to business courses and careers. It begins with a business-oriented review of the basic operations, including whole numbers, fractions, and decimals. Once students have mastered these operations, they a...show morere introduced to the concept of basic equations and how they are used to solve business problems. From that point, each chapter presents a business math topic that utilizes the student's knowledge of these basic operations and equations. In keeping with the philosophy of "practice makes perfect," the text contains over 2,000 realistic business math exercises--many with multiple steps and answers designed to prepare students to use math to make business decisions and develop critical-thinking and problem-solving skills. Many of the exercises in each chapter are written in a "you are the manager" format, to enhance student involvement. The exercises cover a full range of difficulty levels, from those designed for beginners to those requiring moderate to challenge-level Mathematics for Business and Consumers, Brief Edition - With CD
Beginning and Intermediate Algebra : Text / Workbook / With CD by MCKEAGUE Annotated Instructor Edition Description Exceptionally clear and accessible, Pat McKeague's best-selling texts offer all the review, drill, and practice students need to develop solid mathematical proficiency and confidence. McKeague's attention to detail, exceptional writing style, and organization of mathematical concepts make teaching enjoyable and learning accessible. Building on his reputation for student-friendly content and supportive pedagogy, McKeague reaffirms his presence as a leader in developmental mathematics with the introduction of this new paperback title.
Latihan Matematik Tingkatan 4
21057338 / ISBN-13: 9780021057337 It's All Connected "Math Connects"is intended for use in all elementary math classes as a balanced basal approach to teaching mathematics. "Math ...Show synopsis synopsis ...Show more Description:Fair. 0021057338 Well used book with very heavy cover wear and...Fair. 0021057338Description:Like NEW condition! Contains CD/ Like NEW condition! Contains...Like NEW condition! Contains CD/ Like NEW condition! Contains CD/accessory/dust jacket where applicable. Orders ship within 24-36 hours with free tracking. To help ensure your complete satisfaction we accept returns for five days after your order arrives. The interior is perfect the exterior is excellent and may show extremely minor shelf wear around the edges from normal storage. Description:Brand New, may or may not have a school inventory number on side...Brand New, may or may not have a school inventory number on side pages or inside cover.100% money-back guarantee if not satisfied! Description:Very Good. MULTIPLE COPIES AVAILABLE! Macmillan/McGraw-Hill:...Very Good. MULTIPLE COPIES AVAILABLE! Macmillan/McGraw-Hill: Math Connects, Grade 4-Student Edition [Hardcover]. Copyright-2009, ISBN: 0021057338. These books are in VERY GOOD condition with clean interior pages, intact binding blocks, and only MINOR wear to the exterior covers! We ship daily
Introduction The Mathematics Department hopes that all students will take mathematics courses. This said, be careful to take only those courses that are appropriate for your level of experience. Incoming students should take advantage of Harvards Mathematics Placement Test and of the science advising available in the Science Center the week before classes begin. Members of the Mathematics Department will be available during this period to consult with students. Generally, students with a strong precalculus background and some calculus experience will begin their mathematics education here with a deeper study of calculus and related topics in courses such as Mathematics 1a, 1b, 18,19a,b, 21a,b, 23a,b and 25a,b. The Harvard Mathematics Placement Test results recommend the appropriate starting level course, either Mathematics Ma, 1a, 1b, or 21. Recommendation for Mathematics 21 is sufficient qualification for Mathematics 18, 19a,b, 21a, 23a, and 25a. What follows briefly describes these courses: Mathematics 1a introduces the basic ideas and techniques of calculus while Mathematics 1b covers integration techniques, differential equations, and series. Mathematics 21a covers multi-variable calculus while Mathematics 21b covers basic linear algebra with applications to differential equations. Students who do not place into (or beyond) Mathematics 1a can take Mathematics Ma, Mb, a two-term sequence which integrates calculus and precalculus material and prepares students to enter Mathematics 1b. There are a number of options available for students whose placement is to Mathematics 21. For example, Mathematics 19a,b are courses that are designed for students concentrating in the life sciences. (These course are recommended over Math 21a,b by the various life science concentrations). In any event, Math 19a can be taken either before or after Math 21a,b. Math 19b should not be taken with Math 21b. Math 19a teaches differential equations, related techniques and modeling with applications to the life sciences. Math 19b teaches linear algebra, probability and statistics with a focus on life science examples and applications. Mathematics 18 covers selected topics from Mathematics 1b and 21a for students particularly interested in economic and social science applications. Mathematics 23 is a theoretical version of Mathematics 21 which treats multivariable calculus and linear algebra in a rigorous, proof oriented way. Mathematics 25 and 55 are theory courses that should be elected only by those students who have a strong interest in mathematics. They assume a solid understanding of one-variable calculus, a willingness to think rigorously and abstractly about mathematics, and to work extremely hard. Both courses study multivariable calculus and linear algebra plus many very deep related topics. Mathematics 25 differs from Mathematics 23 in that the work load in Mathematics 25 is significantly more than in Mathematics 23, but then Mathematics 25 covers more material. Mathematics 55 differs from Mathematics 25 in that the former assumes a very strong proof oriented mathematics background. Mathematics 55, covers the material from Mathematics 25 plus much material from Mathematics 122 and Mathematics 113. Entrance into Mathematics 55 requires the consent of the instructor. Students who have had substantial preparation beyond the level of the Advanced Placement Examinations are urged to consult the Director of Undergraduate Studies in Mathematics concerning their initial Harvard mathematics courses. Students should take this matter very seriously. The Mathematics Department has also prepared a pamphlet with a detailed description of all its 100-level courses and their relationship to each other. This pamphlet gives sample lists of courses suitable for students with various interests. It is available at the Mathematics Department Office. Many 100-level courses assume some familiarity with proofs. Courses that supply this prerequisite include Mathematics 23, 25, 55, 101, 112, 121, and 141. Of these, note that Mathematics 101 may be taken concurrently with Mathematics 1, 18, 19, or 21. Mathematics 113, 114, 122, 123, 131, and 132 form the core of the departments more advanced courses. Mathematics concentrators are encouraged to consider taking these courses, particularly Mathematics 113, 122 and 131. (Those taking 55a,b will have covered the material of Mathematics 113 and 122, and are encouraged to take Mathematics 114, 123, and 132.) Courses numbered 200-249 are introductory graduate courses. They will include substantial homework and are likely to have a final exam, either in class or take home. Most are taught every year. They may be suitable for very advanced undergraduates. Mathematics 212a, 230a, 231a and 232a will help prepare graduate students for the qualifying examination in Mathematics. Courses numbered 250-299 are graduate topic courses, intended for advanced graduate students. The Mathematics Department does not grant formal degree credit without prior approval for taking a course that is listed as a prerequisite of one you have already taken. Our policy is that a student who takes and passes any calculus course is not normally permitted to then take a more elementary course for credit. A student who has passed Mathematics 21a, for example, will normally not be allowed to take Mathematics 1a, or 1b for credit. The Mathematics Department is prepared to make exceptions for sufficient academic reasons; in each case, however, a student must obtain written permission from the Mathematics Director of Undergraduate Studies in advance. In the case of students accepting admission as sophomores, this policy is administered as follows: students counting one half course of advanced standing credit in mathematics are deemed to have passed Mathematics 1a, and students counting a full course of advanced standing credit in mathematics are deemed to have passed Mathematics 1a and 1b. Primarily for Undergraduates Mathematics Ma. Introduction to Functions and Calculus I Catalog Number: 1981 Enrollment: Normally limited to 15 students per section. Meghan Anderson, Melody Chan, Peter M. Garfield, Meredith Hegg, and members of the Department Half course (fall term). Section meeting times: Section I: M., W., F., at 10; Section II: M., W., F., at 11; Section III: M. W. F., at 12 (with sufficient enrollment); and a twice weekly lab session to be arranged. EXAM GROUP: 3 The study of functions and their rates of change. Fundamental ideas of calculus are introduced early and used to provide a framework for the study of mathematical modeling involving algebraic, exponential, and logarithmic functions. Thorough understanding of differential calculus promoted by year long reinforcement. Applications to biology and economics emphasized according to the interests of our students. Note: Required first meeting: Tuesday, September 3, 8:30 am, Science Center D. Participation in two, one hour workshops are required each week. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning. This course, when taken for a letter grade together with Mathematics Mb, meets the Core area requirement for Quantitative Reasoning. Mathematics Mb. Introduction to Functions and Calculus II Catalog Number: 3857 Enrollment: Normally limited to 15 students per section. Meredith Hegg, Meghan Anderson, Sarah Chisolm, Peter M. Garfield, and members of the Department Half course (spring term). Section I: M., W., F., at 10; Section II: M. W., F., at 11; Section III: M., W., F., at 12 (with sufficient enrollment); and a twice weekly lab session to be arranged. EXAM GROUP: 1 Continued investigation of functions and differential calculus through modeling; an introduction to integration with applications; an introduction to differential equations. Solid preparation for Mathematics 1b. Note: Required first Meeting in spring: Monday, January 27, 8:30 am, Science Center A . Participation in two, one hour workshops are required each week. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning. This course, when taken for a letter grade together with Mathematics Ma, meets the Core area requirement for Quantitative Reasoning. Prerequisite: Mathematics Ma. Mathematics 1a. Introduction to Calculus Catalog Number: 8434 Enrollment: Normally limited to 30 students per section. Peter M. Garfield, Janet Chen, Sarah Chisolm, Sukhada Fadnavis, and members of the Department (fall term); Oliver Knill (spring term) Half course (fall term; repeated spring term). Fall: Section I, M., W., F., at 9 (with sufficient enrollment); Section II, M., W., F., at 10; Section III, M., W., F., at 11; Section IV, M., W., F., at 12; Section V, Tu., Th., 10-11:30; Section Vl, Tu., Th., 11:30-1. Spring: Section I, M., W., F., at 10, and a weekly problem section to be arranged. EXAM GROUP: 1 The development of calculus by Newton and Leibniz ranks among the greatest achievements of the past millennium. This course will help you see why by introducing: how differential calculus treats rates of change; how integral calculus treats accumulation; and how the fundamental theorem of calculus links the two. These ideas will be applied to problems from many other disciplines. Note: Required first meeting in fall: Wednesday, September 4, 8:30 am, Science Center C . This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: A solid background in precalculus. Mathematics 18 (formerly Mathematics 20). Multivariable Calculus for Social Sciences Catalog Number: 0906 Meredith Hegg Half course (fall term). M., W., F., at 9. EXAM GROUP: 2 Focus on concepts and techniques of multivariable calculus most useful to those studying the social sciences, particularly economics: functions of several variables; partial derivatives; directional derivatives and the gradient; constrained and unconstrained optimization, including the method of Lagrange multipliers. Covers linear and polynomial approximation and integrals for single variable and multivariable functions; modeling with derivatives. Covers topics from Math 21a most useful to social sciences. Note: Should not ordinarily be taken in addition to Mathematics 21a or Applied Mathematics 21a. Mathematics 21b can be taken before or after Mathematics 18. Examples draw primarily from economics and the social sciences, though Mathematics 18 may be useful to students in certain natural sciences. Students whose main interests lie in the physical sciences, mathematics, or engineering should consider Math or Applied Mathematics 21a. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning. Prerequisite: Mathematics 1b or equivalent, or a 5 on the BC Advanced Placement Examination in Mathematics. Mathematics 19a. Modeling and Differential Equations for the Life Sciences Catalog Number: 1256 John Hall (fall term) and John Wes Cain (spring term) Half course (fall term; repeated spring term). M., W., F., at 1, and a weekly discussion section to be arranged. EXAM GROUP: 6 Considers the construction and analysis of mathematical models that arise in the life sciences, ecology and environmental life science. Introduces mathematics that include multivariable calculus, differential equations in one or more variables, vectors, matrices, and linear and non-linear dynamical systems. Taught via examples from current literature (both good and bad). Note: This course is recommended over Math 21a for those planning to concentrate in the life sciences and ESPP. Can be taken with or without Mathematics 21a,b. Students with interests in the social sciences and economics might consider Mathematics 18. This course can be taken before or after Mathematics 18. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Mathematics 19b. Linear Algebra, Probability, and Statistics for the Life Sciences Catalog Number: 6144 Peter M. Garfield Half course (spring term). M., W., F., at 1, and a weekly problem section to be arranged. EXAM GROUP: 6 Probability, statistics and linear algebra with applications to life sciences, chemistry, and environmental life sciences. Linear algebra includes matrices, eigenvalues, eigenvectors, determinants, and applications to probability, statistics, dynamical systems. Basic probability and statistics are introduced, as are standard models, techniques, and their uses including the central limit theorem, Markov chains, curve fitting, regression, and pattern analysis. Note: This course is recommended over Math 21b for those planning to concentrate in the life sciences and ESPP. Can be taken with Mathematics 21a. Students who have seen some multivariable calculus can take Math 19b before Math 19a. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Mathematics 23a. Linear Algebra and Real Analysis I Catalog Number: 2486 Paul G. Bamberg Half course (fall term). Tu., Th., 2:30-4. EXAM GROUP: 16, 17 A rigorous, integrated treatment of linear algebra and multivariable differential calculus, emphasizing topics that are relevant to fields such as physics and economics. Topics: fields, vector spaces and linear transformations, scalar and vector products, elementary topology of Euclidean space, limits, continuity, and differentiation in n dimensions, eigenvectors and eigenvalues, inverse and implicit functions, manifolds, and Lagrange multipliers. Note: Course content overlaps substantially with Mathematics 21a,b, 25a,b, so students should plan to continue in Mathematics 23b. See the description in the introductory paragraphs in the Mathematics section of the catalog about the differences between Mathematics 23 and Mathematics 25. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: Mathematics 1b or a grade of 4 or 5 on the Calculus BC Advanced Placement Examination, plus an interest both in proving mathematical results and in using them. Mathematics 25a. Honors Linear Algebra and Real Analysis I Catalog Number: 1525 Benedict H. Gross Half course (fall term). M., W., F., at 10. EXAM GROUP: 3 A rigorous treatment of linear algebra. Topics include: Construction of number systems; fields, vector spaces and linear transformations; eigenvalues and eigenvectors, determinants and inner products. Metric spaces, compactness and connectedness. Note: Only for students with a strong interest and background in mathematics. There will be a heavy workload. May not be taken for credit after Mathematics 23. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: 5 on the Calculus BC Advanced Placement Examination and some familiarity with writing proofs, or the equivalent as determined by the instructor. Mathematics 25b. Honors Linear Algebra and Real Analysis II Catalog Number: 1590 Noam D. Elkies Half course (spring term). M., W., F., at 10. EXAM GROUP: 3 A rigorous treatment of basic analysis. Topics include: convergence, continuity, differentiation, the Riemann integral, uniform convergence, the Stone-Weierstrass theorem, Fourier series, differentiation in several variables. Additional topics, including the classical results of vector calculus in two and three dimensions, as time allows. Note: There will be a heavy workload. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: Mathematics 23a or 25a or 55a. Mathematics 55a. Honors Abstract Algebra Catalog Number: 4068 Dennis Gaitsgory Half course (fall term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17 A rigorous treatment of abstract algebra including linear algebra and group theory. Note: Mathematics 55a is an intensive course for students having significant experience with abstract mathematics. Instructors permission required. Every effort will be made to accommodate students uncertain of whether the course is appropriate for them; in particular, Mathematics 55a and 25a will be closely coordinated for the first three weeks of instruction. Students can switch between the two courses during the first three weeks without penalty. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Mathematics 55b. Honors Real and Complex Analysis Catalog Number: 3312 Dennis Gaitsgory Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17 A rigorous treatment of real and complex analysis. Note: Mathematics 55b is an intensive course for students having significant experience with abstract mathematics. Instructors permission required. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Mathematics 60r. Reading Course for Senior Honors Candidates Catalog Number: 8500 Peter B. Kronheimer Half course (fall term; repeated spring term). Hours to be arranged. Advanced reading in topics not covered in courses. Note: Limited to candidates for honors in Mathematics who obtain the permission of both the faculty member under whom they want to work and the Director of Undergraduate Studies. May not count for concentration in Mathematics without special permission from the Director of Undergraduate Studies. Graded Sat/Unsat only. Mathematics 99r. Tutorial Catalog Number: 6024 Peter B. Kronheimer and members of the Department Half course (fall term; repeated spring term). Hours to be arranged. Supervised small group tutorial. Topics to be arranged. Note: May be repeated for course credit with permission from the Director of Undergraduate Studies. Only one tutorial may count for concentration credit. For Undergraduates and Graduates See also Applied Mathematics and Statistics. Mathematics 101. Sets, Groups and Topology Catalog Number: 8066 Adam Jacob Half course (fall term). M., W., F., at 11. EXAM GROUP: 4 An introduction to rigorous mathematics, axioms, and proofs, via topics such as set theory, symmetry groups, and low-dimensional topology. Note: Familiarity with algebra, geometry and/or calculus is desirable. Students who have already taken Mathematics 23a,b, 25a,b or 55a,b should not take this course for credit. This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning. Prerequisite: An interest in mathematical reasoning. Mathematics 116. Real Analysis, Convexity, and Optimization Catalog Number: 5253 Paul G. Bamberg Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14 Develops the theory of convex sets, normed infinite-dimensional vector spaces, and convex functionals and applies it as a unifying principle to a variety of optimization problems such as resource allocation, production planning, and optimal control. Topics include Hilbert space, dual spaces, the Hahn-Banach theorem, the Riesz representation theorem, calculus of variations, and Fenchel duality. Students will be expected to understand and invent proofs of theorems in real and functional analysis. Prerequisite: Mathematics 23ab, 25ab, or 55ab, or Mathematics 21ab plus at least one other more advanced course in mathematics. Mathematics 117. Probability and Random Processes with Economic Applications Catalog Number: 45584 Sukhada Fadnavis Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17 A self-contained treatment of the theory of probability and random processes with specific application to the theory of option pricing. Topics: axioms for probability, calculation of expectation by means of Lebesgue integration, conditional probability and conditional expectation, martingales, random walks and Wiener processes, and the Black-Scholes formula for option pricing. Students will work in small groups to investigate applications of the theory and to prove key results. Note: A problem-solving section is required MW 2-3 or Th 7:30-9:30 PM Prerequisite: A thorough knowledge of single-variable calculus and infinite series, plus at least one more advanced course such as MATH E-23a that provides experience with proofs and elementary real analysis. Acquaintance with elementary probability is desirable. [Mathematics 141. Introduction to Mathematical Logic] Catalog Number: 0600 Instructor to be determined Half course (fall term). M., W., F., at 11. EXAM GROUP: 4 An introduction to mathematical logic with applications to computer science and algebra. Formal languages. Completeness and compactness of first order logic. Definability and interpolation. Decidability. Unsolvable problems. Computable functions and Turing machines. Recursively enumerable sets. Transfinite induction. Note: Expected to be given in 2014–15. Prerequisite: Any mathematics course at the level of Mathematics 21a,b or higher, or permission of instructor. Mathematics 143. Set Theory Catalog Number: 6005 Peter Koellner Half course (fall term). W., 1–3. EXAM GROUP: 6, 7 An introduction to set theory covering the fundamentals of ZFC (cardinal arithmetic, combinatorics, descriptive set theory) and the independence techniques (the constructible universe, forcing, the Solovay model). We will demonstrate the independence of CH (the Continuum Hypothesis), SH (Suslins Hypothesis), and some of the central statements of classical descriptive set theory. Note: An additional hour of lecture will be scheduled independently. Prerequisite: Any mathematics course at the level of Mathematics 21a or higher, or permission of instructor. Mathematics 145. Set Theory II - (New Course) Catalog Number: 19964 Peter Koellner Half course (spring term). W., 1–3, and an additional hour of lecture will be scheduled independently. EXAM GROUP: 6, 7 An introduction to the hierarchy of axioms of infinity in set theory, their applications and their inner models. Note: An additional hour of lecture will be scheduled independently. [Mathematics 152. Discrete Mathematics] Catalog Number: 8389 ---------- Half course (spring term). M., W., F., at 11. EXAM GROUP: 4 An introduction to finite groups, finite fields, finite geometry, discrete probability, and graph theory. A unifying theme of the course is the symmetry group of the regular icosahedron, whose elements can be realized as permutations, as linear transformations of vector spaces over finite fields, as collineations of a finite plane, or as vertices of a graph. Taught in a seminar format, and students will gain experience in presenting proofs at the blackboard. Note: Expected to be given in 2014–15. Students who have taken Mathematics 23a,b, 25a,b or 55a,b should not take this course for credit. Mathematics 154. Probability Theory Catalog Number: 4306 Clifford Taubes Half course (fall term). M., W., F., at 12. EXAM GROUP: 5 An introduction to probability theory. Discrete and continuous random variables; distribution and density functions for one and two random variables; conditional probability. Generating functions, weak and strong laws of large numbers, and the central limit theorem. Geometrical probability, random walks, and Markov processes. Note: This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning and the Core area requirement for Quantitative Reasoning. Prerequisite: A previous mathematics course at the level of Mathematics 19ab, 21ab, or higher. For students from 19ab or 21ab, previous or concurrent enrollment in Math 101 or 112 may be helpful. Freshmen who did well in Math 23, 25 or 55 last term are also welcome to take the course. [Mathematics 168. Computability Theory] Catalog Number: 31297 ---------- Half course (spring term). M., W., F., at 12. EXAM GROUP: 5 An introduction to computability theory (also known as recursion theory). A discussion of the problem of determining what it means for a set or function to be computable, including primitive recursion, Turing machines, and the Church-Turing Thesis. The theory of Turing degrees and the computably enumerable sets. Topics: the halting set, Turing reducibility and other reducibilities, Posts problem, the Recursion Theorem, priority arguments, and more. Note: Expected to be given in 2014–15. Prerequisite: The student must have the ability to read and write mathematical proofs. Mathematics 233a. Theory of Schemes I Catalog Number: 6246 Igor Andreevich Rapinchuk Half course (fall term). M., W., F., at 11. EXAM GROUP: 4 An introduction to the theory and language of schemes. Textbooks: Algebraic Geometry by Robin Hartshorne and Geometry of Schemes by David Eisenbud and Joe Harris. Weekly homework will constitute an important part of the course. Prerequisite: Mathematics 221 and 232a or permission of instructor. Mathematics 265x. Reasoning via Models - (New Course) Catalog Number: 73059 Enrollment: Limited to 20. Eric S. Maskin, Barry C. Mazur, and Amartya Sen Half course (fall term). Tu., 2–4. EXAM GROUP: 15, 16, 17 An examination of how formal models are used in different disciplines. Examples will be taken from economics, mathematics, physics and philosophy, among other fields. Note: This course may not be counted towards the required eight letter-graded half-courses in mathematics for the concentration requirement 1a, but may be counted as one of the four half-courses in mathematics or related fields, requirement 1b. This is cross-listed in Economics, History of Science, and Philososphy. Prerequisite: There are no specific course prerequisites, but ease and familiarity with formal reasoning is essential. Mathematics 270x. Topics in Automorphic Forms - (New Course) Catalog Number: 70229 Benedict H. Gross Half course (fall term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13 We will give an introduction to the theory of modular and automorphic forms, with an emphasis on applications to algebraic number theory. Topics to be covered include the formalism of L-groups, functoriality, trace formulae, and the construction by Chenevier and Clozel of number fields with limited ramification. Nature of Evidence Professor Noah Feldman, FAS Professor Barry Mazur Fall 2012 Seminar Meets: Th 1:00pm - 3:00pm in WCC Room 3008 2 classroom credits Co-taught with mathematician Barry Mazur, this interdisciplinary, cross-listed class will explore and compare the nature of evidence and proof in a number of different fields: law, mathematics, the sciences, social sciences, and humanities. It will ask: What is considered evidence? How does what counts as evidence illuminate what it means to say we want to know and understand the truth? How can we communicate it across disciplines and contexts? Permission of instructors required. Single paper. Background in allied fields helpful but not required.
Multiplication with Exponents Division with Exponents Operations with Monomials Addition and Subtraction of Polynomials Multiplication with Polynomials Binomial Squares and Other Special Products Dividing a Polynomial by a Monomial Dividing a Polynomial by a Polynomial Summary Review Cumulative Review Test Projects 5. FACTORING The Greatest Common Factor and Factoring by Grouping Factoring Trinomials More Trinomials to Factor The Difference of Two Squares Factoring: A General Review Solving Equations by Factoring Applications Summary Review Cumulative Review Test Projects Review of Solving Equations Equations with Absolute Value Compound Inequalities and Interval Notation Inequalities Involving Absolute Value Factoring the Sum and Difference of Two Cubes Review of Systems of Equations in Two Variables Systems of Equations in Three Variables Summary Review Cumulative Review Test Projects 8. EQUATIONS AND INEQUALITIES IN TWO VARIABLES The Slope of a Line The Equation of a Line Linear Inequalities in Two Variables Introduction to Functions Function Notation Algebra with Functions Variation Summary Review Cumulative Review Test Projects Used, Acceptable Condition, may show signs of wear and previous use. Please allow 4-14 business days for delivery. 100% Money Back Guarantee, Over 1,000,000 customers served. $132132.20 +$3.99 s/h New Textbookcenter.com Columbia, MO Ships same day or next business day! UPS(AK/HI Priority Mail)/ NEW book $142.95 +$3.99 s/h New Textbook Barn Woodland Hills, CA PAPERBACK New 0534398790 Premium Books are Brand New books direct from the publisher sometimes at a discount. These books are NOT available for expedited shipping and may take up to 14 business day...show mores to receive. ...show less $172.25
Discrete Mathematics for Computer Scientists (2nd Edition) This is a new edition of a successful introduction to discrete mathematics for computer scientists, updated and reorganised to be more appropriate for the modern day undergraduate audience. Discrete mathematics forms the theoretical basis for computer science and this text combines a rigorous approach to mathematical concepts with strong motivation of these techniques via practical examples. Customer Reviews: Packed, pithy, and clear! By Zak Goichmann "Equosia -+*" - August 28, 2005 I will have to agree with the other reviewer that it seems as if Truss is trying to cram lots and lots of discrete mathematics into an indiscrete stack of 500pp but i think he has done very well. At least in addressing those who need to skim over the material quickly, though they would love instead to relish on Grimaldi's. :) Skims the Surface By Paul "kras" - December 12, 2000 I am a teacher's assistant for an undergraduate computer science course that uses this book. I have to say that it really is a terrible book for students to learn from who have never had much exposure to non-calculus math and the concept of the "mathematical proof". It skims over topics without providing enough exposition on the topics to allow students to have a fair grasp on the subject. This may just be the nature of teaching discrete math, but there seem to be far too many topics that Truss is trying to squeeze into too small of a space. He tries to throw in some more advanced topics such as formal machines and complexity theory, but only at the cost of having the overall quality of the material be watered down. Sadly, though, from what I have heard, this is the best current intro discrete math book out there. This book introduces readers to the mathematics of computer science and prepares them for the math they will encounter in other college courses. It includes applications that are specific to computer ... The two-volume textbook Comprehensive Mathematics for the Working Computer Scientist, of which this is the second volume, is a self-contained comprehensive presentation of mathematics including sets, ... Helps you understand the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. This work also helps you to rediscover the mathematical techniques ...
match the emphasis in today's courses, this clear study guide focuses entirely on plane trigonometry. It summarizes the geometry properties and theorems that prove helpful for solving trigonometry problems. Also, where solving problems requires knowledge of algebra, the algebraic processes and the basic trigonometric relations are explained carefully. Hundreds of problems solved step by step speed comprehension, make important points memorable, and teach problem-solving skills. Many additional problems with answers help reinforce learning and let students gauge their progress as they go.
Precalc is Algebra 2 on steroids. Lots of topics and concepts, lots of methods, lots of tough problem solving. Any weakness that a student has in Algebra will be exposed here and must be addressed to succeed in this course. ...With help anyone can overcome their math anxiety and succeed. Most math hiccups come from fear rather than any inability. The most important key to success is finding the appropriate means of learning for the student and consistent work.
Video 1 in this series that will take you from your A-Level maths through to a reasonable, detailed understanding of Fast Fourier Transforms - enough to implement a Cooley-Tukey algorithm and to use other FFT implementations! This is video 1 in the series. It introduces the series and presents an explanation of Fourier Transforms and gives a general overview of what they do and how they can be used. It also shows some graphical examples of basic combinations of sine waves and their transforms along with presenting ideas about noise suppression. This series will take you from your A-Level maths through to a reasonable, detailed understanding of Fast Fourier Transforms - enough to implement a Cooley-Tukey algorithm and to use other FFT implementations! The series looks at a general knowledge of Fourier Transforms through to conceptual understanding and then looks at the maths from the continuous Fourier Transform to the 2-Radix Cooley-Tukey algorithm for the Fast Fourier Transform. The series uses simple examples with graphical samples to aid understanding. Videos 2 and 3 of the series look at the maths behind Fourier Transforms with some basic proofs and Videos 3 and 4 look at the discrete and fast Fourier Transforms and why they work.
It probably is. I don't remember it being taught that way, though - I remember the term "compounding," but there was no real-world stuff in any of it. I have a few math degrees myself. Just from my recollections: From the times I TA'd and, later, taught calculus, there were always examples of compounding interest problems. Later in advanced calc there was the derivation of e shown as an example of taking the limit of compounding period down to zero. Then there are all of the financial examples in prob/stat if you go that route. That being said, I agree with Peter Lynch when he said (paraphrasing) that all the math you'll ever need for financial matters you should have learned by junior
New Tech Network Exemplary Project Project Title: Can You Hear Me Now? Subject: Math Course: AlgebraTable of Contents Teacher Materials and Resources 3-6 Project Documents and Instructions 7-15 Project Related Resources and Links 16-21 Assignments and Homework 22-27 Assessment and Evaluation 28-31 Please note: The following page (2) is a screen capture taken from the NTN Echo New Tech Project Library. The remaining pages (3-31) are the individual Project Resources that exist within this project's Project Briefcase. They have been compiled into this document to facilitate their access and viewing. Subject: Math Course: Algebra Project Title: Can You Hear Me Now?PROJECT BRIEFCASE Teacher Materials and Resources Project Library Submission Form  Facts and Stats o Subject Areas: Algebra I o Length (Weeks): 3 o Grade Levels: 9th o Quarter Used: 1st  Project Summary: Students will analyze cell phone plans in order to make a recommendation to customers on which plan is best for their needs. Students will also research phone plans online, and find the plan that is right for their own daily usage.  Project Overview: In this project students will be investigating 4 different cell phone plans and making a recommendation to customers about which plan best fits their needs. Each plan will be presented to the students in a different format: written text, graphically, function form, and table form. Students must identify key information, create a table and graph, and write a function for each plan. Following their analysis, they will make recommendations to 3 customers with different cell phone needs. They must support their recommendations with the data they have collected. The main objectives of this project are to introduce the students to function notation, develop their skills of writing and graphing functions, and to be able to identify the domain and range of a function.  Content Standards Addressed o 17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression. o 18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.  21st Century Skills Addressed o Written Communication: Students created a written report which described their findings o Oral Communications: Students presented their findings to a customer o Technology Literacy: Students used excel to graph and creating a power point presentation o Collaboration: Students worked in a group on daily assignments and to complete the project o Critical Thinking: Students looked at calculations, graphs, and data in order to make a recommendation to a customer o Math Content: Students learned how to identify variables, write equations, make tables and graphs, and analyze information  Driving Question or Problem Statement: How can we analyze data for key information and represent it in different formats?  Scaffolding Activities and Assignments o Determine what information should be included in a cost analysis of a cell phone plan o Analyze each plan: write a function, create a table, create a graph, find the cost per minute, etc. o Make a recommendation for each customer based on their needs  Final Product(s) and Assessment Methods o Scaffolding Activities  Cost Analysis  Presentation to Customer o How is it assessed? (peer, panel, presentation)  Project Resources (books, movies, web links, materials and supplies): Online Math Help (  Teacher Notes and Comments (suggestions, next steps, etc.): Each plan is presented in a different format so that students get used to analyzing data in a variety of ways. It also gives them an example of what a function, graph, or table looks like. They can work off of these examples to create their own functions, graphs, etc. This project was a great way to introduce function notation. The students could see the value of using appropriate variables in their equations. It also made the idea of domain and range easy to understand because it was tied to a real world example. I started each class with a warm-up that connected the project with the concepts being taught. This allowed for time to clarify any confusion or to discuss any new ideas. Another key piece of the project was that I had the students come up with the criteria for the cost analysis. This gave the students more ownership over the project. Finally, I had parents act as the customers. They were given surveys to fill out which assessed the student's presentation and knowledge. This made the project seem more realistic to the students. Teacher Guidelines and Instructions  Summary: In this project students will be investigating 4 different cell phone plans and making a recommendation to customers about which plan best fits their needs. Each plan will be presented to the students in a different format, including in written text, graphs, and function form. Students must identify key information, create a graph, and write a function for each plan. Following their analysis, they will make recommendations to 3 customers with different cell phone needs. They must support their recommendations with the data they have collected.  Driving Question: How can we analyze data for key information and represent it in different formats? Project Calendar  Day 1: Project Launch o read entry document o group contracts o read customer profiles o brainstorm key information  Day 2: Report Outline o Decide on key information for report o Determine monthly charges and cost per minute of each plan o Lesson on functions - function notation / domain and range o HW 1  Day 3: Creating a Table and Graph o Complete a table for minutes and monthly fees of each plan o Lesson on Piece-wise functions o HW: Graph each plan using your tables  Day 4: Writing Functions o Graph plans on the computer o Lesson - writing and evaluating functions o Write each plan as a function o Begin working on key information o HW 2  Day 5: Draft of Report o Customer Questions Journal o Work on a rough draft of your report o Review functions - evaluating, domain and range, graphing o HW 3  Day 6: Work on Project o Work on reports - complete all key information, begin working on a recommendation for each customer o Review o HW: Review Problems  Day 7: Quiz o Work on reports - finalize recommendations o Prepare for presentations - complete presentation plan o QUIZ  Day 8: Project Due/Meet the Customers o Turn in final draft of report o Present reports to customers (have customers fill out a survey for each group) Journal Prompts Used  Please review the customer profiles and key information below. If there is any information you feel your group needs in order to complete your analysis, please submit those questions in a response. o Customer Profiles o Key Information Warm-ups  Warm-up #1 The following graph shows the monthly fee for Cellular Plus. Use the graph to answer the following questions: 1. What is the monthly fee? 2. How many minutes are included in the monthly fee? 3. If a customer goes over the minutes included in the fee, how much will they be charged per minute? 4. What would the customer pay if they used 700 minutes?  Warm-up #2 Cellular Now charges $35.00 per month for 250 minutes. All additional minutes are $.20. 1. Find the monthly fee for each of the minutes listed below: Total Minutes Monthly Fee 100 200 300 400 500 2. Does this plan represent a function? Why or why not? 3. If the plan is a function, list the domain and range. 4. Write an equation for the plan in function notation. 5. Graph the plan below  Warm-up #3 Cell Star is offering a cell phone plan for $60 per month for 600 minutes. Any additional minutes are $.60 per minutes. 1. Write a function for the plan 2. Use the functions to find the fee for using 1000 minutes 3. If the domain of the function is {200, 300, 400} find the range of the function  Warm-up #4 1. If f(x) = -3x ? 2, evaluate when x = 4 2. If c(t) = 2t ? 5 and the domain is {1, 4, 10}, find the range 3. If f(x) = 5x3 + 2x2 ? x + 1, evaluate when x = t Functions Quiz Recognitions: This project was adapted from curriculum produced by Ready to Teach: Project Documents and Instructions Group Contracts Please complete a group contract. You may use the template below or create your own. Group Contract  I. Members: o Please list all group member names  II. Absence Policy o What is your policy for a group member being absent the day of a presentation or when an assignment is due?  III. Work Policy o What is the policy on contributing to the group, meeting deadlines, and sharing the workload? o What if one of your group members commits plagiarism?  IV. Leadership o Who will be your group leader? o What is the role of the group leader?  V. Member Dismissal o What circumstances will lead to a member being dismissed? o Will your group vote to dismiss a member? o Can a group member leave under their own will? o Who will maintain possession of the work completed prior to a member leaving the group? Project Calendar Monday Tuesday Wednesday Thursday Friday Read entry doc Decide on key information for report Group Contracts Determine monthly Read customer profiles charges and cost per minute of each plan Brainstorm key information Lesson on functions HW 1 Lesson on writing and Complete a table for evaluating functions Submit questions to minutes and monthly customers fees of each plan Write each plan as a function Work on a rough draft Lesson on Piece-wise of your report functions Begin working on key information Review functions HW: Graph each plan using your tables HW 2 HW 3 Work on reports Prepare for Project Due presentations Review Presentations Quiz HW: Review Customer Profiles Celia, Jim, and Linda have consulted Cell Zone for assistance in choosing a wireless plan that is right for each of them. They have supplied Cell Zone with the following information about the cell phone usage: Customer Name Profile Celia is an attorney who spends most of her time in court, so she has to conduct her daily business between sessions. She spends over two hours Celia on her cell phone each day, checking with her assistant and returning calls to clients. She also travels among four courthouses, and needs to call ahead if she is going to arrive late. Jim is a retired pediatrician who lives alone and spends the winter months in Florida. He is writing a book about asthma with a colleague, and confers Jim with him by phone for about an hour each week. Jim also likes to check in with his children and their families on weekends. On weekdays during the day, he occasionally calls friends up north to socialize, or calls his grandchildren after they're home from school to hear about their day. Linda is a high school math teacher who has a one-year-old daughter and an ailing mother at home. She has an aide, Fiora, who stays with them Linda while Linda is at work. Linda calls home several times a day, and has also instructed Fiora to call her if there is any kind of emergency. But the school phone is often tied up. Linda wants to purchase a cell phone so that she can check in with Fiora during her free periods, call her husband, or take care of errands by phone when she can grab a few minutes. Phone Plans Analyzing a Cell Phone Plan: Your three customers are anticipating a report from you with key information about available plans. Your manager would like to know what information you are going to be presenting. As a group, brainstorm ideas about what information should be included in your report. Be sure to consider how needs of customers differ, as well as how different plans have very different fees and limitations. Key Information for Report  Your group will meet with each of the 3 customers. During your meeting, please provide a report on the following information for each plan: 1. Monthly fee 2. Number of peak minutes included in monthly fee 3. Cost per minute (beyond peak minutes) 4. Fee for night and weekend minutes 5. Long distance and/or roaming charges 6. Monthly cost for 100 - 1000 minutes (in the form of a table) 7. A graph for each plan (done on the computer) 8. A function (equation) for each plan 9. Pros and Cons of each plan  When you have completed all of the above tasks for each plan, your group will need to review the information and make a recommendation for each customer, as outlined below: 10. Customer recommendation - which plan should they choose and why?  Be sure to use specific information about the customer and each plan  You will need to submit a typed copy of your report Analyzing Monthly Fees (part 1)  When you meet with each of your 3 customers, you need to be able to tell them which plan is the cheapest for different monthly minutes.  In order to do this you will need to find the monthly fee of each plan, for the minutes listed below.  Begin by filling in the following tables: o Verizon Cingular o T-Mobile AT & T Analyzing Monthly Fees (part 2)  Complete the tables below and graph the information for each plan on a separate graph. o Verizon AT & T o Cingular T-Mobile Finding a Plan That's Right for You Research cell phone plans online. Decide which plan is best for your own usage and do an analysis of that plan. Explain why you selected that plan, what your monthly fee would be for at least 3 different monthly minutes, provide a graph, and write a function. Customer Satisfaction Survey Customer Satisfaction Survey Please help us serve you and others better by completing our Customer Satisfaction Survey. Your participation will help ensure that Cell Zone representatives are providing customers with useful, accurate, and complete information. Did the Cell Zone Representatives… (1 = did not meet expectations, 5 = exceeded expectations) 1. Clearly answer all of your questions? 1 2 3 4 5 2. Provide a recommendation that will best meet your needs? 1 2 3 4 5 3. Provide sufficient information about each available plan? 1 2 3 4 5 4. Provide clear and informative graphics, such as tables or charts? 1 2 3 4 5 5. Appear to be professional and knowledgeable? 1 2 3 4 5 Please provide any additional information or comments below: Thank you for your time and feedback! Project Related Resources and Links Notes on Functions I. Key terms: Function: A set of points or equation where every input has exactly one output. In other words, for every x, there is only one} Range: The set of all y-coordinates in a function. Ex) The range of the function above is {3, 0, 5} II. Function Notation a. Whatb. Why do we use function notation? Function notation helps to specify what an equation is talking about. By using variables that represent the quantities in the problem, we are making our work more clear and precise. c. How... d(t) = 50t III. Evaluating a Function a. Remember that parenthesis in function notation do not indicate multiplication. "f(x)" means "plug in a value for x". b. You evaluate a function just as you would evaluate any equation. Substitute or plug in the value of x. Ex) Given f(x) = 3x2 + 5x ? 6, evaluate at x = 2. f(2) = 3(2)2 + 5(2) ? 6 f(2) = 3(4) + 5(2) ? 6 f(2) = 12 + 10 ? 6 f(2) = 22 ? 6 f(2) = 16 This means (2, 6) is a point in the function. IV. Piecewise Functions a. A piecewise function is any function that is in, well, pieces! b. Piecewise functions usually indicate intervals for each part of the function. Ex) f(x) =). f(t) = 6t + 8 VI. Finding the Range a. You can use a function and its given domain to find its range. Evaluate the function at each given value of the domain. Ex) Given f(x) = 3x ? 5 and the domain is {0, 2, -1} find the range. f(0) = 3(0) ? 5 = -5 f(2) = 3(2) ? 5 = 1 f(-1) = 3(-1) ? 5 = -8 Therefore the range is {-5, 1, -8}. VII. Graphing a Function a. Ifxy 01 12 23 34 45 56 Functions Review I. Key terms: Function: A set of points or equation where every input has exactly one output. In other words, for every x, there is only one}. Range: The set of all y-coordinates in a function. Ex) The range of the function above is {3, 0, 5}. II. Function Notation WhatWhy do we use function notation? Function notation helps to specify what an equation is talking about. By using variables that represent the quantities in the problem, we are making our work more clear and precise. How… d(t) = 50t III. Evaluating a Function Remember that parenthesis in function notation do not indicate multiplication. "f(x)" means "plug in a value for x". You evaluate a function just as you would evaluate any equation. Substitute or plug in the value of x. Ex) Given f(x) = 3x2 + 5x – 6, evaluate at x = 2. f(2) = 3(2)2 + 5(2) – 6 f(2) = 3(4) + 5(2) – 6 f(2) = 12 + 10 – 6 f(2) = 22 – 6 f(2) = 16 This means (2, 6) is a point in the function. IV. Piecewise Functions A piecewise function is any function that is in, well, pieces! Piecewise functions usually indicate intervals for each part of the function. 2 x  1 x2  Ex) f(x) =  x4 x2) f(t) = 6t + 8 VI. Finding the Range You can use a function and its given domain to find its range. Evaluate the function at each given value of the domain. Ex) Given f(x) = 3x – 5 and the domain is {0, 2, -1} find the range. f(0) = 3(0) – 5 = -5 f(2) = 3(2) – 5 = 1 f(-1) = 3(-1) – 5 = -8 Therefore the range is {-5, 1, -8}. VII. Graphing a Function IfWeb sites that may be useful for this project: Online Math Help ( Assignments and Homework Functions HW 1 State the domain and range for each. Is the relation a function? 1. {(6, -8), (-1, -3), (7, -3), (-7, -3), (1, 9)} 2. {(-3, 9), (7, -6), (2, 1), (4, -7), (4, -1), (1, -7)} 3. {(-3, -1), (-5, -9), (0, 3), (-5, 6)} 4. {(0, 4), (4, 4), (-8, -5)} 5. {(63, 152), (124, 152), (-13, 147), (-19, 152)} 6. {(-41, -78), (-35, 81), (-16, -119)} 7. {(21.44, -177.42), (48.36, -168.55), (48.36, -182.44)} 8. {(-11, -33), (19, -79), (51, -27)} 9. {(99, -166), (75, -154), (-34, 124)} 10. {(164, -118), (-19, -115), (-40, -118)} Solve: 11. n ÷ 28 = 2 12. 59 = a – 16 13. 66.4 = 16.6a 14. x - 32 = 12 15. x + 37 = 57 + 34 16. 14 + 57 = 49 + y b y 23214 2 17.  7.3 18.  19. x   11 11 53 318 11 1 2576 20. b 21. 2744 = 49a 22. 570 = 57a 14 56 Functions HW 2 Functions HW 3 Functions HW Review Assessments and Evaluation Content Rubric Oral Presentation Rubric Written Communication Rubric Content Standards Covered by this Unit  17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.  18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the
Mathematics and Statistics Courses The Courses The Department offers courses in mathematics and statistics for students with various interests and mathematical backgrounds. MATH 100 is a basic mathematics course which satisfies the General Education R1 requirement; it is not a pre-calculus course. The courses numbered 011, 101, 102, 103, and 104 are intended to assist the student in preparation for an introductory calculus course. MATH 127-128 is a calculus sequence for business and life and social science students. MATH 131-132 is the calculus sequence for students in fields such as mathematics, physics, chemistry, computer science, and engineering.
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing... This is an undergraduate textbook that reveals the intricacies of geometry. The approach used is that a geometry is a space together with a set of transformations of that space (as argued by Klein in his Erlangen programme). The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case the key results are explained carefully, and the relationships between the geometries are discussed. This richly illustrated and clearly written text includes full solutions to over 200 problems, and is suitable both for undergraduate courses on geometry and... This book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geometries associated with non-split extensions of symplectic groups over a field of two elements. Besides that there are twelve exceptional Petersen and tilde geometries. These exceptional geometries are related to sporadic simple groups, including the famous Monster group and this volume gives a construction for each of the Petersen and tilde... The link between the physical world and its visualization is geometry. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. The wide range of topics includes curve theory, a detailed study of surfaces, curvature,... The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above. The last part of the book... This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The... Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. It also has connections to discrete tomography, geometric probing in robotics and to stereology. This comprehensive study provides a rigorous treatment of the subject. Although... Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this...... This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are... The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal... Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential... Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the... Translating Euclid reports on an effort to transform geometry for students from a stylus-and-clay-tablet corpus of historical theorems to a stimulating computer-supported collaborative-learning inquiry experience. The origin of geometry was a turning point in the pre-history of informatics, literacy, and rational thought. Yet, this triumph of human intellect became ossified through historic layers of systematization, beginning with Euclid's organization of the Elements of geometry. Often taught by memorization of procedures, theorems, and proofs, geometry in schooling rarely conveys its... This work represents the first book to focus on basic algorithms for isosurface construction. It also gives a rigorous mathematical perspective on some of the algorithms and results. In color throughout, the book covers the Marching Cubes algorithm and variants, dual contouring algorithms, multilinear interpolation, multiresolution isosurface extraction, isosurfaces in four dimensions, interval volumes, and contour trees. It also describes data structures for faster isosurface extraction as well as methods for selecting significant isovalues. ... Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures,... The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar.... With numerous examples and exercises throughout, this book describes the control behavior of mechanical objects, such as wave equations, plates, and shells. It presents a complete and up-to-date account of many important advances in the modeling and control of vibrational and structural dynamics. The text applies the differential geometric approach to waves, plates, shells, and quasilinear systems and describes differential geometric energy methods that are generalizations of classical energy methods. To make the book self-contained, the author gives an introduction to Riemannian... Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as... The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book...
First in a three course sequence to prepare students for Math 1. Delivered at a slower pace than other preparatory math courses. Upon completion of the three course sequence, students must enroll in MATH 1.

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