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Algebra Problem Solver 1.00 (1 votes) Document Description Get answers to all Algebra problems Solver online with TutorVista. Our online Algebra tutoring program is designed to help you get all the answers to your Algebra word problems giving you the desired edge in excelling in the subject. To Online Algebra Questions Our FromAdd New Comment Mathematics is a subject that is included in every stream of education and its problems gets tougher as student moves further in his studies. That's why proper assistance in solving math problems is ... The current market trend, inflation and job scarcity is at its peak. It is a good idea to choose alternative career option and earn more money for a safe future. If you are looking for peaceful yet ... Get answers to all Algebra word problems online with TutorVista. Our online Algebra tutoring program is designedBefore talking about linear programming, I would like to tell you the meaning of "linear". Linear is a Latin word which means pertaining to or resembling a line. In mathematics, linear equation means ... In mathematics algebra plays very important role or we can say that the general math that we use in our day to day life is all about algebra. Algebra, and important math part consists of several ... Content Preview Algebra Problem Solver Get answers to all Algebra problems Solver FromThe digit can be arranged in 3 ways or 6 ways. We have already investigated 2 of these ways. We can now try one of the remaining 4 ways. One of these are n = 95 100n + 70 + 8 = 693 - 99n 199n = 615 After solving, we get n = 3 Answer: The unknown digit is 3. College Algebra Word Problem Solver Back to Top College Algebra problems Solver help students to solve the word problems step by step. They teach students how to understand the data given in the statement and solve for the value to be found out. The online Algebra tutors serve as Algebra Solver who would help students in interpreting the word problems. Let us go over a few important Math equivalents of English for numbers and algebra word problems so as to make the interpretation of word problems easier. * Add---- sum, total of, added to, together, increased by * Subtract-difference between, minus, less than, fewer than * Multiplication-of times, by a factor * Division-per, out of, ratio of, percent The above words are suggestive of the operations associated with them. Students can learn more in depth about them on understanding Algebra problems Solver and tke the help of online Algebra Solvers. Thank You TutorVista.com
Analysis: With an Introduction to Proof (4th Edition) By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises. A thorough reference for readers who need to increase or brush up on their advanced mathematics skills. Customer Reviews: Definitely a good first text By Charlie Johnson - September 4, 2002 I bought this book because I have been looking for a Introductory analysis text that isn't too advanced, but yet doesn't gloss over the essential stuff, and I found it in Lay's book. For the self-studier, this book is excellent! I have several books on analysis: Shilov, Kolomogorov, Rosenlicht, Ross,etc... For the beginner, this book is superior to all of them. A plethora of examples. Also, a good range of problems:from straight forward problems requiring only the use of a definition to more advanced problems requiring a little thought. If you already have had some Analysis, then this book is probably not for you. But, if you are a student who wants to learn Analysis on your own, then this book would be hard to beat. After this book, one should be able to tackle "Papa Rudin". For according to Rudin, all that is needed to study his "Real and Complex Analysis" tome, is the first seven chapters of his "Principles of Mathematical Analysis". This... read more This book was surprisingly good By Zachary Turner - July 2, 2002 I didn't think this book was going to be very good, but the author has "proved" me wrong ;-) This book starts out so basic that in my class (which was the first analysis course in our math department) we actually skipped the first 1/3 or so of the book. The first 9 or 10 sections consist of stuff like basic set theory, logic, definition of a function, etc. I would think that even the most elementary Analysis books would completely leave this out and expect that the reader is already familiar with this. So if you need it, this book will be a good resource for you.Then the book goes into a very nice introduction to topology. Basic concepts like open/closed sets, accumulation points, compact sets, etc. Topology can be a little intimidating simply because it's _so_ abstract, but this book makes the basic concepts very easy to understand, and prepares one for a more advanced course in topology. Alot of (good) Elementary Analysis books leave topology out, but I'm glad this book... read more Acceptable but could have been better. By Gregory E. Hersh - April 20, 2008 This is fairly basic introduction to Principles of Analysis, on intermediate undergrad level, strictly in R^1. The only other similar book I'm familiar is Kirkwood. The books of Rudin, Apostol, etc present the subject on much higher level. My original intention was to take a course with Rudin, but after I've realized I had a hard time digesting his style, I've decided to take more elementary course. I knew the course would be using Lay, so I got this textbook and tried to learn it on my own, but wasn't sure how I was doing and ended up taking the course (still with Lay) anyway. So I'm quite familiar with this textbook. The only topics we didn't cover is "series" and "sequences and series of functions". Now overall I would say it's a mixed bag. First, the good things. The first few introductory sections on sets and proof techniques are excellent, highly recommended, that's how I learned how to prove. I found exercises very useful.
Course at a glance... All assignments listed in one week are due by 6:00 a.m. the Monday of the following week. Tests must be taken on the date indicated either at 8:00-8:50 a.m. or at 4:00-4:50 p.m. in room Hibbard 101. All assignments assigned prior to a test are due PRIOR to the time the test is taken. Any homework practice or Quiz associated with the Unit that is NOT completed prior to taking the Test for that unit will be recorded as a "0". Be sure to have everything completed prior to taking the test! - Note: If additional help is needed throughout the course, see the tutors in the Math CARE Center in HHH 218 or check out other related videos at BrightStorm or Kahn Academy. Although you may find a calculator helpful to check your answers, you will need to fine tune your basic arithmetic skills without the aid of a calculator. Therefore, calculator-based examples and problems are not included in the assigned readings. Be sure you know your Basic Multiplication Facts. UNIT 1– be sure to list key concepts in this unit on workbook pages 21-22 For those wanting to complete Math 10 on the "Fast Track" and complete Math 20 prior to taking a summer class starting June 10, here is the Combined Detailed Schedule for 10 and 20. NOTE: one must register for and pay for Math 20 as a SUMMER special course for this option. One may also take a slower pace and complete the special SUMMER Math 20 by June 28 before the last half summer classes begin or in time for Fall. Both options of these special SUMMER offerings of Math 20 MUST be completed by 6/ 28.
Basic Mathematics : A Text/Work sections in Enhanced WebAssign to practice your skills and demons... MOREtrate your knowledge. The traditional text for the modern student--Pat McKeague's BASIC MATHEMATICS, 8E--is user-friendly for both students and instructors with concise writing, continuous review, and contemporary applications. Retaining its hallmark strengths of clarity and patience in explanation and concept development, this new edition contains new examples, applications, and a closer integration with Enhanced WebAssign. In a course in which many students enter with math anxiety, the author helps students connect mathematics to every day examples through the use of relevant applications and real data. In addition, Enhanced WebAssign, an online homework management system, is fully integrated with the new edition providing interactive, visual learning support with thousands of examples and practice exercises that reinforce the text's pedagogical approach.
MATH 50 - Pre-Algebra (3 units) This course covers the Fundamental principles of mathematics designed to ease the transition from arithmetic to algebra. Concepts, computational skills, thinking skills and problem-solving skills are balanced to build proficiency and mastery.
MatrixCalc What Is MatrixCalc? MatrixCalc is a matrix calculator written to eliminate the tedious task of manually multiplying matrices. It is especially useful for students taking Finite Mathematics courses, and anyone else who needs to determine the product of two matrices.
The following are activities that I have developed for TI-Nspire and TI-Nspire CAS. There is a brief explanation of the file(s), the Nspire files to download, and any accompanying files (like pdf's) for the student or teacher. Feel free to pass them along and please contact me with any suggestions. Completing the Square Parabolas Algebra 1, Algebra 2, Precalculus This document is designed to either introduce or review how to use "completing the square" to rewrite an equation of a parabola from standard form into vertex form. Four different examples will be illustrated, step-by-step. The graphs validate the work. Complex Numbers – An Introduction to i, Adding, Subtracting, Multiplying, and Powers of i Algebra 2, Precalculus This document assists the student in learning about the Imaginary Numbers for the first time. Explanations are supplied and 15 examples/exercises are illustrated for the student to do along with the document. I used this with great success in Algebra 2. Given the Roots of a Quadratic Equation, Find the Equation in Both Forms Algebra 2 The student is given the solutions (roots, zeros) to a quadratic equation and is asked to find the quadratic equation that has those solutions. The equation must be stated in both forms: Standard Form and Vertex Form. Three examples are illustrated completely followed by four exercises to be completed by the student. Thisformula is used to calculate the area of any triangle if given the lengths of the 3 sides. This very short document presents both parts of the formula and illustrates how to use it with an example. Each step is shown clearly. A great introduction to this topic. This document has 4 examples that clearly illustrate how to use the Law of Cosines to solve triangles with different sets of data supplied. Each step is clearly shown and a fifth example is supplied for the student to test his/her understanding. A great first day assignment. In fact, I used this in place of teaching the Law of Cosines this year! Two pdf documents are included as accompanying files. This document contains two examples. The first example illustrates how to use the sine function to calculate the area of a triangle given certain dimensions. The second example illustrates how to use the Law of Sines to solve a triangle given certain dimensions. This activity asks the student to find the rectangle with maximum area under a given parabola. To assist the student in generating the correct equation, there is an interactive graph that illustrates the many possible rectangles. And the student can check to see if his/her equation is correct by graphing on top of the data that is generated. MANUFACTURING A GALLON CAN -- A MINIMIZATION PROBLEMDesk Top Demonstration Calculus, Precalculus A metal can in the shape of a rectangular solid with a square base (top and bottom) is to be manufactured at a minimum cost for materials. Your responsibility is to find the dimensions of the can (to the nearest hundredth of an inch) that minimizes the cost (to the nearest tenth of a penny). This has an interactive graph/picture that shows all possible configurations for the can and its costs. This interactive activity is designed for the student to investigate how area bounded by a curve and the x-axis can be approximated with areas of rectangles using LRAM, RRAM, and MRAM. The student can change the function definition and see the resulting change in areas. The student can change the x-coordinate of the either endpoint of the interval. This uses only 4 rectangles. This program approximates the area bounded by a curve and the x-axis over a closed interval using LRAM, RRAM, MRAM. The student can decide the function, the left endpoint, the right endpoint, and the number of subintervals. A graph of a quadratic equation will be shown. Also shown is the equation of the parabola in vertex form: y = a(x - h)^(2) + v. The user is able to change any/all of the 3 parameters: a, h, v, and the graph will automatically change to reflect those changes in parameters. The student is slowly taken through how to solve a quadratic equation using the Quadratic Equation. Each step is shown and clearly explained. This is good to use as an introduction or to use as a review. A graph of a parabola will be shown. You are asked to find the equation of the parabola in vertex form: y = a(x - h)^(2) + v.Press enter on the double up arrow in the Ans section to see the answer. There are 19 different graphs. Great practice to learn about translations. This is the Nspire version of my all time favorite applied problem that can be used in Geometry, Trigonometry, or Calculus. I have 3 different versions of this: Student (handheld), Teacher (handheld), and a Dynamic Extension that is best used on a desktop. Interactive activity is designed for students to 'discover' what a fractional exponent means by using the Calculator APP to explore expressions like25 to the one-half power, or 64 to the one-third power. Students are shown how to factor expressions using several different techniques, each module shows a different technique. Module 1: GCF;Module 2: Sum and Difference of 2 Squares;Module 3: Trinomials by Trial 'n Success with leading coefficient 1;Module 4: Trinomials by Trial 'n Success with leading coefficient not 1;Module 5: Sum of 2 Cubes;Module 6: Difference of 2 Cubes;Module 7: By Grouping (4 terms);Module 8: Summary of previous 7 modules.Exercises are given and the correct answers are supplied using the Q & A feature of Nspire. This acitivity is designed for calculus students. Problem: you are given 100 feet of fence and you are to enclose a figure that looks like a basketball key: consisting of a rectangle with a semicircle attached to the top of the rectangle. Find the dimensions of this shape that uses 100 feet of fence to enclose it and also has the maximum area. Find that maximum area. This activity is designed for students to investigate how to calculate the distance from a point to a line. Multiple representations are used: pencil and graph paper, graphing calculator, CAS. Eventually the student will generate (derive) the Distance From a Point to a Line formulas using CAS. This activity uses the Notes Q & A feature to simulate electronic flash cards. Right now there are the trig unit circle values in both radian and degree modes, either from 0 to 2 pi or 0 to 360 degrees. More will be added later. This activity uses the Notes Q & A feature to simulate electronic flash cards. This is very similar to BG_1 except that the graphs have been translated. There are 17 Basic Graphs, each on its own "card". Students will be asked to state the equation that is graphed.
Type or write (neatly) your assignment on notebook-sized paper. If you handwrite your assignments, use a pen, since I find pencilled writing hard to read. Make sure that the reader can understand what the problem is without having to look it up. Be sure to leave plenty of space for comments. Usually you should leave a third of a page per proof, plus nice-sized margins. Be sure to staple the pages together. You should own a stapler by now, but if you forget, there is a stapler in the third floor computer lab. Make sure that you cut off the squigglies on paper ripped out of a spiral notembook. For problems that don't involve proofs, you should show enough work so that any student in the class can follow your solution. Just writing the answer is never enough. Proofs should be written in complete English sentences. Proofread what you have written to make sure it makes sense. Don't try to fake a proof. Instead, acknowledge the gap in your proof. Better yet, come talk with me beforehand and see if I can help you close the gap. Each mastery problem should be written on a separate page. Rewritten versions can be written at the bottom of the marked page, or on another page. Fasten together all versions of a problem, with the most recent version at the front. Practice problems will be submitted in class. Each Monday, you will submit the problems assigned for the previous week. They should be in a form that you find easy to read and review. Honor problemsshould be done completely on your own, without outside help from anyone, including me, other professors, your fellow students, webpages, etc.
TI-83/84 Plus and TI-89 Manual for Intro Stats Summary Organized to follow the sequence of topics in the text, and it is an easy-to-follow, step-by-step guide on how to use the TI-83/84 Plus and TI-89 graphing calculators. It provides worked-out examples to help students fully understand and use the graphing calculator.
Book Description: Make the grade with PRECALCULUS and its accompanying technology! With a focus on teaching the essentials, this streamlined mathematics text provides you with the fundamentals necessary to be successful in this course--and your future calculus course. Exercises and examples are presented in the same way that you will encounter them in calculus, familiarizing you with concepts you'll use again, and preparing you to succeed. In-text study aids further help you master concepts.
Book DescriptionMost universities recommend this for 1st year undergraduates, probably rightly. Varian is quite clear with intuitive explanations of the basic concepts. However in terms of the maths he becomes incredibly confusing, as he insists on relegating all calculus (which is vital to even 1st year micro) to appendices and using deltas (aka triangles) in the main text. This has three consequences. Firstly it makes his reasoning less rigorous. Secondly he doesn't really explain how the calculus relates to the intuitive concepts or present the mathematical steps in too much detail, so it is often difficult to follow. Thirdly you have to spend a lot of time piecing together proofs from triangles and actual partial derivatives if you want to make use of a proof for an essay or exercise. Some of my friends used the Perloff text (I think it's called microeconomic theory and applications of calculus or something like that) instead, and claimed it was better. I used Varian in first year and got a first in micro, but had to rely on my maths for economists textbook a lot. Definitely too basic for finalists. This is a great introductory intermediate text if that makes sense. It's more involved and mathematical than the micro section in a typical introductory economics textbook (nothing a good grasp of calculus won't cope with) but less challenging mathematically than an advanced intermediate student would expect. If you've outgrown the former but not yet the latter then this is perfick! Nothing more likely to discourage studying than struggling with both concepts and calculations at the same time. With Varian, you'll get the theory right which should set you (me) up for the hard work to come. Hal Varian's Intermediate Microeconomics was the recommended text book for my recent 2nd year micro economics module at university. The material is presented in a very clear and straightforward manner, using minimal mathematical notation. If you want to use a book to help you understand the actual concepts of intermediate microeconomics this is the book for you. The explanation of concepts is concise and the book covers the vast majority of topics covered in a 2nd year micro course. One word of warning; for most intermediate courses in economics in the UK this book falls short of the level of analytics likely to be required. It is however still a very useful complement to either a more technical text or lecture notes.
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Musimathics: The Mathematical Foundations of Music 9780262516563 MIT PRESS Music; Theory of music & musicology; Techniques of music & music tutorials; Mathematics Paperback 584 pages $46.95$42.25 In stock ready to ship order qty:Mathematics can be as effortless as humming a tune, if you know the tune, writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music--a commonsense, self-contained introduction for the nonspecialist reader.Volume 2 of Musimathics continues the story of music engineering begun in volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short time Fourier transform, and the wavelet transform. These subjects provide the theoretical underpinnings of today's music technology. The material in volume 1 is all preparatory to the subjects presented in this volume, although either volume can be read independently. Cross-references to volume 1 are provided for concepts introduced in the earlier volume, and additional mathematical orientation is offered where necessary. The topics are all subjects that contemporary composers, musicians, and music engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Additional material can be found at a companion web site. From his long and successful experience as a composer and computer-music researcher, Gareth Loy knows what is challenging and what is important. That comprehensiveness makes Musimathics both exciting and enlightening. The book is crystal clear, so that even advanced issues appear simple. Musimathics will be essential for those who want to understand the scientific foundations of music, and for anyone wishing to create or process musical sounds with computers. -- Jean-Claude Risset, Laboratoire de Mecanique et d'Acoustique, CNRS, France
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Short Description for Cambridge Checkpoint Maths: Student's Book Bk. 3 These market leading resources are used in schools throughout the world and are matched to the Curriculum Framework to provide superb support for you and your students. Full description Full description for Cambridge Checkpoint Maths: Student's Book Bk. 3 This widley-used and highly-respected Student's Book, for Cambridge Secondary 1 Maths, is fully matched to the Curriculum Framework, Cambridge Checkpoint Tests and the Cambridge Progression Tests. It includes sections on calculations and mental strategies that provide accessible guidance through these difficult topics. There are also chapters that focus on ICT, investigations and problem-solving, helping your students to apply Maths to real-life situations.
- Approximation of functions by polynomials: Chebyshev (best approximation, polynomial series), L2 norm (best average approximation, orthogonal polynomial series, Fourier series). - Interpolation of functions divided by polynomials: Lagrange and Newton formulas, divided differences, iterative methods of Neville, formulas of finished differences. - Numerical integration: Gaussian methods, formulas of finished differences. - Error estimation and applications: Peano theorem, Euler-Maclaurin formula, extrapolation to the limit (Romberg scheme, etc.) Modalities of organisation: exercises: in class, in relation with the material seen. This activity will receive a grade that will come into play in the final points. Exam: oral on the material seen in class (closed book), partially with written preparation. Aims In-depth analysis of diverse methods and algorithms representative in the matter of numerical resolution by computers of significant classes of scientific or technical problems, in relation with the themes underlying the applied mathematics Content See at the following address : Other information See at the following address :
Product Details: From the Publisher: Manhattan GMAT's Foundations of Verbal provides a refresher of the basic verbal concepts tested on the GMAT. Designed to be user-friendly for all students, this book provides easy-to-follow explanations of fundamental concepts and step-by-step application of these concepts to examples. It's an invaluable resource for students who want to cement their understanding of basic principles such as grammar, logic, and reading, while building core verbal skills for the GMAT. The content of this book is aligned to the Official Guide for GMAT Review, 13th Edition . Purchase of this book includes access to the Foundations of Verbal Homework Bank of extra practice questions and detailed explanations not included in the book, as well as to the Foundations of Verbal Bonus Drill Set.A comprehensive math review for the GRE, GMAT, and SAT. This math refresher workbook is designed to clearly and concisely state the basic math rules and principles of arithmetic, algebra, and geometry which a student needs to master. This ...
Traditional texts for this course include Ahlfors' Complex Analysis and Lang's book of the same title. Also useful is the second half of Rudin's Real and Complex Analysis. A weakness in the later parts of all these sources is in the treatment of algebraic functions, and of solutions to ordinary differential equations with regular singular points. And some so-called 'special functions' such as the gamma function deserve fuller treatment, especially with an eye to applications in other parts of mathematics. And the ultra-classical aspects of elliptic functions and modular forms deserve a quick and decisive treatment in this context, since all the crucial techniques at this level do really belong to 'complex analysis', as opposed to 'number theory' or anything else. And the connection between the Riemann Hypothesis on the zeta function and error terms in the Prime Number Theorem is hard to ignore, motivating as it did a great deal of work in classical complex analysis.
what maths courses to take? I am interested in getting a PhD in finance, in the area of asset pricing. So I am currently catching up with my mathematics background. I have decided to take some Statistics Theories and Stochastic Processes, but there's one more course that I can take. Which of the following you think is most important? 1, Mathematical Modeling and Applied Mathematics. 2, Numerical Analysis and Scientific Computing. 3, Theory of PDE. They are all PhD level courses offered by the Maths Department. Thank you for your suggestion. It's gonna be really helpful!
(Adopted from Chapter Zero Instructor Resource Manual by Carol Schumacher with a nod to Dr. Dana C. Ernst) Aside from the obvious goal of wanting you to learn how to write rigorous mathematical proofs, one of my principal ambitions is to make you the student independent of me. Nothing else that I teach you will be half so valuable or powerful as the ability to reach conclusions by reasoning logically from first principles and being able to justify those conclusions in clear, persuasive language (either oral or written). Furthermore, I want you to experience the unmistakable feeling that comes when one really understands something thoroughly. Much "classroom knowledge" is fairly superficial, and students often find it hard to judge their own level of understanding. For many of us, the only way we know whether we are "getting it" comes from the grade we make on an exam. I want you to become less reliant on such externals. When you can distinguish between really knowing something and merely knowing about something, you will be on your way to becoming an independent learner. Lastly, it is my sincere hope that all of us (myself included) will improve our oral and written communications skills. Expectations This course will be different than most math classes that you have taken. You are used to being asked to do things like: "solve for ," "take the derivative of this function," "integrate that function," etc. Accomplishing tasks like these usually amounts to mimicking examples that you have seen in class or in your textbook. The steps you take to "solve" problems like these are always justified by mathematical facts (theorems), but rarely are you paying explicit attention to when you are actually using these facts. Furthermore, justifying (i.e., proving) the mathematical facts you use may have been omitted by the instructor. And, even if the instructor did prove a given theorem, you may not have taken the time or have been able to digest the content of the proof. This course is all about "proof." Mathematicians are in the business of proving theorems and this is exactly our endeavor. You will be exposed to what "doing" mathematics is really all about. In a typical course, math or otherwise, you sit and listen to a lecture. (Hopefully) These lectures are polished and well-delivered. You may have often been lured into believing that the instructor has opened up your head and is pouring knowledge into it. I absolutely love lecturing and I do believe there is value in it, but I also believe that the reality is that most students do not learn by simply listening. You must be active in the learning you are doing. I'm sure each of you have said to yourselves, "Hmmm, I understood this concept when the professor was going over it, but now that I am alone, I am lost." In order to promote a more active participation in your learning, we will incorporate ideas from an educational philosophy called the Moore method (after R.L. Moore, a former professor of mathematics at the University of Texas, Austin). Modifications of the Moore method are also referred to as inquiry-based learning (IBL) or discovery-based learning. Much of the course will be devoted to students proving theorems on the board and a significant portion of your grade will be determined by how much mathematics you produce. I use the work "produce" because I believe that the best way to learn mathematics is by doing mathematics. I learned to ride a bike by getting on and then falling off, and in a similar fashion, you will learn mathematics in this course by attempting it and sometimes falling off. In this course, everyone will be required to read and interact with course notes on your own; write up quality proofs to assigned problems; present proofs on the board to the rest of the class; participate in discussions centered around a student's presented proof; call upon your own prodigious mental faculties to respond in flexible, thoughtful, and creative ways to problems that may seem unfamiliar on first glance. As the semester progresses, it should become clear to you what the expectations are. Course Notes We will not be using a textbook this semester, but rather we will be using a theorem-sequence adopted for inquiry-based learning and the Moore method for teaching mathematics. The theorem-sequence that we are using is an adaptation of the notes by Ron Taylor by The Journal of Inquiry Based Learning in Mathematics. The published original version of the notes can be found here Attendance Regular attendance is expected and is vital to success in this course. If you miss more than 6 classes you cannot pass this class. Proofs More or less all of the work you will be assessed on in this course involves writing or presenting proofs. You will be assigned proofs for practice, proofs to read, proofs to present, and the exams will involve doing proofs. It will be a semester long exercise in learning proofs by doing proofs. Traditionally in a course like this students are discouraged from working togather but, unlike a traditional Moore method course, you are allowed and encouraged to work together. You can use the online forum at or you can meet up and work togather. You should however be careful that you aknowledge any help you recieve. I have written some Proof guidelines to give you a sense of what I will look for when grading your proofs. Class Presentations Most days there will be proofs presented by students. These will be written up in sets (several at a time). Then each proof will be presented by its author. To steamline this process I will ask that you claim proofs in advance (in the online forum) to present. This way you can see what proofs are still open for presentation. You will notice that the grade calculation includes a class participation component. This gives you incentive to pay attention to the presentations. You will get graded on how you interact with the people presenting. Also, you should keep a notebook with all of the proofs presented in class. To make this easier I will ask that each proof presented be written up in the online forum. You will recieve some participation credit for this. Exams There will be a midterm exam and a cumulative final exam. All exams will may consist of an in-class part and a take-home part. Each exam will be worth roughly 25 percent of your overall grade. Make-up exams will only be given under extreme circumstances, as judged by me. In general, it will be best to communicate conflicts ahead of time. Rules of the Game You should not look to resources outside the context of this course for help. That is, you should not be consulting the web, other texts, other faculty, or students outside of our course. On the other hand, you may use each other, the course notes, me, and your own intuition. Basis for Evaluation Your final grade will be determined by the scores of your presentations, class participation, and exams. grade calculation Additional Information Getting Help There are many resources available to get help. First, I recommend that you work on homework in groups as much as possible. You should come see me whenever you can. Also, you are strongly encouraged to ask questions in the course forum, as I will post comments there for all to benefit from. Closing Remarks (Adopted from pages 202-203 of The Moore Method: A Pathway to Learner-Centered Instruction by C.A Coppin, W.T. Mahavier, E.L. May, and G.E. Parker) There are two ways to approach this class. The first is to jump right in and start wrestling with the material. The second is to say, "I'll wait and see how this works and then see if I like it and put some problems on the board later in the semester after I catch on." The second approach isn't such a good idea. If you try every night to do the problems, then either you will get a problem (Shazaam!) and be able to put it on the board with pride or you will struggle with the problem, learn a lot in your struggle, and then watch someone else put it on the board. When this person puts it up you will be able to ask questions that help you and the others understand it, as you say to yourself, "Ahhh, now I see where I went wrong and now I can do this one and a few more for the next class." If you do not try problems each night, then you will watch the student put the problem on the board, but perhaps will not quite catch all the details and then when you study for the exams or try the next problems you will have only a loose idea of how to tackle such problems. And then the anxiety will build and build and build. So, take a guess what I recommend that you do. If you are struggling too much, then there are resources available for you. Work together and help each other learn. Use the course forum! I am always happy to help you. If my office hours don't work for you, then we can probably find another time to meet. It is your responsibility to be aware of how well you understand the material. Don't wait until it is too late if you need help. Ask questions! NC Policy The NC policy has changed beginning with this semester. For a 100% refund the date is August 23 and for a 50% refund the date is September 1. The last day to obtain an NC is Friday Oct. 23. This is a hard deadline and will be enforced as such. The department will not approve any late NC requests. Students must request an NC through MetroConnect; faculty approval is no longer required. Holidays: Observance of religious holidays follows College policy, which is posted on the web at in the Academic and Campus Policies for Students section. Each student is responsible for understanding and abiding by the policy. Accommodations for Students with Disabilities The Metropolitan State College of Denver is committed to making reasonable accommodations to assist individuals with disabilities in reaching their academic potential. If you have a disability that may impact your performance, attendance, or grades in this class and are requesting accommodations, then you must first register with the Access Center, located in the Auraria Library, Suite 116, 303-556-8387. The Access Center is the designated department responsible for coordinating accommodations and services for students with disabilities. Accommodations will not be granted prior to my receipt of your faculty notification letter from the Access Center. Please note that accommodations are never provided retroactively (i.e., prior to the receipt of your faculty notification letter.) Once I am in receipt of your official Access Center Faculty Notification Letter, I would be happy to meet with you to discuss your accommodations. All discussions will remain confidential. Further information is available by visiting the Access Center website
This course is designed to provide a study in mathematical ideas suitable for education majors and those needing course work for teacher re-certification. The topics covered will include number sense, concepts and operations, measurement, geometry and spatial sense, algebraic thinking, data analysis and probability. The topics are in alignment with the National Council of Teachers of Mathematics standards, the Sunshine State Standards, math curriculum of Marion, Citrus and Levy counties, and the FCAT.
Pre-Algebra: Percents (Resource Book Only) eBook Grade 6\|Grade 7\|Grade 8\|Grade 9\|Grade 10\|Grade 11\|Grade 12 Sale! Ships Free! Price:5.00$4.25MathSkills reinforces math in three key areas: Pre-Algebra, Geometry, and Algebra. These reproducible activities supplement any math textbook. Pages can be used in the classroom as lesson previews or reviews. The activities are perfect for homework or end-of-unit quizzes.
In maths A Level, you have 4 core modules (C1, C2, C3, C4) and 2 applied modules (S, D, and M). In further maths A Level, you have 2 or 3 further pure modules (FP1 and FP2 and/or FP3), and then either 3 or 4 applied modules, depending on how many further pure units you took. There shouldn't be any mechanics in the other modules, so if you just want mechanics, I'd just stick to M1, M2 and M3.
Algebra II expands on the mathematical content of Algebra I and Geometry. While the topics in Algebra II are interesting and important in their own right, they also serve as a basis for the material presented in subsequent mathematics courses, e.g. trigonometry and calculus. Emphasis will be on functions and algebraic solu- tions to various types of problems. Abstract thinking skills (including some proofs, and the notion of 'generality of a statement') will be introduced and cultivated. No ELL version 1 Credit American Government – Credit Recovery American Government is the study of the historical backgrounds, governing princi- ples, and institutions of the government of the United States. The focus is on the principles and beliefs upon which the United States was founded and on the struc- ture, functions, and powers of government at the national, state, and local levels. The principles of popular sovereignty, separation of powers, checks and balances, republicanism, federalism, and individual rights will be examined as will the roles of individuals and groups in the American political system. Students will compare the American system of government with other modern systems and assess the strengths and problems associated with the American system.
Competency in College Mathematics, 5th Edition, guarantees coverage of the concepts and skills traditionally expected of a liberal arts student. More than 4,000 exercises are presented with answers, along with numerous solved problems, examples and exercises that allow continuous review. Competency in College Mathematics also features the most complete presentation on logic found in any liberal arts mathematics text. A complete testing battery consisting of multiple forms of each chapter test is included upon adoption. Competency in College Mathematics thoroughly prepares students for the College-Level Academic Skills Test (CLAST) administered by the state of Florida at the completion of the college sophomore year. The book has been revised to reflect the latest CLAST requirements. The Appendix includes an 130-questions sample exam with explained answers.
With comprehensive coverage of basic skills, the Spectrum Math Series features easy-to-follow instructions that give students a clear path to success in math fundamentals. The series emphasizes skill development, computation, problem solving, and provides practice with terminology. Workbooks are available separately in Grades 5-8, or as a four-book set. The successful series is ideal for students who need special help with the basics. Because of the nature of the content and the students for whom the series is written, readability has been carefully controlled to comply with each mathematical level. Each 150-page workbook contains a pretest, practice pages, problem-solving pages, and Answer Key. Each book also contains a handy Scope and Sequence reference chart of all the skills covered in the Spectrum Math Series. Developmental exercises are provided at the top of the page when new skills are introduced. These exercises involve students in learning and serve as an aid for individualized instruction or independent study. Spectrum Math, Grade 5. Table of Contents: Addition and Subtraction (1 digit through 6 digit) Multiplication (2 digit by 1 digit through 4 digit by 3 digit) Division (2-, 3-, and 4-digit dividends) Division (4- and 5-digit dividends) Metric Measurement Customary Measurement Fractions Multiplication of Fractions Addition of Fractions Subtraction of Fractions Geometry Spectrum Math, Grade 6. Table of Contents: Addition and Subtraction of Whole Numbers Multiplication and Division of Whole Numbers Multiplication of Fractions Addition and Subtractions of Fractions Division of Fractions Addition and Subtraction of Decimals Multiplication of Decimals Division of Decimals Metric Measurement Customary Measurement Percent Geometry Spectrum Math, Grade 7. Table of Contents: Operations Involving Whole Numbers Operations Involving Fractions Operations Involving Decimals Ratio and Proportion Decimals, Fractions, and Percent Percent Interest Metric Measurement Geometry Perimeter and Area Volume Statistics and Probability Spectrum Math, Grade 8. Table of Contents: Operations Involving Whole Numbers, Decimals, and Fractions Equations Using Equations to Solve Problems Ratio, Proportion, and Percent Interest Metric Measurement Measurement and Appreciation Geometry Similar Triangles and the Pythagorean Theorem Perimeter, Area, and Volume Graphs Probability Special Features: An Assignment Record Sheet is provided in each workbook for students to keep track of their assignments and scores. A Record of Test Scores is provided so students can chart their progress as they complete each chapter test.
Saturday, March 14, 2009 I'm not planning our Algebra 1 classes this year, so I have not been producing much for it. But I did put together a scaffolded introduction to inequalities. The objectives are for students to: Compare numbers using a number line (i.e. "<" means "to the left of") Understand the difference between open and closed circles Graph the solutions of a statement like "x < 3" Understand graphically why adding/subtracting by any number or multiplying/dividing by a positive number does not change the relative position of two numbers, while multiplying/dividing by a negative number does. In other words, students should understand when and why to "flip the inequality sign" when solving inequalities. Continuing with the lessons, we learned to factor difference of squares expressions. I used a geometric approach to help make sense out of the pattern, and it has really helped some students figure out how to more easily factor the nasty ones like 25x^2 - 16y^4. A quick sketch of the squares, labeled with their side lengths, has proven quite useful. It's been a while since I posted. The last week of February was our Junior Trip, in which we take all of our junior class on a 4-day-long trip around California to visit various CSU campuses. It's an incredibly important part of our program, because it is the time when our juniors really start to imagine themselves as college students. The tours, the student panels, seeing the dorms and classrooms, the admissions directors, and the DCP alumni all bring things into sharper focus for the 11th graders. We moved the trip earlier this year (it used to be in April) because kids come back inspired and ready to make positive changes, and so we wanted them to have more time to improve their grades before the end of the semester. It's also a great time for students and staff to bond and get to know each other in different ways. Needless to say, a 4-day, 3-night field trip with 80 high schoolers is tiring. We're all pretty much recovered now, and it's been back to business as usual. Time to catch up on some lesson postings. In Algebra 2, we're nearing the end of the polynomials and factoring unit. I've been focusing on basic factoring techniques (look for the GCF first, then either use trinomial factoring or difference of squares, if possible). I'm still deciding whether to throw sum/difference of cubes into the mix this time around. I decided to bring simplifying and multiplying rational expressions into this unit (instead of waiting for the rationals unit) because it seemed like a good way to have them get more practice with factoring without repeating the same exact problems again and again. Plus, these questions are prominently featured on the STAR test. One thing that has been helping students deal with factoring out the GCF is teaching them to write the prime factorization of each term in the polynomial, every time (including a -1 factor when there is a minus sign). Though it takes longer, this is pretty much a foolproof way of factoring out the GCF - many students have a lot of difficulty with the "what's the largest expression that divides into both" method
The videos in this application are designed to teach you what you need to know about Vectors and Vector Functions. This means that we`ll cover basics like vector magnitude, length, notation, and equations. Additionally, we`ll look at more advanced applications and vector concepts like dot products, cross products, torque, domain, limits, and problems that require you to find where lines intersect planes or find equations of planes. To learn about these concepts, we`ll cover the topic through a series of video lessons, each of which will cover pertinent ideas and related problems. The video content in this application will include a lesson on each of the following: * Vectors: Finding Magnitude or Length * Vectors: Finding Equations of Lines * Vectors: The Dot Product * The Cross Product of Two Vectors * Torque: An Application of the Cross Product * Finding Where a Line Intersects a Plane * Domain of a Vector Function * Limit of a Vector Function * Finding the Equation of a Plane Given 3 Points This is one of several Calculus apps from me, PatrickJMT. I have been putting up math videos for a few years on YouTube and now have the most popular `math only` channel on YouTube!, Affter much encouragement and many requests from my YouTube friends, I`ve finally decided to organize the videos and put them out as an App. I`ve been teaching math for >8 years at the college/university level and tutoring for over 20 years. In the past, I have taught at Vanderbilt University (a top 20 ranked university), the University of Louisville and at Austin Community College. The "Download" link for Vectors & Vector Functions: PatrickJMT Calculus Videos 1.1 directs you to the iTunes AppStore, where you have to continue the download process.You must have an iTunes account to download the application. This download link may not be available in some countries.
Excellent book for beginning courses This book is ideal for an undergraduate course in number theory. The combination of theory, problems and biographical sketches of the principals who made it what it is today is an excellent pedagogical technique. It allows an instructor to show how number theory began very early in mathematical history and how it has progressed over the centuries. Number theory holds the distinction as being the reservoir of most of the easily stated yet difficult problems. As Paul Erdös said, "If it is a simply stated problem that has remained unsolved for centuries, it is almost certainly one in number theory." In this book, you learn the reasons for this situation. It is also well-suited for anyone with an interest in number theory who wishes to learn more about it. The explanations are well-written and a large number of exercises are included. Solutions to the odd numbered problems are given at the end. Review, supplementary and computer exercises are also included at the end of each chapter. The bulk of the explanatory text consists of examples worked out in complete detail. This is the book that I would use if I were teaching a course in beginning number theory. It is a complete package, not only demonstrating what is known and unknown, but the path to how it got that way. Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … more Wiki The advent of modern technology has brought a new dimension to the power of number theory: constant practical use. Once considered the purest of pure mathematics, it is used increasingly now in the rapid development of technology in a number of areas, such as art, coding theory, cryptology, computer science, and other necessities of modern life. Elementary Number Theory with Applications is the fruit of years of dreams and the author's fascination with the subject, encapsulating the beauty, elegance, historical development, and opportunities provided for experimentation and application. This is the only number theory book to show how modular systems can be employed to create beautiful designs, thus linking number theory with both geometry and art. It is also the only number theory book to deal with bar codes, Zip codes, International Standard Book Numbers (ISBN), and European Article Numbers (EAN). Emphasis is on problem-solving strategies (doing experiments, collecting and organizing data, recognizing patterns, and making conjectures). Each section provides a wealth of carefully prepared, well-graded examples and exercises to enhance the readers' understanding and problem-solving skills. This is the only number theory book to: Show how modular systems can be employed to create beautiful designs, thus linking number theory with both geometry and art Deal with bar codes, Zip codes, International Standard Book Numbers (ISBN), and European Article Numbers (EAN) Emphasize ...
The following computer-generated description may contain errors and does not represent the quality of the book: In the following pages I have endeavored to put into form what in my opinion should constitute an Intermediate Algebra, intermediate in the sense that it is not intended for absolute beginners, nor yet for the accomplished algebraist, but as a stepping-stone to assist the student in passing from the former stage to the latter. The work covers pretty well the whole range of elementary algebraic subjects, and in the treatment of these subjects fundamental principles and clear ideas are considered as of more importance than mere mechanical processes. The treatment, especially in the higher parts, is not exhaustive; but it i hoped that the treatment is sufficiently full to enable the reader who has mastered the work as here presented, to take up with profit special treatises upon the various subjects. Much prominence is given to the formal laws of Algebra and to the subject of factoring, and the theory of the solution of the quadratic and other equations is deduced from the principles of factorization.
Course: F17SI1, Introductory Mathematics A (2012-13) Aims This course provides an introduction to mathematics for those who wish to pursue a wide range of studies such as science, engineering and economics. It is aimed at students who have not specialised in mathematics. Much of the course is concerned with algebraic manipulation and solving equations. This is vital for later topics and other areas of study, since the development of algebraic skills is important.
Only English language versions of Microsoft® Windows® are supported. Microsoft® Windows ® RT is NOT supported. More Details Do you want your child to look forward to learning algebra? Using Switched-On Schoolhouse 9th Grade Math from Alpha Omega Publications, your child will! How does this dynamic, computer-based homeschool curriculum work? It's very simple and easy. Just install, and in minutes your child will have a whole years' worth of algebra lessons ready at his fingertips. Must-have lessons in this Alpha Omega curriculum include engaging multimedia tools—like video clips, learning games, and animation—all integrated into content to encourage student learning! You won't find that in other traditional math textbooks. But wait, Switched-On Schoolhouse has much more. This dynamic, cutting-edge homeschool curriculum is packed with time-saving features parents will absolutely love—like automatic grading and lesson planning, a built-in calendar, and handy message center. We've just made homeschooling easier, and much more exciting! In this math course, your child will receive an in-depth, comprehensive introduction to algebra and basic algebraic principles. Plus, Switched-On Schoolhouse 9th Grade Math has integrated, step-by-step solution keys when viewing problems from the SOS Teacher application. Come see how fun homeschooling and teaching algebra can really be. Just order Switched-On Schoolhouse 9th Grade Math
Help me find good math questions for my students. I am a teacher at 西铁一中。 I teach mathematics in English for students going abroad. Now this is my problem, there are few mathematics books written in English that are at the level of high school, most are geared towards graduate school. The book for the school is very dry and basic. I would like to be able to present better problems for my classes. I need help finding good problems, ones with some historical context or from real life events. Example: using a closed Leontief input-output model for linear algebra. Or Something along this line: The quality of oxygen that can dissolve in water depends on the temperature of the water. (So thermal pollution influences the oxygen content of water.) The graph shows how xoygen solubility S varies as a function of the water temperature T. (a) What is the meaning of the derivatives S'(T)? What are its units? (b) Estimate the value of S'(16) and interpret it. with graph From Calculus (6th Edition) by James Stewart. My other problem is that I got a group of 6 students that are uber smart. I gave them the AMC 10 & 12 problems, they solve them in class, then I gave them the USAMO problems, and they solve 4 problems in an hour (I gave them both days). Should I just give them the Putnam exams? Now, English text books cost a lot and I have to buy them out of my own pocket, could you help me find online resources that are at the level a high school student that is just learning calculus understand the more advance mathematical topics. Most I have found are just beyond their mathematical understanding. The other 24 students are must lower ability than those 6 students. In summary: 1) Where to find more realistic and historical problems for calculus and prob/stats classes? To help engage my students and improve their English. The graphs and data for the problems, don't worry I can solve it for the answers. Problems, that bring in the other subjects : history, economics, etc. 2) What to do about the ubersmart students? How to structure the class so the ubersmart students don't get board, but I don't leave the rest of the students behind? 3) Are there any books that are really graduate analysis, number theory, etc; however, are written for high school students?
Ray's Arithmetic Curriculum by Mott Media Used in the 1800's, Ray's Arithmetic taught math to generations. This set presents principles and follow up each one with examples which include difficult problems to challenge the best students. Students who do not master a concept the first time can return to it later, work the more difficult problems, and master the concepts. Thus in these compact volumes is a complete arithmetic course to study in school, to help in preparation for ACT and SAT tests, and to use for reference throughout a lifetime. NOTE: The publisher, Mott Media, made the decision to keep prices down by switching from hardback to paperback. When each of the books in the series is reprinted, it will be in the paperback version. At present, the Primary Arithmetic and Intellectual Arithmetic are paperbacks. Ray's Arithmetic 8-Volume Set Ray's Arithmetic 8 Volume Set By Joseph Ray, Publisher: Mott Media Included in the Ray's Arithmetic 8-Volume Set are one of each of the following books: Key to Ray's New Higher Arithmetic Key to Ray's Higher Arithmetic Key to Ray's Higher Arithmetic has answers to problems in the higher book. This key provides basic answers. Hardback ISBN-13: 9780880620567 List $12.99 Sale Price $11.95 Parent Teacher Guide Parent-Teacher Guide for Ray's New Arithmetics By Ruth Beechick, Publisher: Mott Media The Ray's New Arithmetics Parent-Teacher Guide gives unit by unit helps for teaching; suggests grade levels for each book; provides progress chart samples for each grade and tests for each unit. It is written by Dr. Ruth Beechick who is known for her practical and academic approach to teaching. If you want help with teaching, planning, and structuring your curriculum, then you need this guide.
Originally posted by Speedbump If you have not done the infinite series/Fourier/Laplace math yet, then I'll bet that is what discrete math is. Don't worry, it would be easy if you are good at integration. Just some formulae to remember. I am not that great at integration, and managed to do the series stuff just fine. You will use Fourier/Laplace a lot in "real life" engineering, but you won't have to do it the way they teach you in math classes. You'll use MathLab or some other program to do it all for you I think Nebraska will still have a lot of work to do next year. I am not at all inpressed with Jamaal Lord at QB, and our defense has to get over losing Charlie McBride a few years ago and then Craig Bohl last year. At least Solich got smart and hired himself an offensive coordinator. K State runs our offense better than we do right now. If Lord is our QB, and our defense isn't any better than last year, I say the sign stays Purple. Integration? Can we quit with the integration already? I'm so sick of it . Actually I just use my TI-89, it does most of it for me. I just have to disguise it and make it look like I'm showing work come exam time . Integration is NOT my strongpoint LOL, there's a little too much guesswork in it. Memorizing formulas though, that I can do. Photographic memory... that's how I survive Oh, and uh... MathLab is GOOD!!! I personally hope the sign changes back to red. Not because I don't like my team, but because I think K-State purple is the UGLIEST color known to man. I like red though. My car is blood red, I like it so much hm... I think there should be a Homework/School related Discussion Forum under AMDforum~@!!! ok... i got 2 questions related to my I.T. assignment that I can't solve right now... I will keep reading my books but wanna know if you guys can help me a bit... 1. Consider the interrupt that occurs at the completion of a disk transfer. Describe the steps that take place after the interrupt occurs... (This is da question... I was wondering if Disk Transfer = DMA Transfer???) 2. Anyone here knows what is LMC (Little Man Computer)??? If one of you do know what i m talking about... then I will post the question here cause it's a long one..... THX guys.... sorry to turn this thread into Personal/School-related thread AGAIN~!!! ... but i really need help~!@ for the disk transfer question.. i tried my best to B.S. a "sounds-like" answer and i hope it's correct.... for the "LMC" .. here's da question... Suppose that the instruction format for a modified LMC requires 2 consecutive locations for each instruction. The high-order digits of the instruction are located in the first mail slot, followed by the lower-order digits. The IR (Instruction Register) is large enough to hold the entire instruction and can be addressed as IR [high] and IR [low] to load it. You may assume that the op code part of the instruction uses IR [high] and that the address is found in IR [low]. Write the fetch-execute cycle for an ADD instruction on the machine. if anyone know what's LMC or know how's LMC function... plz teach me what is it... I rather you teach me the concept of it (i have a hard time how the register work...) than tell me a straight forward answer.... anyways... thx Speedbump and Sephiroth for trying to help... I was wondering why da hell I (people in I.T.) have to leran this kinda stuff... isn't this related to Hardware/Software Enginner student??? The ol' softmodded 9500 got me 16,611 in 3dmark01 and 5,264 in 3dmark03 now that it has a decent chipset and proc to back it up. I decided to post my most recent results with the 2 benches in my sig. \| \| \| \/
This is a challenging and rigorous course offered to those students who have demonstrated an advanced proficiency in mathematics in sixth grade. The material covered in the accelerated course is presented at a faster pace with the expectation that the students have retained their advanced skills and can perform with greater proficiency and on their own.The accelerated course focuses on using the order of operation principles, solving equations and inequalities, applying rational numbers and integers to real life problems, relating rates, proportions, and percents, developing spatial thinking skills and exploring linear functions.A course grade of 85% in the 6th grade advanced course is recommended.
In this calculus learning exercise, students find the limit using the Limit Comparison Test and solve problems with series based on the p-series. They tell whether an equation will converge or diverge. There are 7 problems. In this Calculus worksheet, students assess their understanding of various topics, including the derivatives of trigonometric functions, evaluating integrals, sigma notation, and convergent and divergent series. The one page interactive worksheet contains fifty-two problems. Answers are not provided. In this college level Calculus learning exercise, students use the ratio test to determine if a series converges or diverges. The one page learning exercise contains six problems. Solutions are not provided. Students analyze geometric series in detail. They determine convergence and sum of geometric series, identify a series that satisfies the alternating series test and utilize a graphing handheld to approximate the sum of a series. Students investigate sequences and series numerically, graphically, and symbolically. In this sequences and series lesson, students use their Ti-89 to determine if a series is convergent. Students find the terms in a sequence and series and graph them. Students use summation notation to determine the sum of a sequence. In this infinite series instructional activity, students use comparisons to determine convergence for improper integrals. They use the integral test for infinite series. Students state the reasons they believe a given integral is converging or diverging.
Using the author's considerable experience of applying Mathcad to engineering problems, Essential Mathcad introduces the most powerful functions and features of the software and teaches how to apply these to create comprehensive calculations for any quantitative subject. The simple, step-by-step approach makes this book an ideal Mathcad text for professional engineers as well as engineering , science, and math students. Examples from a variety of fields demonstrate the power and utility of Mathcad's tools, while also demonstrating how other software, such as Excel spreadsheets, can be incorporated effectively. A companion CD-ROM contains a full non-expiring version of Mathcad (North America only). Many more applied examples and exercises from a wide variety of engineering, science, and math fields New: more thorough discussions of differential equations, 3D plotting, and curve fitting. * Full non-expiring version of Mathcad software included on CD-ROM (North America only) * A step-by-step approach enables easy learning for professionals and students alike less
This course will interest you if you need to create mathematical models or if you use numerical software in industry, science, commerce or research. It's concerned with the skills needed to represent real optimization problems as mathematical models, and with techniques used in numerical analysis and operational research for solving these models by computer. Explaining how and when modelling and numerical techniques can be applied, the course covers solutions of non-linear equations; systems of linear and non-linear equations and mathematical modelling; linear and integer programming; and non-linear optimization for unconstrained and constrained minimisation problems. Knowledge from Level 2 study of calculus and matrices is assumed. Modules at Level 3 assume that you are suitably prepared for study at this level. If you want to take a single module to satisfy your career development needs or pursue particular interests, you don't need to start at Level 1 but you do need to have adequately prepared yourself for OU study in some other way. Check with our Student Registration & Enquiry Service to makeThe course is divided into three blocks of work: solutions of non-linear equations, systems of linear and non-linear equations and mathematical modelling; linear and integer programming; and non-linear optimization for unconstrained and constrained minimization problems. About a quarter of your study time will be devoted to practical work. Computer programming is not part of the course. In the broad area of operational research, the course will enable you to formulate a real problem in mathematical terms; to recognise whether the problem can be solved numerically; to choose a suitable method; to understand the conditions required for the method to work; to evaluate the results and to estimate their accuracy and their sensitivity to changes in the data. Optimization is a practical subject, although it is supported by a growing body of mathematical theory. Problems that require the creation of mathematical models and their numerical solutions arise in science, technology, business and economics as well as in many other fields. Creating and solving a mathematical model usually involves the following main stages: formulation of the problem in mathematical terms: this is the creation of a mathematical model devising a method of obtaining a numerical solution from the mathematical model making observations of the numerical quantities relevant to the solution of the problem calculating the solution, usually with a computer or at least with a scientific calculator interpreting the solution in relation to the real problem evaluating the success or failure of the mathematical model. Many of the problems discussed in the course arise in operational research and optimization: for example, how to get the most revenue from mining china clay when there is a choice of several mines. In this example the mathematical model consists of a set of linear inequalities defining the output from each mine, the number of mines that can be worked, the correct blend of clay and the total amount of clay mined each year. The method of solving the problem uses mixed linear and integer programming; the numerical data that need to be observed include the financial implications of opening a mine, the number of mines that can be worked with the labour force, and the quality of clay from potential mines. These data will be fed into a computer, which will combine them with the chosen method of solving the equations to produce solutions consisting of outputs from each mine in each year of operation. This course examines all the stages but concentrates on: the first stage, creating the mathematical model; the second stage, devising a method; the fourth stage, calculating numerical solutions; and the fifth stage, interpreting the solution. Each of the three blocks of work takes about ten weeks of study: Block II Formulation and numerical solution of linear programming problems using the revised simplex method; formulation of integer programming problems and the branch and bound method of solution; sensitivity analysis. Block III Formulation and numerical solution of unconstrained and constrained non-linear optimization problems using, among others, the DFP and BFGS methods with line searches; illustrative applications. You will learn Successful study of this course should enhance your skills in: mathematical modelling operational research linear programming and non-linear optimization methods the use of iterative methods in problem solving the use of Computer Algebra Packages for problem solving. Entry This is a Level 3 course. Level 3 courses build on study skills and subject knowledge acquired from studies at Levels 1 and 2. They are intended only for students who have recent experience of higher education in a related subject, preferably with The Open University. You are expected to bring to the course some knowledge of: Calculus Definition of differentiation and integration; ability to differentiate and integrate a variety of functions; Taylor's theorem with remainder; partial derivatives; understanding of continuity and convergence You could get the necessary background from our Level 2 mathematics courses Pure mathematics (M208), or Mathematical methods and models (MST209), or the equivalent. Students are more likely to successfully complete this course if they have acquired their prerequisite knowledge through passing at least one of these recommended OU courses. Your regional or national centre will be able to tell you where you can see reference copies, or you can buy selected materials from Open University Worldwide Ltd. Regulations As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are available on our Essential documents website. If you have a disability YouWe recommend you access the internet at least once a week during the course to download course resources and assignments, and to keep up to date with course news. Computing requirements How to register To register a place on this course return to the top of the page and use the Click to register button. Student Reviews "One course has to be the least enjoyable and, for me, I am afraid it was M373. The only letter ..." Read more "This was a thoroughly testing course that I strongly recommend as a Level 3 module for anyone doing a maths
Web Link Review This on-line glossary contains common mathematical terms used in English, their translation in Spanish, and a brief definition of the term in Spanish. Spanish-speaking middle school students might find this particularly useful, and teachers can use it as a reference to work with students. The entries represent a good cross-section of terms commonly used in middle school mathematics, including beginning algebra and geometry. The glossary is presented in one long file, with links to the different letters in the alphabetical listing. However, it loads quickly and is easy to use. It is also easy to print and runs to about 17 pages. First Posted: 11/30/2000 Homesite Description - This resource is contained in the following Web site MathNotes - MathNotes is a Web site to support use of the users of the Lial/Hornsby/Miller Paperback Series offered by Longman. Support materials are offered for teachers, and students can use the provided interactive tutorials and study aids to deepen their understanding. -
Details of prerequisites: standard calculus and linear algebra; familiarity with the statement of the implicit function theorem (students may consult any good textbook in multivariate calculus); some familiarity with algebraic concepts such as groups and rings is desirable, but no knowledge of group theory or ring theory is assumed; some familiarity with basic topological notions (topological spaces, continuous maps, Hausdorff property, connectedness and compactness) may be beneficial, but is not assumed. Future topics requiring this course unit: there are no particular courses directly following this one; however, differentiable manifolds are used in almost all areas of mathematics and its applications, including physics and engineering. Last modified: Thursday 12 (25) April 2013. (Refresh the browser to get the updated page.) Differentiable manifolds are among the most fundamental notions of modern mathematics. Roughly, they are geometrical objects that can be endowed with coordinates; using these coordinates one can apply differential and integral calculus, but the results are coordinate-independent. Examples of manifolds start with open domains in Euclidean space Rn, and include "multi-dimensional surfaces" such as the n-sphere Sn and n-torus Tn, the projective spaces RPn and CPn, and their generalizations, matrix groups such as the rotation group SO(n), etc. Differentiable manifolds naturally appear in various applications, e.g., as configuration spaces in mechanics. They are arguably the most general objects on which calculus can be developed. On the other hand, differentiable manifolds provide for calculus a powerful invariant geometric language, which is used in almost all areas of mathematics and its applications. In this course we give an introduction to the theory of manifolds, including their definition and examples; vector fields and differential forms; integration on manifolds and de Rham cohomology. Textbooks: No particular textbook is followed. Students are advised to keep their own lecture notes and use my notes posted on the web. There are many good sources available treating various aspects of differentiable manifolds on various levels and from different viewpoints. Below is a list of texts that may be useful. More can be found by searching library shelves.
This is the second course in a sequence of courses designed to provide students with a rigorous program of study in mathematics. It includes: complex numbers, quadratic, piecewise, and exponential functions, right triangles, and right triangular trigonometry, properties of circles, and statistical inference. (Prerequisite: Successful completion of Math 1.) past view calendar Current Events and Homework There are no current calendar items. Class Downloads Math Department Help Session CalendarQuiz #1 Review Answer Key (91.83 KB) Answers to the Review Guide! Math 2 Review for Test #1 Unit 1A Mid Unit Test (258.66 KB) Use these to check your answers for the review! Come prepared to ask any questions that you do not understand!!! Math 2 Practice Test for Unit 1B 10/4/9012 (244.24 KB) Parent Letter GO CATS!!!! (70.91 KB) Materials and Notebook Set Up (17.59 KB) Syllabus Math 2 (38.14 KB) M2 Unit 2 Test #3 Review Answer Key (186.57 KB) M2 Test Review Unit 2 Test #3 Trying to Get It Right (93.08 KB) Blank Review Sheet for you to practice!!! Make sure you have your yellow sheet with you!! Math 2 Review for Quiz Arcs and Chords (119.3 KB) M2 Review for Angles, Arcs, Chords and Segments (Blank) (43.19 KB) Math 2 Unit 3 Review Guide Blank Copy for Circular Knowledge Unit (69.56 KB) Use this to practice for your test! Then check your answers with your answer key!!! M2 Unit 3 Study Guide Answers page 1 (56.66 KB) M2 Unit 3 Study Guide Answers page 2 (79.43 KB) M2 Final Exam Review Guide Page 1 (643.48 KB) M2 Final Exam Review Guide Page 2 (564.41M2 Final Exam Review Guide Page 3 (533.29 KB) M2 Final Exam Review Guide Page 4 (527.86 KB) M2 Final Exam Review Guide Page 5 (608.8 KB) M2 Final Exam Review Guide Page 6 (706.85 KB) M2 Final Exam Review Guide Page 7 (618.76 KB) Practice Grids for Standard Deviation (17.23 KB) Unit 4 Practice Test The Meaning of Mu (21.51 KB) Here is an extra copy if you lost yours! M2 Notes on Solving Absolute Value Equations and Inequalities (7.09 MB) These are the notes and assignment for March 25, 2013! Just in case you didn't get all the notes!
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education. EE236A (Fall 2007-08)Lecture 11 The simplex method extreme points adjacent extreme points one iteration of the simplex method degeneracy initialization numerical implementation111Idea of the simplex methodmove from one extreme point to an adjacent ex MT 3802 NUMERICAL ANALYSIS2008/2009Dr Clare E Parnell and Dr Stphane Rgnier e eOctober 1, 2008Chapter 0Handout0.1 NotationThroughout this course we will be using scalars, vectors and matrices. It is essential that you know what they are and can tel Chapter 2Iterative Methods2.1 IntroductionIn this section, we will consider three different iterative methods for solving a sets of equations. First, we consider a series of examples to illustrate iterative methods. To construct an iterative method, we cep 2008/09MT3802 - Numerical AnalysisTutorial Sheet 2 1. For a sub-ordinate matrix norm and an invertible matrix A, where Ax = b, show that (i) (ii) As AssN1 x A-1 A b2. Assume that (A + A)-1 is computed as an approximation to A-1 . Show that (A + ScriptEase: A Pattern Based Approach to ScriptingCurtis Onuczko Thursday, January 19, 2006Overview What is ScriptEase? Why use ScriptEase? When to use ScriptEase? How to use ScriptEase Tips and TricksWhat is ScriptEase?Why use ScriptEase?A tool to Overview Game Creation ProcessCMPUT 299 Winter 2006 Thursday January 12 ! Making a computer game is a lengthy process, involving many creative people! High-profile productions often take 2-3 years ! Challenging games can involve > 100 people!! This lec Lecture Review Sheet: Game Design Finnegan Southey CMPUT 299 Winter 2006 Terms and Definitions MDA n A model for game design that views the user experience as a three part process: mechanics, dynamics, and aesthetics Funativity n A model for types of "fun OpeningNarrative:Concepts of Narrative in Interactive New Media Art FormsLecture Goals for the next two classes1. Introduce concepts of traditional narrative, most of which apply to later technologies. 2. Discuss the application of these concepts to n Meetings, Bloody Meetings How To Run MeetingsCMPUT 299 H. James Hoover Fall 2005 2005-09-23,27 Version 1.0CMPUT 299 - Fall 2005 How to Run Meetings Written by John Cleese and Antony Jay Starring John Cleese and Robert Hardy Video Arts, 1993 34 minMee The Early Days Graphics and GenresCMPUT 299 ! The very earliest video games (pre-1975) were custom built machines. ! Designed/built by engineers (like a TV).Tennis for Two(Brookhaven Labs,1958)Finnegan Southey XBox Live GamerTag: AleaCMPUT 299 - Fall Lecture Review Sheet: The culture of Gaming Sean Gouglas CMPUT 299 Winter 2006Main Ideas and Concepts A. Introduction Culture describes social actors, the webs of significance that allow for social actors to communicate and understand each other, and the THE DIGITAL MILLENNIUM COPYRIGHT ACT OF 1998U.S. Copyright Office SummaryDecember 1998INTRODUCTIONThe Digital Millennium Copyright Act (DMCA)1 was signed into law by President Clinton on October 28, 1998. The legislation implements two 1996 World Inte National University Course Outline ACC640M Governmental and Non-profit Accounting Please Note: We will be using e-college. All handouts, and other class materials are available in e-college under DOC Sharing Tab at top of page. Make copies of your handout
Mathematics Find Mathematics Schools or Programs Near You: Program Summary A general program that focuses on the analysis of quantities, magnitudes, forms, and their relationships, using symbolic logic and language. Includes instruction in algebra, calculus, functional analysis, geometry, number theory, logic, topology and other mathematical specializations.
Applied and Computational Mathematics What are the best red-yellow-green light timings for traffic signals in a congested urban traffic network? How can we analyze brainwave signals to predict a possible epileptic seizure? How can a bank find potential customers least likely to default on a loan? What are the chances of failure for a particular missile guidance system? Today's advances in areas as diverse as biomedicine, the Internet, communications, defense technologies, and commerce all require individuals with a sound background in applied mathematics and computation. Mathematical tools make it possible to create representations of the world that facilitate analysis of a problem. The computational side provides the means for producing the numbers, graphics, rules and other output that enable designers and decision-makers to solve the problem. EP's Applied and Computational Mathematics (ACM) trains you in both of these essential aspects of modern analysis—mathematical and computational—preparing you to understand and then solve critical problems in a wide range of application areas. Highlights include:
the biggest focus of elementary school math remains on addition, subtraction, multiplication, division, fractions, decimals, percents, and ratios. Differential equations are equations that involve an unknown function and one or more of its derivatives. They are solved by determining the functions that satisfy the equations
At Fresh we love to share helpful tools and here's a website we know you're going to love playing around with. Wolfram Alpha is basically a website (they call it an engine) for computing answers to a wide range of questions and it displays or provides the knowledge and/or answer in a variety of ways. It essentially works by using its vast store of expert-level knowledge and algorithms to automatically answer questions, do analysis, and generate reports. How cool is that?! Whether you're at school and have a tricky equation you want to solve AND see the answer displayed in different graph forms or whether you're just trying to calculate the amount of interest you're going to pay on a mortgage or loan, this resource will soon have you addicted to putting in all kinds of information!
The... MathML .NET Control 2.0 is a Equation editor component designed for the .NET Framework. MathML .NET Control is an Equation editor for all users ranging from students and teachers to the high-end science and technical publishers. It provides you with very easy user interface allowing to create every imaginable form of mathematical expressions. Every formula can be saved as a Jpeg image or exported to a bitmap (Jpeg, Gif, Bmp, Tiff, Wmf, ...) file with resolution of your choice (96 dpi, 300... With With Features: * Using Newton's... ...DensCalc is a sea water equation of state calculator for the Palm OS. It will compute any two of the following four parameters: temperature, conductivity, salinity, and density, from the other two parameters and it will do this for any depth in the ocean. The program also computes the speed of sound, specific heat, freezing point, adiabatic lapse rate, sigma-t, potential temperature, and potential density. The full source code is available on the authors web site.. . Use symbolic calculator and function plotter to analyze your math expressions. Math teachers can make exams in electronic format. AutoAbacus is a powerful equation solving library that finds solutions to equation sets with a snap. A set of equations can be passed in as text, while AutoAbacus attempts to find a solution that satisfies all constraints. The equations are not limited to be only linear, but can also be polynomial or include arbitrary functions. By profiling the types of equations in the system and their dependencies on each other, AutoAbacus uses appropriate solution methods to solve individual subsets of... Learn the secret mathematical equation for profiting in the Forex market by predicting what will happen using this secret formula. Predict all major price movements in Forex well in advance using this easy yet accurate equation formula. Learn how to trade Forex easy using no contradicting indicators or complicated trading systems. Being able to predict Forex is easy using our Forex profit formula.Welcome to the website that may very well change the way you trade forever. We will start by... In this game you need to complete a equation by picking filling in numbers from a grid of numbers. The equation becomes longer and harder as the game advances. The faster you complete the equation, the higher the score you get MathCast is a free and open source application. Feel free to use it to help your studies, to add mathematics to your website, etc. MathCasta€™s powerful and... MathType is a powerful interactive equation editor for Windows and Macintosh that lets you create mathematical notation for word processing, web pages, desktop publishing, presentations, elearning, and for TeX, LaTeX, and MathML documents. More Ways to Create Equations * Entering Math by Hand: Enter equations as easily as you would write math with paper and pencil! This feature uses the built-in handwriting recognition in Windows 7. * Point-and-Click... be any - linear, square, cubic or, for instance, of the 7-th power. The program finds the roots of the equation - both real and imaginary. You just enter an equation you see in your... EnergyRB is an application which numerically finds the eigenenergies and eigenfunctions for the time independent SchrA¶dinger equation in one dimension. The application uses REALbasic's RbScript, so almost any potential energy function can be entered by the user. This function is translated into machine language, so the numerical calculation proceeds as rapidly as if the potential function had been compiled into the application from the source code. EnergyRB uses a... ... frequentlyFloat number converters can convet the number in binary,octal,decimal,hex... EJB Component Suite...
focus in ALGEBRA: INTRODUCTORY & INTERMEDIATE is on you, the student. You are encouraged to be active participants both in the classroom and in your own studies as you work through the How To examples and the paired Examples and You Try It problems. The role of "active participant" is crucial to your success. ALGEBRA: INTRODUCTORY & INTERMEDIATE presents worked examples, and then provides you with the opportunity to immediately work similar problems, helping to build your confidence and eventually master the concepts. This simple framework, known as the Aufmann Interactive Method (AIM) is the foundation for your success. All lessons, exercise sets, tests, and supplements are organized around a carefully-constructed hierarchy of objectives. This "objective-based" approach helps you clearly organize your thoughts around the content making the pages easier for you to follow
Allows complex mathematical calculations and simulations. Uses mathematical functions to solve problems in the engineering, finance, mathematics, actuarial, statistics, physics, chemical computing and scientific fields. As well as the standard licence, cheaper licences for students and teachers are available. Registration is necessary before
This workbook of 250 pages was developed by the RADMASTE Centre of the University of the Witwatersrand. Although it is aimed at the second level for FET Colleges, nothing prevents it being used at schools. It covers Numbers, Functions, Space, Shape and Orientation, Statistical and Probability Models as well as Financial Mathematics. With adaptation many of the exercises can also be used for Mathematical Literacy. The solutions are provided at the back of the workbook. The workbook is written for the student who is not coping well with mathematics and who needs some additional explanation and practice. A three part investigation on trigonometric graphs which I did with my grade 11 class. I have also included the notes we completed in class after the investigations were done. The Zip file contains 4 MS Word 2003 documents. This helpful resource was created by Sinclair Tweedie in Ms Excel. According to him the licence agreement is "Use, abuse, change, give away or whatever." It works best on a 17" monitor with Excel2003. This interactive resource is all about Statistics.
Mathematics 470 Here's a list of resources that come to my mind quickly (mostly those shared in class on opening day): NCTM Journal The Mathematics Teacher is available in Milne library going back to its very beginning in 1908. William Dunham's Journey through Genius is in Milne (QA21.D78 1990) and is on one-day reserve. If you can't find it on the shelf, ask at the front desk - if you can't find it at all - please tell me soon). Ronald Calinger's A Contextual History of Mathematics is the book that connects history of mathematics with the rest of history. It's also in Milne (QA21.C188 1999). Browsing the library in the QA21 section in general is a good idea. Here are some other sources that I think highly of: Morris Kline - Mathematical Thought from Ancient to Modern Times Victor Katz - A History of Mathematics: An Introduction John Stillwell - Mathematics and Its History Historia Mathematica is a journal of history of mathematics - we have this in the library as well. Ronald Calinger's Classics of Mathematics is a source book of original sources, as is Dirk Struik's Mathematical Source Book I have several more sources, but this should be enough to get you started. Tell me if you seek something. More will be added to this page as the semester progresses. Please ask me if there is something you would like to see included. This page, like the course, will be designed by you, the students.
If you need help in preparing for the math part of the GRE general test, you have come to the right place. Note that you do not have to be a student at WTAMU to use this study session. It was created as a service to anyone who needs help getting ready for this test. If this is your first visit to our website, please read the disclaimer. Under each specific concept, you will find links to in-depth tutorials that will help learn and review the material. These tutorials come from the WTAMU Virtual Math Lab, which I created. Within these tutorials, you will find pertinent definitions, formulas, step-by-step explanations, an answer/discussion section with step-by-step solutions, and links to other credible webpages that can help you further with that topic. In math, when you study a specific topic, a lot of times you are incorporating other mathematical topics into solving the problem. Some of the tutorials will overlap each other. This will help reinforce the concepts you need to know for the GRE. Under the algebra area, there is a lot of overlapping between the different levels (beginning, intermediate, and college) of tutorials. Find the algebra level that agrees with you most and do all of the tutorials under that level. If you start below college level algebra, make sure that you make your way up through college algebra before you take the GRE general test. When you are done with a tutorial, you can come back to this webpage by clicking on the back arrow link marked GRE Math Help Page found on the top left corner of the tutorial page OR clicking on the back arrow on the top left of your Internet window until you are back to this page. Arithmetic The first area that we will be looking at is arithmetic. You know, fun things like making sure you have the negative in the right place and remembering when you have to find the common denominator of your fractions. Don't worry, I have the utmost confidence that you will do much better with arithmetic than Calvin. SPECIAL NOTE: You need to go to all the links that are under each topic for arithmetic to get the full benefit. SPECIAL NOTE: You need to go to all the links that are under each topic for Algebra to get the full benefit. Note that most of the topics under Algebra contain tutorials from three levels (lowest to highest): beginning, intermediate, and college. Ideally, for the Algebra section, you want to be able to work the college level by the time you take the GRE test. There will be some overlapping between the levels. If a topic has tutorials in more than one level, try going under the highest level first. If that is too hard for you, go to the tutorials of the next level down, if available. If that is too hard for you, go to the tutorials of the next level down, if available. Once you find a level to start with, make sure that if it is below college level, in the end you work your way up to college algebra. The beauty of this is it is individualized. You can go at your own pace at the comfort of your own computer. You know better than anyone else what your algebra skills are. simplifying exponential expressions involving multiplying like bases, zero as an exponent, dividing like bases, raising a base to two exponents, raising a product to an exponent and raising a quotient to an exponent simplifying exponential expressions involving multiplying like bases, zero as an exponent, dividing like bases, negative exponents, raising a base to two exponents, raising a product to an exponent and raising a quotient to an exponent Disclaimer: Note that we can not guarantee that you will pass your test after going through any of the tutorials in this website. However, it will definitely help you to better understand the topics covered. WTAMU and Kim Seward are not responsible for how a student does on any test for any reason including not being able to access the website due to any technology problems. GRE and Graduate Record Examination are the registered trademarks of Educational Testing Service (ETS). The material here has neither been reviewed nor endorsed by ETS. Throughout this website, we link to various outside sources. WTAMU and Kim Seward do not have any ownership to any of these outside websites and cannot give you permission to make any kind of copies of anything found at any of these websites that we link to. It is purely for you to link to for information or fun as you go through the study session. Each of these websites have a copy right clause that you need to read carefully if you are wanting to do anything other than go to the website and read it. We discourage any illegal use of the webpages found at these sites. All contents copyright (C) 2003 - 2008, WTAMU and Kim Seward. All rights reserved. Last revised on August 8, 2008 by Kim Seward.
Hist. 638: This course examines the development of mathematics from the inventions of calculus to the supposed foundational crisis at the turn of the 20th century. Among its topics are the differential equations devised for mechanics and astronomy by Euler, Lagrange, and Laplace, the metric system proposed during the French Revolution, the evolution of satisfactory foundations for mathematical analysis from Cauchy to Weierstrass, the algebras of Galois and Boole, the creation of non-Euclidean geometries, and Cantor's transfinite sets. Students will explore internal controversies and the dynamics of mathematics in larger intellectual and social settings, such as the rise to power of Russia and Prussia as well as the evolution of two modern research-intensive universities, the Ecole polytechnique and University of Berlin.
Princeton Companion to Mathematics Published by Princeton University Press This is a one of a kind reference for anyone with a serious interest in mathematics. It presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music, and much, much more. This work surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties
Introduction Jacqueline A. Stedall Publisher: Oxford University Press DOI:10.1093/acprof:oso/9780198526025.003.0001 This introductory chapter begins with a background on Thomas Harriot. It then details Harriot's relationship with Nathaniel Toporley and their mutual interest in Viète's mathematics. Harriot's notation, Harriot's algebra after 1621, and Harriot's reputation and influence
Algebra to Algorithms Description: Western science relies on mathematics as a powerful language for expressing patterns that appear in the natural world. Mathematical models allow predictions, more or less, of complex natural systems, and modern computing has both magnified the power of those models and helped shape new models that increasingly influence 21st-century decisions. Computer science, the constructive branch of mathematics, relies on mathematics for its culture and language of problem solving, and it also enables the construction of mathematical models. Patterns that appear in the natural world and are expressed in mathematical models also sometimes appear in the visual arts. In this program, we will explore connections between mathematics, computer science, and the natural sciences, and develop mathematical abstractions and the skills needed to express, analyze and solve problems arising in the sciences. In addition, we will explore how to program interesting visual shapes using simple geometry. The regular work of the program will include seminars, lectures, problem solving workshops, programming labs, problem sets, and seminar papers. The emphasis will be on fluency in mathematical thinking and expression along with reflections on mathematics and society. Topics will include concepts of algebra, algorithms, programming and problem solving, with seminar readings about the role of mathematics in modern education and society. This program is intended for students who want to gain a fundamental understanding of mathematics and computing before leaving college or before pursuing further work in the sciences or the arts. Computability and Language Theory Description: The computer is a tremendously useful tool. Is there anything it can't do? Through studying topics in advanced computer science, this program will explore what computers can do, how we get them to do it, and what computers still can't do. It is designed for advanced computer science students and students with an interest in both mathematics and computer science. Topics covered will include formal computer languages, systems of formal logic, computability theory, and programming language design and implementation. Students will also study a functional programming language, Haskell, learn the theoretical basis of programming languages and do an in-depth comparison of the properties and capabilities of languages in the four primary programming paradigms: functional, logic, imperative, and object-oriented. Program seminars will explore selected advanced topics in logic, language theory and computability. Topics will be organized around three interwoven themes. The Formal Languages theme will cover the theoretical basis of language definitions, concluding with a study of what is computable. The Logic theme will cover traditional logic systems and their limits, concluding with some non-traditional logic systems and their applications to computer science. In the Programming Language theme we will study both the theoretical basis and practical implementation of programming language definitions by comparing the implementations of the four programming language paradigms. Students will have an opportunity to conclude the program with a major project, such as a definition and implementation of a small programming language. Computer Science Foundations Description: The goal of this program is to learn the intellectual concepts and skills that are essential for advanced work in computer science. Students will have the opportunity to achieve a deeper understanding of increasingly complex computing systems by acquiring knowledge and skills in mathematical abstraction, problem solving, and the organization and analysis of hardware and software systems. The program covers material such as algorithms, data structures, computer organization and architecture, logic, discrete mathematics and programming in a liberal arts computer science curriculum. In both quarters the program content will be organized around four interwoven themes. The computational organization theme covers concepts and structures of computing systems from digital logic to operating systems. The programming theme concentrates on learning how to design and code programs to solve problems. The mathematical theme helps develop mathematical reasoning, theoretical abstractions and problem solving skills needed for computer scientists. The technology and society theme explores social, historical or philosophical topics related to science and technology. Students who take the program Data and Information: Computational Linguistics in fall quarter, or who have equivalent experience, will be well prepared for this program. Data and Information: Computation and Language Description: Have you ever wondered how web searches work? It is often claimed that one can successfully search for web sites, maps, blogs, images…just by entering a few "key words". How do they do it? More generally, how can computers be programmed to interpret texts and data? This program will bring together faculty and students with interest and expertise in language and computer science with the goal of exploring these questions: When we (or Google's computers) read a text, how do we (or they) understand what the text means? We humans bring to our reading of the text three critical things: 1) knowledge of the language in which the text is written—its grammar and the meanings of the words, and how words are put together into sentences and paragraphs, 2) our understanding of how the world works and how humans communicate, and 3) our natural human intelligence. Even with these abilities, however, we often misinterpret text (or data) or are faced with too much information. The help a computer gives us, however, is sometimes different from how we naturally think about the words, images, maps or other information that we encounter. In this program we will explore how to use computing to understand language. Although the task is complex, an understanding of the abstract structure, logic and organization of language will guide us to successful computational processing of the more complex human languages. In logic, our work will include looking at the structure of words, sentences, and texts (syntax) as well as their meanings (semantics and reasoning). We will examine the underlying grammatical structure of language and its close connection to computing and computer programming. In addition, we will learn to program in Python and study how computers are used to "understand" texts and data. Lectures, seminar and case studies will examine how to make data from text and text or meaning from data. Programming in C++ and Robotics Description: We will explore computers, programming and AI through robotics. The robot we will use is the Scribbler by Parallax. Students will work on a project in groups after learning the basics about the robot. They will also learn the fundamentals of programming in C++. This is ideal for students who have programmed in another language. Students will develop an understanding of concepts such as object-oriented programming, program design, problem solving and C++ pointers. Undergraduate Research in Scientific Inquiry Description: Many faculty members in the Scientific Inquiry planning unit have ongoing research projects that offer students the opportunity to participate in research at the undergraduate level. Students typically begin by working in apprenticeship with faculty or laboratory staff and gradually take on more independent projects within the context of the specific research program as they gain experience. Well-prepared students are encouraged to take advantage of Evergreen's flexible learning structure and excellent equipment to work closely with faculty members on original research. Faculty offering undergraduate research opportunities are listed below. Contact them directly if you are interested. Judith Bayard Cushing studies how scientists might better use information technology in their research. She would like to work with students who have a background in computer science or one of the sciences (e.g., ecology, biology, chemistry or physics), and who are motivated to explore how new computing paradigms, such as object-oriented systems and new database technologies, can be harnessed to improve the individual and collaborative work of scientists. Neal Nelson and Sheryl Shulman are interested in working with advanced computer topics and current problems in the application of computing to the sciences. Their areas of interest include simulations of advanced architectures for distributed computing, advanced programming languages and compilers, programming languages for concurrent and parallel computing, and hardware modeling languages. Richard Weiss works on robotics, computer vision and artificial intelligence. He is also interested in computer architecture and security.
(Original post by Dreamweaver) I was in exactly the same position as you a couple of weeks ago. Chapter 2 mixed is painful. Thankfully, the actual exam questions don't seem to be too bad. Yeah the last 2 chapters are hard to self teach. Livemaths seems really good for this. Matrices aren't as bad as Vectors (IMHO) so it might be worth starting with those although vectors do pop up in one or two of the questions. How are you finding the integration? (Original post by JohnyTheLad)Yeah it's like WTF at the beginning. Get the edexcel FP3 book. It explains most bits well. for a unit vector, you basically write the vector out and divide it by its modulus. Scalar dor product -> you get a number Vector cross product -> you get a vector Both have useful applications, i.e. finding the area of a triangle etc.. No, not just death. I want it to be locked up in permanent spiked chastity, forced to worship the feet of the many women who were forced to go through D1 and be caned and whipped eternally. And as for D2, we can have it castrated and forced to become a sissy maid.
RELATED LINKS Math110 College Algebra 4 credits Section 1MWF1:10 - 2:00MC 420 Th1:00 - 1:50MC 420(note this time!!) Dr. Mark Saegrove Office MC 525Ph. 796-3657Home Phone 1-608-735-4789 CATALOG COURSE DESCRIPTION: Review of basic algebra, second degreeproblems and to be able to communication solutions and explore options. 3.Life Value Skills: A. Develops an appreciation for the intellectual honesty of deductive reasoning; a mathematician's work must stand up to the scrutiny of logic, and it is unethical to try to pass off invalid work. B. Understands the need to do one's own work, to honestly challenge yourself to master the material. 4. Cultural Skills: A.Learns to read, write and manipulate mathematical notation B.Experiences mathematics as a culture of its own, with its own language and modes of thinking. 5.Aesthetic Skills: A. Develops an appreciation for the austere intellectual beauty of deductive reasoning. B. Develops an appreciation for mathematical elegance. General Course Objectives: This course is designed to cause the student to learn traditional college algebra concepts and problem solving skills.It should serve to prepare students for Math 180, Math 230, Math 265, or Math 270. Prerequisite: Acceptable placement score or C grade in Math 001 or equivalent (typically high school algebra). See me right away if you have a question about your math background as it relates to this requirement. A valid verifiable excuse must be presented in order to make up missed exams or quizzes." Extra Help: If you find that you need extra help, see me right away. Tutoring can be made available from the Learning Center if necessary320, 796-3085) within ten days to discuss your accommodation needs. Note: accommodation for special test-taking needs will be made only after these needs are confirmed in writing by Mr. Wojciechowski.
Description Selected metadata Identifier: mathphyspapers02stokrich Copyright-evidence-operator: scanner-julie-l Copyright-region: US Copyright-evidence: Evidence reported by scanner-julie-l for item mathphyspapers02stokrich on Mar 20, 2006; no visible copyright symbol and date found; stated date is 1883; the country of the source library is the United States; not published by the US government.
Math Java Applets (Popularity: ): About 15 applets covering a number of math problems and principles. Manipula Math with Java (Popularity: ): Over 200 applets for middle school students, high school students, college students, and all who are interested in mathematics. Interactive programs and a lot of animation that helps with understanding ... Java Demos for Probability and Statistics (Popularity: ): College professor's applets. Chaos and Fractals Applets (Popularity: ): Several java applets for use in exploring the topics of chaos and fractals. Experimental Math Applets (Popularity: ): Some applets covering Besicovitch sets, conformal compactifaction, honeycombs, exponent calculator, the complex plane, elementary complex maps, Möbius transforms, multi-valued functions, the complex derivative, the complex integral, Taylor and Laurent expansions. Euclid's Elements, An Introduction (Popularity: ): Includes the entire 13 books on plane geometry, geometric and abstract algebra, number theory, incommensurables, and solid geometry. Uses java applets to illustrate the principles. Spirograph Applet (Popularity: ): Makes a spirograph, just like the kid toy. TenBlocks and IntegerZone (Popularity: ): TenBlocks turns the times tables into a series of puzzles. IntegerZone lets users explore aspects of arithmetic and number theory using the integers themselves as the interface. Graph Explorer (Popularity: ): A Java applet for graphing functions, with smooth zooming and panning across graphs, and variable parameters which can be used for animation. Java Applets for Visualization of Statistical Concepts (Popularity: ): These applets are designed for the purpose of computer-aided education in statistic courses. The intent of these applets is to help students learn some abstract statistics concepts easier than before. ... Online Tutor (Popularity: ): on-line math tutor and science tutor for school age children - Place values to Probability, geometry, ratios, percentages, fractions and measurements, solar system, weather and human body
recipes_helperRecipesHelper end m 406 Section 0101 Exam 3 Topics and Samples 1. Multiplicative functions. Definition. (a) Define (1) = 1 and (n) = 2r where r is the number of distinct primes in the PF of n. Show that is multiplicative. 2. Euler -function. Definition, how to fin Chapter 10SolitonsStarting in the 19th century, researchers found that certain nonlinear PDEs admit exact solutions in the form of solitary waves, known today as solitons. There's a famous story of the Scottish engineer, John Scott Russell, who in Hypertext and E-CommerceInformatics 211 November 6, 2007The Basics of Hypertext Theconcept: interrelated information Content (the information) Structure (the links between the information) View (what part of the content and structure one s Project: Design an Online Travel Agency This is a group project (5-6 students each group). You are assigned to design a website and its underlying software architecture for a travel agency located in southern California. The agency wants the website The Mythical Man-Month by Fred Brooks (I) Published 1975, Republished 1995 Experience managing the development of OS/360 in 1964-65 Central Argument Large programming projects suffer management problems different in kind than small ones, due to OPTIMIZATION AND LEARNINGWe can define learning as the process by which associations are made between a set of stimuli and a set of responses. We can visualize this process on a coordinate system, where the independent variable is the set of stimul Review Questions, Calc I and App. E, 5.1-5.2 Here are some selected topics from Calculus I that you might want to review if its been a while since you've seen them: Topic: Definition of continuity Where is f (x) continuous? What is the domain of f (x
Applications of Trigonometry Lesson 3: Dot Product of Vectors lesson includes dot products of vectors, projection of vectors, work, and various applications in real-world situations. There is an eight-page "Bound-Book" style foldable to accompany the lesson, along with a *.pdf file of the completed set of notes. Compressed Zip File Be sure that you have an application to open this file type before downloading and/or purchasing. 1938.34
Students will use concepts to describe, classify, model, and predict topical phenomena, aided by inductive (experimental) and deductive (rational) methods, including calculus. Students will develop analytical skills appropriate to solve both symbolic and numerical problems involving quantities associated with the topical phenomena. When obtaining a solution from calculator, spreadsheet or simulation software, students will critically evaluate the method (e.g., How valid are my assumptions?) and significance (e.g., how certain are my values and do my units check?) of. Students will be able to describe the role physical quantities and principles play in existing environmental and technological systems. Students will be able to understand foundational concepts they can use in later classes, such as the waves and electricity & magnetism. The mission of the Mathematical Sciences General Education component is: to educate students in excellent problem solving skills and the quantitative analysis of Mathematics, Statistics, Physics, and Computer Science, to challenge students to live out their faith in their vocation as they become servant leaders in society, church , and the world, and encourages the development of knowledge, skills, and attitudes of intellect, character, and faith that Christians use in lives of service, leadership and reconciliation.
Students must pass 20 credits of mathematics. 10 Credits must be from Algebra or Integrated Math 1 and 10 Credits must be in Geometry or Integrated Math 2 UC/CSU A-G Subject Requirement: (C Category) Students must complete three years of college prepatory mathematics, however 4 years is recommended. Students must complete the three minimum courses of: Algebra 1, Geometry and Algebra 2 Intervention and Support Services for mathematics Algebra and CAHSEE support classes are available to students as determined by their Academic Counselors. Algebra and Geometry credit recovery is available afterschool and on Saturdays. Algebra 2 make ups may be available during summer school. Tutorial services are available for all levels of math afterschool from 3:00 to 4:45 M-Th Math Courses Offered at Yerba Buena High School Algebra 1 Grades 9 -12 (UC, CSU) Prerequisites: None Algebra 1 is the first course in the traditional four-year college preparatory mathematics sequence. In light of California 's mandated assessment programs, namely the STAR and the High School Exit Exam, the first year program has been divided into six major strands, one for each grading period. The strands are: Working with Linear Equations Part I (1.5 credits) Working with Linear Equations Part II (1.5 credits) Working with Linear Equations in Two Variables (2.0 credits) Working with Polynomials and Rational Expressions (1.5 credits) Working with Quadratics (1.5 credits) Working with Geometry, Probability and Statistics (2.0 credits) The grading standard for Algebra 1 is as follows: 90-100% A; 80-89% B; 70-79% C; Below 70% F. Students who do not achieve a C or better on each strand must attend afterschool recovery sessions in order to obtain credit for the class. Students must earn 10 credits in Algebra 1 to continue on to the next course in math. Geometry Grades 9 -12 (UC, CSU) Prerequisites: Algebra 1 or Integrated Mathematics 1 This course is the second course in the traditional four-year college preparatory mathematics sequence. It is an investigation of the properties and their applications in area, volume, and proportion. It includes an introduction to analytic geometry that is a study of the structure of logical, deductive, inductive, and intuitive reasoning, and the development of proofs and demonstrations. Algebra 2 Grades 9 -12 (UC, CSU) Prerequisites: C or better in Algebra 1 or Integrated Math 1 & Geometry or Integrated Math 2 This course is the third course in the traditional four-year college preparatory mathematics sequence. The material covered complements and expands the mathematical content and concepts of Integrated Math I and Geometry. Students who master Algebra 2 will gain experience with algebraic solutions of problems in various content areas, including the solution of systems of quadratic equations, logarithmic and exponential functions, the binomial theorem and the complex number system. Math Analysis Grades 10 -12 (UC, CSU) Prerequisites: C (B preferred) in Algebra 2 This rigorous and demanding course consists of a study of selected topics of advanced high school mathematics, including trigonometry, and is intended to provide the student with sufficient background to pursue college mathematics or a field related to mathematics. It is recommended for all college preparatory students preparing for a career in science, mathematics, and engineering. Upon successful completion each of the following 3 courses, the student will take the appropriate AP examination and, with an appropriate score, receive college credit for the course. Calculus AP/AB Grades 10 -12 (UC, CSU) Prerequisites: C (B preferred) in Math Analysis This is rigorous and demanding course designed to teach college-level curriculum. The student will study from a primarily intuitive, rather than totally abstract approach, the following topics: function relationships, analytic geometry and rectilinear motion, limits and continuity, differentiation of algebraic and trigonometric functions, maximum and minimum values with applications, and the study of areas using integration. Investigations will help the students examine the usefulness of Calculus in the natural and social sciences. A graphing calculator is needed for both the course and the Advanced Placement test. *Statistics (Advanced Placement) Grades 10 – 12 (UC, CSU) Prerequisites: B or better in Algebra 2, or a C or better in Math Analysis. However, this course could be taken concurrently with Math Analysis or with Calculus AP/AB. Must be at grade level in English. This course introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students will study four broad conceptual themes: Exploratory Data (observing patterns and departures from patterns), Planning a Study (deciding what and how to measure), Anticipating Patterns (producing models using probability and simulation), and Statistical Inference (confirming models). Topics explored in this course include: distributions of univariate data, exploring bivariate data and categorical data, correlation and linearity, methods of data collection, planning and conducting surveys/experiments, random samples, random variables, mean and standard deviation, probability, sampling distribution, normal distribution, statistical inference, confidence intervals, tests of significance and mathematical modeling.
Over the past few months, many parents have contacted us, asking if we plan to make a DIVE CD to teach the new Saxon Algebra 1, 4th edition textbook. The short answer is "no", and the short reason is that we believe the newer Saxon textbooks have strayed too far from John Saxon's (1923-1996) original, tried and tested vision for teaching mathematics. This new textbook was not published by John Saxon, but by Houghton Mifflin Harcourt (HMH). If you would like to know more about our reasons, please read on. Physical Differences Saxon Algebra 1 4th ed. (left), Saxon Algebra 1 3rd ed. (center), and Leonhard Euler's Elements of Algebra (right), a text that most modern algebra books are based upon. The 4th edition cover is noticeably different from earlier Saxon editions. For comparison, I have included a copy of Leonhard Euler's Elements of Algebra, a textbook whose subject matter is the foundation of most modern algebra courses. Euler lived from 1707-1783, and is considered by most scholars to be one of the best, if not the best, mathematician ever. While I am in awe of his ability to write original research at the rate of 800 pages per year for most of his adult life, I am more impressed by his understanding of God. One of my favorite quotes is from his book, Letters to a German Princess: "It is God, therefore, who places men, every instant, in circumstances the most favourable, and from which, they may derive motives the most powerful, to produce their conversion." Euler was a genius, but he was also a humble, Christian family man, and I think his biblical understanding of the world helped him excel at mathematics. Helping students understand the importance of a biblical foundation to their education is one way our DIVE Math lectures differ from instruction found in either new or traditional Saxon textbooks. When I titled this post "Weighing the Differences", I meant it, literally! I put the books on a scale, and the 4th edition is quite a monster at 4.75 lbs, a 58.3% increase over the 3rd edition.
The math foundations workbook is for people who are a bit rusty on math. It was designed for people who haven't taken a math course in a number of years. The other book, Kaplan Math Workbook, is more advanced and goes a bit more in-depth when it teaches the concepts. So, the better book for you really depends on your comfort level concerning math. _________________
Math made easier: advice from experts Many students struggle with various kinds of math, including positive and negative number signs, fractions, factoring, graphing and word problems, instructors in the department of mathematics and statistics said. In fall 2011, the success rate for college algebra, a core math course, was 59 percent, said Mellisa Hardeman, senior instructor in the department. The success rate dropped anther percentage point the following year, she said. In fall 2012, 50 to 60 percent of pre-core math students had difficulties solving math problems, said Denise LeGrand, director of the Mac I math lab. Ike McPhearson, math tutor, explained why students may have trouble comprehending math. One reason is that students may come from a home where education is not valued, he said. A bad experience with an instructor can also change students' attitudes about math. "You can't take yourself too seriously as a teacher," said Hardeman. Instructors can never give a student too much help passing math, she said. Students who took a math course in high school before going to college are less likely to struggle with math, Hardeman said. Some students go to college years after graduating high school, however, and may forget everything they learned in their math classes. Fortunately, there are a number of strategies that can help students overcome these challenges and develop a better understanding of math. "In order to make math easy for students, show different ways of how to understand it," said McPherson, who has tutored high school and college students. Another way of making math fun for students is to create different games, he said. According to LeGrand, the most important way to become better at math is to practice math exercises for 20 to 30 minutes. "They won't see the results right away," said LeGrand, " but if they go to class and focus on work required, they will be successful and they will build confidence." In addition, students can get help from tutors at the math lab. Each semester, the lab hires 12 tutors, LeGrand said. For the math-impaired, there is a new math course called Quantitative and Mathematical Reasoning. The course was designed for students who are not science, technology, engineering or mathematics majors. It focuses on practical math, for example, currency exchange rates. The course fulfills the core math requirement, in place of college algebra. Pre-core math courses, developmental math courses students take if they do not have the prerequisites for college math classes, are becoming more successful, said Tracy Watson, coordinator for pre-core math. The success rate for those courses rose to 77 percent in fall 2012, she said. Previously, the success rate was 37 percent for a 4-year period, she said. This semester, there are 80 math majors at the university. "We all like how math works because it all fits together," Watson said. "Students who major in math develop a sense of thinking and solving problems," said Thomas McMillan, department chair. Once students better understand math, they will have the confidence to solve not only math problems, but problems in everyday life as well
mathematics to problem solving rather than derivation of theory. It provides a balance between physical and chemical hydrogeology. Numerous case studies cultivate student understanding of the occurrence and movement of ground water in a variety of geologic settings. You can earn a 5% commission by selling Applied Hydrogeology
it is basic introduction to pre-algebra. In includes the arithmetic operations on directed numbers. simplifying algebraic expression, solving equations, inequality of open and closed type, two inequalities at the same time, compound inequalities, how to construct formula, change subject of the formula, find the value of the formula
Introductory Introductory Algebra or Beginning Algebra. The engaging Martin-Gay workbook series presents a student-friendly approach to the concepts of basic math and algebra, giving students ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the worktexts are to build confidence, increase motivation, and encourage mastery of basic skills and concepts. Martin-Gay ensures that students have the most up-to-date, relevant text preparation for their next math course; enhances ... MOREstudents' perception of math by exposing them to real-life situations through graphs and applications; and ensures that students have an organized, integrated learning system at their fingertips. The integrated learning resources program features text-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. Introductory Algebra is typically a 1-semester course that provides a solid foundation in algebraic skills and reasoning for students who have little or no previous experience with the topic.& The goal is to effectively prepare students to transition into Intermediate Algebra. R. Prealgebra Preview. Factors and the Least Common Multiple. Fractions. Decimals and Percents.
This three-page handout asks students to create systems of equations that can be used to solve real-life problems. There are 13 problems and an opportunity for students to create their own problem that involves a system of equation. This document was created by the seller, Stephanie Long. Additional documents involving 7th, 8th, and 9th grade math and Algebra can be obtained by contacting the seller.
understand relations and functions and select, convert flexibly among, and use various representations for them; • analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior; • understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions; • understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions; approximate and interpret rates of change from graphical and numerical data. In the vision of school mathematics in these Standards, middle-grades students will learn that patterns can be represented and analyzed mathematically. By the ninth grade, they will have represented linear functions with tables, graphs, verbal rules, and symbolic rules and worked with and interpreted these representations. They will have explored some nonlinear relationships as well. In high school, students should have opportunities to build on these earlier experiences, both deepening their understanding of relations and functions and expanding their repertoire of familiar functions. Students should use technological tools to represent and study the behavior of polynomial, exponential, rational, and periodic functions, among others. They will learn to combine functions, express them in equivalent forms, compose them, and find inverses where possible. As they do so, they will come to understand the concept of a class of functions and learn to recognize the characteristics of various classes. High school algebra also should provide students with insights into mathematical abstraction and structure. In grades 9–12, students should develop an understanding of the algebraic properties that govern the manipulation of symbols in expressions, equations, and inequalities. They should become fluent in performing such manipulations by appropriate means—mentally, by hand, or by machine—to solve equations and inequalities, to generate equivalent forms of expressions or functions, or to prove general results. The expanded class of functions available to high school students for mathematical modeling should provide them with a versatile and powerful means for analyzing and describing their world. With utilities for symbol manipulation, graphing, and curve fitting and with programmable software and spreadsheets to represent iterative processes, students can model and analyze a wide range of phenomena. These mathematical tools can help students develop a deeper understanding of real-world phenomena. At the same time, working in real-world contexts may help students make sense of the underlying mathematical concepts and may foster an appreciation of those concepts. Understand patterns, relations, and functions High school students' algebra experience should enable them to create and use tabular, symbolic, graphical, and verbal representations and to analyze and understand patterns, relations, and functions with more sophistication than in the middle grades. In helping high school students learn about the characteristics of particular classes of functions, teachers may find it helpful to compare and contrast situations that are modeled by functions from various classes. For example, the functions that model the essential features of the situations in figure 7.4 are quite different from one another. Students should be able to express them using tables, graphs, and symbols. Fig. 7.4. Three situations that can be modeled by functions of different classes p. 297 For the first situation, students might begin by generating a table of values. If C is the cost in cents of mailing a letter and P is the weight of the letter in ounces, then the function C = 33 + (P – 1)(22) describes C as a function of P for positive integer values of P up through 13. » Students should understand that this situation has some linear qualities. For real-number values of P, the points on the graph of C = 33 + (P – 1)(22) lie on a line, and the rate of change is constant at 22 cents per ounce. However, the actual cost of postage and the linear function agree only at positive integer values of P. Students must realize that the graph of postal cost as a function of weight is a step function, as seen in figure 7.5. Fig. 7.5. A comparison of step and linear functions For the second situation described in figure 7.4, teachers could encourage students to find a general expression for the function and note how its form differs from the step function that describes the postal cost. Some students might generate an iterative or recursive definition for the function, using the population of a given year (NOW) to determine the population of the next year (NEXT): NEXT = (1.02) • NOW, start at 6 billion (See the discussion of NOW-NEXT equations in the "Representation" section of chapter 6.) Moreover, students should be able to recognize that this situation can be represented explicitly by the exponential function f(n) = 6(1.02)n, where f(n) is the population in billions and n is the number of years since 1999. A discussion of whether this formula is likely to be a good model forever would help students see the limitations of mathematical models. p. 298 For the third situation, students could begin by graphing the given data. It will help them to know that everywhere on earth except at the equator, the period of sunlight during the day increases for six months of the year and decreases for the other six. From the graph, they should be able to see that the daily increase in daylight is nonconstant over the first half of the year and that the decrease in the second half of the year also is nonconstant. Students could be asked to find a function that models the data well. The teacher could tell them that the length of » daylight can indeed be modeled by a function of the form T(t) = Tave + TA() sin(t + ), where t is the time, Tave = average daylight time = 12 hours; TA() = amplitude, depending on latitude (changes sign at the equator); = frequency = 2/(12 months), and = phase (depending on choice of the initial time, t0). Students will see such formulas in their physics courses and need to understand that formulas express models of physical phenomena. It is also important to note that the parameters in physical equations have units. After exploring and modeling each of the three situations individually, students could be asked to compare the situations. For example, they might be asked to find characteristics that are common to two or more of the functions. Some students might note that over the intervals given, the first function is nondecreasing, the second is strictly increasing, and the third both increases and decreases. Students need to be sensitive to the facts that functions that are increasing over some intervals don't necessarily stay increasing and that increasing functions may have very different rates of increase, as these three examples illustrate. Students could also be asked to consider the advantages and disadvantages of the different ways the three functions were represented. The teacher should help students realize that depending on what one wants to know, different representations of these functions can be more or less useful. For instance, a table may be the most convenient way to initially represent the postage function in the first example. The same may be so for the third example if the goal is to determine quickly how much sunlight there will be on a given day. Despite the convenience of being able to "read" a value directly, however, the table may obscure the periodicity of the phenomenon. The periodicity becomes apparent when the function is represented graphically or symbolically. Similarly, although students may first create tables when presented with the second situation, graphical and symbolic representations of the exponential function may help students develop a better understanding of the nature of exponential growth. High school students should have substantial experience in exploring the properties of different classes of functions. For instance, they should learn that the function f(x) = x2 – 2x – 3 is quadratic, that its graph is a parabola, and that the graph opens "up" because the leading coefficient is positive. They should also learn that some quadratic equations do not have real roots and that this characteristic corresponds to the fact that their graphs do not cross the x-axis. And they should be able to identify the complex roots of such quadratics. p. 299 In addition, students should learn to recognize how the values of parameters shape the graphs of functions in a class. With access to computer algebra systems (CAS)—software on either a computer or calculator that carries out manipulations of symbolic expressions or equations, can compute or approximate values of functions or solutions to equations, and can graph functions and relations—students can easily explore the effects of changes in parameter as a means of better understanding classes of functions. For example, explorations with functions of the form y = ax2 + bx + c lead to some interesting results. The consequences of changes in the parameters a and c on the graphs of functions are relatively easy to observe. Changes in b are not as obvious: changing b results in a translation of the parabola along a » nonvertical line. Moreover, a trace of the vertices of the parabolas formed as b is varied forms a parabola itself. Exploring functions of the form f(x) = a(x – h)2 + b(x – h) + c and seeing how their graphs change as the value of h is changed also provides a basis for understanding transformations and coordinate changes. As high school students study several classes of functions and become familiar with the properties of each, they should begin to see that classifying functions as linear, quadratic, or exponential makes sense because the functions in each of these classes share important attributes. Many of these attributes are global characteristics of the functions. Consider, for example, the graphs of the three exponential functions of the form f(x) = a • bx+ c, with a > 0 and b > 1, given in figure 7.6. Fig. 7.6. Graphs of exponential functions of the form f(x) = a • bx + c To help students notice and describe characteristics of these three functions, teachers might ask, "What happens to each of these functions for large positive values of x? For large negative values of x? Where do they cross the y-axis?" One student might note that the values of each function increase rapidly for large positive values of x. Another student could point out that the y-intercept of each graph appears to be a + c. Teachers should then encourage students to explore what happens in cases where a < 0 or 0 < b < 1. Students should find that changing the sign of a will reflect the graph over a horizontal line, whereas changing b to 1/b will reflect the graph over the y-axis. The graphs will retain the same shape. This type of exploration should help students see that all functions of the form f(x) = a • bx + c share certain properties. Through analytic and exploratory work, students can learn the properties of this and other classes of functions. Represent and analyze mathematical situations and structures using algebraic symbols p. 300 Fluency with algebraic symbolism helps students represent and solve problems in many areas of the curriculum. For example, proving that the square of any odd integer is 1 more than a multiple of 8 (see the related discussion in the "Number" section of this chapter) can involve representing odd numbers and operating on that representation algebraically. Likewise, the equations in figure 7.7 suggest an algebraic justification of » a visual argument for the Pythagorean theorem. And many geometric conjectures—for example, that the medians of a triangle intersect at a point—can be proved by representing the situation using coordinates and manipulating the resulting symbolic forms (see the "Geometry" section of this chapter). Straightforward algebraic arguments can be used to show how the mean and standard deviation of a data set change if sample measurements are converted from square meters to square feet (see the "Reasoning and Proof" section of this chapter). Fig. 7.7. An algebraic explanation of a visual proof of the Pythagorean theorem Students should be able to operate fluently on algebraic expressions, combining them and reexpressing them in alternative forms. These skills underlie the ability to find exact solutions for equations, a goal that has always been at the heart of the algebra curriculum. Even solving equations such as requires some degree of fluency. Finding and understanding the meaning of the solution of an equation such as calls for seeing that the equation can be written as a quadratic equation by making the substitution u = e2x. (Such an equation deserves careful attention because one of the roots of the quadratic is negative.) Whether they solve equations mentally, by hand, or using CAS, students should develop an ease with symbols that enables them to represent situations symbolically, to select appropriate methods of solution, and to judge whether the results are plausible. Being able to operate with algebraic symbols is also important because the ability to rewrite algebraic expressions enables students to reexpress functions in ways that reveal different types of information about them. For example, given the quadratic function f(x) = x2 – 2x – 3, some of whose graphical properties were discussed earlier, students should be able to reexpress it as f(x) = (x – 1)2 – 4, a form from which they can easily identify the vertex of the parabola. And they should also be able to express the function in the form f(x) = (x – 3)(x + 1) and thus identify its roots as x = 3 and x = –1. p. 301 The following example of how symbol-manipulation skills and the ability to interpret graphs could work in concert is a hypothetical composite of exploratory classroom activities, inspired by Waits and Demana (1998): » A teacher asks her students to analyze the function and make as many observations about it as they can. Some students begin by trying to graph the function, plotting points by hand. Some students use a CAS and others perform long division by hand, producing the equivalent form Some graph the original function or the equivalent form on a computer or on graphing calculators; the zoom feature enables them to see various views of the graph, as seen in figure 7.8. Fig. 7.8. Different views of the function It is hard to interpret some of the graphs near x = 2, a matter the class returns to later. Focusing on a graph where the zoom-out feature has been used a number of times (see fig. 7.8c), some students observe, "The graph looks like a straight line." The teacher asks the class to decide whether it is a line and, if so, what the equation of the line might be. To investigate the question, the teacher suggests that they find several values of f(x) for large positive and negative values of x and use curve-fitting software to find the equation of the line passing through those points. Different groups choose different x-values and, as a result, obtain slightly different values for the slope and the y-intercept. However, when the class discusses their findings, they discover that the lines that fit those points all seemed "close" to the line y = 2x + 15. Some students point out that this function is part of the result they obtained after performing the long division. The class concludes that the line y = 2x + 15 is a good approximation to f(x) for large x-values but that it is not a perfect fit. This conclusion leads to the question of how the students might combine the graphs of g(x) = 2x + 15 and h(x) = 36/(x – 2) to deduce the shape of the graph of f(x). Hand-drawn and computer plots help students explore how the graph of each function "contributes to" the graph of the sum. Examining the behavior of leads to a discussion of what "really" happens near x = 2, of why the function appears to be linear for large values of x, and of the need to develop a sense of how algebraic and graphical representations of functions are related, even when graphing programs or calculators are available. p. 302 Students in grades 9–12 should develop understandings of algebraic concepts and skill in manipulating symbols that will serve them in situations that require both. Success in the example shown in figure 7.9, for example, requires more than symbol manipulation. There are several ways to approach this problem, each of which requires understanding algebraic concepts and facility with algebraic symbols. For example, to complete the first row of the table, students need only know how to evaluate f(x) and g(x) for a given value of x. However, to complete the second row, students must know what it means to compose functions, including the role of the "inner" and "outer" function and the numbers » on which they act in a composition. They also must understand how to read the symbols fg(x)) and g(f(x)). Students might reason, using an intuitive understanding of the inverse of a function, that because g(x) = 4, x must be either 1 or –3. They can then determine that x cannot be 1, because g(f(1)) is not 81. Use mathematical models to represent and understand quantitative relationships Modeling involves identifying and selecting relevant features of a real-world situation, representing those features symbolically, analyzing and reasoning about the model and the characteristics of the situation, and considering the accuracy and limitations of the model. In the program proposed here, middle-grades students will have used linear functions to model a range of phenomena and explore some nonlinear phenomena. High school students should study modeling in greater depth, generating or using data and exploring which kinds of functions best fit or model those data. Teachers may find that having students generate data helps generate interest in creating mathematical models. For example, students could conduct an experiment to study the relationship between the time it takes a skateboard to roll down a ramp of fixed length and the height of the ramp (Zbiek and Heid 1990). Teams of students might set ramps at different heights and repeatedly roll skateboards down the ramps and measure the time. Once students have gathered and plotted the data, they can analyze the physical features of the situation to create appropriate mathematical models. Their knowledge of the characteristics of various classes of functions should help them select potential models. In this situation, as the height of the ramp is increased, less time is needed, suggesting that the function is decreasing. Students can discuss the suitability of linear, quadratic, exponential, and rational functions by arguing from their data or from the physics of the situation. Curve-fitting software allows students to generate possible models, which they can examine for suitability on the basis of the data and the situation. In making choices about what kinds of situations students will model, teachers should include examples in which models can be expressed in iterative, or recursive, form. Consider the following example, adapted from National Research Council (1998, p. 80), of the elimination of a medicine from the circulatory system. p. 303 A student strained her knee in an intramural volleyball game, and her doctor prescribed an anti-inflammatory drug to reduce the swelling. She is to » take two 220-milligram tablets every 8 hours for 10 days. If her kidneys filtered 60% of this drug from her body every 8 hours, how much of the drug was in her system after 10 days? How much of the drug would have been in her system if she had continued to take the drug for a year? Teachers might ask students to conjecture about how much of the drug would be in the volleyball player's system after 10 days. They might also ask about whether the drug keeps accumulating noticeably in the athlete's system. Students will tend to predict that it does, and they can be asked to examine the accumulation in their analysis. Students might begin by calculating a few values of the amount of the drug in the player's system and looking for a pattern. They can proceed to model the situation directly, representing it informally as NEXT = 0.4(NOW) + 440, start at 440 or more formally as a1 = 440 and an + 1 = 0.4an + 440 for 1 n 31, where n represents the dose number (dose 31 would be taken at 240 hours, or 10 days) and an represents the amount of the drug in the system just after the nth dose. By looking at calculator or spreadsheet computations like those in figure 7.10, students should be able to see that the amount of the drug in the bloodstream reaches an after-dosage "equilibrium" value of about 733 1/3 milligrams. Students should learn to express the relationship in one of the iterative forms given above. Then the mathematics in this example can be pursued in various ways. At the most elementary level, the students can simply verify the equilibrium value by showing that 0.4(733 1/3) + 440 = 733 1/3 milligrams. They can be asked to predict what would happen if the initial dose of the anti-inflammatory drug were different, to run the simulation, and to explain the result they obtain. Fig. 7.10. A spreadsheet computation of the "drug dosage" problem This investigation opens the door to explorations of finite sequences and series and to the informal consideration of limits. (For example, spreadsheet printouts for "large n" for various dosages strongly suggest that the sequence {an} of after-dosage levels converges.) Expanding the first few terms reveals that this is a finite geometric series: Students might find it interesting to pursue the behavior of this series. To investigate other aspects of the modeling situation, students could also be asked to address questions like the following: If the athlete stops taking the drug after 10 days, how long does it take for her system to eliminate most of the drug? p. 305 How could you determine a dosage that would result in a targeted after-dosage equilibrium level, such as 500 milligrams? » Students should also be made aware that problems such as this describe only one part of a treatment regimen and that doctors would be alert to the possibility and implications of various complicating factors. In grades 9–12, students should encounter a wide variety of situations that can be modeled recursively, such as interest-rate problems or situations involving the logistic equation for growth. The study of recursive patterns should build during the years from ninth through twelfth grade. Students often see trends in data by noticing change in the form of differences or ratios (How much more or less? How many times more or less?). Recursively defined functions offer students a natural way to express these relationships and to see how some functions can be defined recursively as well as explicitly. Analyze change in various contexts Increasingly, discussions of change are found in the popular press and news reports. Students should be able to interpret statements such as "the rate of inflation is decreasing." The study of change in grades 9–12 is intended to give students a deeper understanding of the ways in which changes in quantities can be represented mathematically and of the concept of rate of change. The "Algebra" section of this chapter began with examples of three different real-world contexts in which very different kinds of change occurred. One situation was modeled by a step function, one by an exponential function, and one by a periodic function. Each of these functions changes in different ways over the interval given. As discussed earlier, students should recognize that the step function is nonlinear but that it has some linear qualities. To many students, the kind of change described in the second situation sounds linear: "Each year the population changes by 2 percent." However, the change is 2 percent of the previous year's population; as the population grows, the increase grows as well. Students should come to realize that functions of this type grow very rapidly. In the third example, students can see that not only is the function periodic but because it is, its rate of change is periodic as well. Chapter 6 gives an example in which middle-grades students are asked to compare the costs of two different pricing schemes for telephone calls: a flat rate of $0.45 a minute versus a rate of $0.50 a minute for the first 60 minutes and $0.10 a minute for each minute thereafter. In examples of this type, the dependent variable typically changes (over some interval) a fixed amount for each unit change in the independent variable. In high school, students should analyze situations in which quantities change in much more complex ways and in which the relationships between quantities and their rates of change are more subtle. Consider, for example, the situation (adapted from Carlson [1998, p. 147]) in figure 7.11. Fig. 7.11. A problem requiring a sophisticated understanding of change p. 305 Working problems of this type builds on the understandings of change developed in the middle grades and lays groundwork for the study of calculus. Because students tend to confuse velocity with position, teachers should help them think carefully about which variables are represented in the diagram and about how they change. First, for example, students must realize that the variable on the vertical axis is velocity, rather than position. To answer part a of the question, they need to reason that because the velocity of car A is greater than that of car B at every point in the interval 0 < t < 1, car A has necessarily traveled a » greater distance than car B. They can read the answer to part b directly off the graph: at t = 1 hour, both cars are traveling at the same velocity. Answering part c calls for at least an intuitive understanding of instantaneous rate of change. Acceleration is the rate of change of velocity. At t = 1 hour, the velocity of car B is increasing more rapidly than that of car A, so car B is accelerating more rapidly than car A at t = 1 hour. Part d is particularly counterintuitive for students (Carlson 1998). Since car B is accelerating more rapidly than car A near t = 1 hour, students tend to think that car B is "catching up" with car A, and it is, although it is still far behind. Some will interpret the intersection of the graphs to mean that the cars meet. Teachers need to help students focus on the relative velocities of the two cars. Questions such as "Which car is moving faster over the interval from t = 0.75 hour to t = 1 hour?" can help students realize that car A is not only ahead of car B but moving faster and hence pulling away from car B. Car B starts catching up with car A only after t = 1 hour.
Algebra 1 textbook answers and problem sets designed to illustrate all chapters covered in Algebra 1. All answers are illustrated with "motion lines" and explanations. Contributed by offering instant math help for struggling algebra students
Basic Math Posted on Oct 26, 2010 in \| Comments Off This course is designed for seventh and/or eighth grade students who need a comprehensive study of basic mathematics from simple addition to pre-algebra. The learning approach is based on content mastery facilitated by a combination of practice and reasoning. Each math concept is explained, defined and illustrated with at least two examples. Activity problems are crafted carefully to move the student from known to unknown material. The writers and editors have demonstrated their extensive experience with guided individualized learning approaches. Students can move through the course and grasp math concepts with very little dependence on teachers. This course provides excellent remedial studies for high school level students or adults who need a refresher course prior to algebra. *FREE Math Skills Diagnostic Test that pinpoints exactly where students need to start in Basic Math Skills. Click here to download the diagnostic test in PDF format; and for the diagnostic key click here. Basic Math Skills Samples available for download: Basic Math Skills Diagnostic Test This instrument identifies where students stopped learning basic math skills between fourth and ninthgrade. It diagnoses and prescribes where the student should begin learning basics in order to grasp Algebra I. The Diagnostic test places students in the appropriate chapters of Basic and Intermediate Math Skills (designed for 7th and 8th grades, and high school refresher math).
Ages: 10+ Grade Levels: 5-12 Availability:Sold out and no longer available from Timberdoodle Co. Product Code:345-500 Sold Out! Timberdoodle's review Introduce your students to algebra in simple terms. KeyAbout the Key To... series: The Key To... series was developed by the same folks who produce Miquon Math. Though not manipulative dependent, there are scads of illustrations to make the concepts crystal clear. There is also a lot of white space, large type, and only one concept is presented per page. The Key to ... books are not only easy to learn from, but also to follow along with if you, the teacher, are a little foggy on these topics! These books are self-directed, which means your child works independently at his own pace. What will you do with all your spare time?!? Answer books are included in each pack, and the answers are clearly worked out, in case you need to bluff your way through!! More than 5 million of these workbooks have been bought since their creation over 30 years ago! Most workbooks are printed on recycled paper.
Technology and the Future of Mathematical Problem Solving 04.11.13 @ 09:00 AM - 10:00 AM Location: Kellas 104 The advent of sophisticated computer programs into the classroom has made many problems found in the traditional mathematics curriculum somewhat obsolete for they can be easily solved by software. The presentation (aimed at the general audience) will discuss ways of developing problems that are both technology-enabled and technology-immune in the sense that whereas technology may be used in support of problem solving, its direct application is not sufficient for achieving the end result.
Tutorial 1 Once you have access to an installation of Mathematica, you need to know how to use it. Opening the Program In an on-campus computer lab, go to Start Menu, then Programs, then Wolfram Mathematica. Click on the icon for Mathematica, named Spikey. Up will pop an introductory window. On the left hand side of this button is an option to create a new Mathematica notebook or open an old one. The notebook is where all your interactions with the program will take place. First steps with Mathematica Open the file. The file should look like a "Powerpoint" Presentation. If it does not, go to the Format Menu and click on "Format > Screen Environment > SlideShow". Follow this tutorial step-by-step and discuss the most interesting aspects with your neighbors. At the end of the tutorial, you should use the remaining time to explore the power of Mathematica. I suggest looking in the Documentation Center (Help Menu) or at the Wolfram Demonstrations Project. Feel free to explore on your own or with your neighbors. If you are having trouble getting started, here is what I do when I am exploring: I go to the Documentation Center and type in a command (such as Manipulate) I do a quick look at the selected examples that are given and see if they are interesting. If so, I want to see all the examples. So I select the entire notebook (Ctrl-A or Apple-A) and then open all subgroups (Cell Menu: "Grouping > Open All Subgroups"). I play around with the examples, moving sliders, changing variables to see what happens. If I see a command I do not know, I will search for it in the Documentation Center At the bottom of the file is a "See Also" section, which tells you similar commands. Also at the bottom are links to more in depth tutorials, which can be useful sometimes. Other Items of Note! In Mathematica, it is important to distinguish between parentheses (), brackets [], and braces {}: Parentheses (): Used to group mathematical expressions, such as (3+4)/(5+7). Brackets []: Used when calling functions, such as N[Pi]. Braces {}: Used when making lists, such as {i,1,20}. If you use the wrong symbols in the wrong places or if you do not have a closing symbol for every opening symbol, Mathematica will give you an error. Mathematica is Case-SenSitive (AA is not the same as aA), so be careful about what you type. Many of your initial errors will come about because of one of the two above problems. In Mathematica, there are four types of equals: =, :=, ==, and ===. You need to understand the difference between the first two. To define a variable to store it in memory, use =. For example, to define z to be 3, write z=3. You use == to check for equality. For example, 1-1==0 will evaluate to True and 1==0 will evaluate to False. You use := to define your own command. (This is advanced.) You will likely not use === in this class. One of the most important things to do is explore. If you are having trouble with a certain function, use the ? command to ask for help. Enter ? Table and the output will be a yellow box with a quick synopsis of the command. For more detailed information, click the blue >> at the bottom right of this yellow box. This will open the Documentation Center which gives examples of using the command in action, available options for this command, and anything else you might want to know about the command. Algebra and Calculus Mathematica will do everything your calculator can and more. Use ^ to put something to a power. pi is Pi, e is E and sqrt(-1) is I. If you want to see the numerical approximation to a fraction or irrational number, use the function N. For example, to find the decimal represenation of pi, write N[Pi]. Use E^x or Exp[x] to represent the function ex. To take the derivative of a function, use D and specify the derivative with respect to which variable. For instance D[x^2 + 3x, x]. To take the integral of a function, use Integrate and specify the integral with respect to which variable. For instance Integrate[x^2 + 3x, x]. To solve for the roots of ax2+bx+c=0 symbolically, use Solve[a x^2 + b x + c == 0, x]. Notice the double equals sign. (Mathematica is searching for when the expression is True.) Coefficient[(1 + x)^10, x^3] gives the coefficient of x3 in the expansion of (1 + x)10.
Practice general math problems with Aberdeen Academy's free program designed for teens and adults who require online continuing education. To find out more about Aberdeen's course and what it entails, go to High School Diploma. Welcome to our new statistic section. Get ready to have a fun practicing the most important topics in statistics. Calculate the mean, mode and median of a set of data. Find the quartiles, deciles and percentiles of a set of data (include formulae for grouped data). Provides problems, explanations, and solutions. Central Tendency and Dispersion measures are introduced. Solve right angled triangles by using the Pythagorean Theorem. Solve real life word problems using the Pythagorean Theorem. Use Pythagorean Triples to save your time on any test. Find the relationships between the sides of a 45-45-90 triangle or a 30-30-60 triangle. There are many applications for the Pythagorean Theorem: it can be used to find the distance between two points, to find the length of a space diagonal,... Provides problems, explanations, and solutions. Revise your understanding of proportional reasoning in maths. Here you will find exercises on ratios and proportions, direct proportions, inverse proportions, equal shares, time and distance and mixture word problems. You will learn to solve problems using real life situations. Provides problems, explanations, and solutions. Revise your understanding of variations, permutations and combinations. Solve exercises about variations, permutations and combinations with and without repetition. Provides problems, explanations, and solutions. Revise your understanding of the inner product of two vectors. Solve exercises about inner product: calculate the value of the inner product of two vectors. Provides problems, explanations, and solutions. Revise your understanding of trigonometry. Calculate the trigonometric functions of acute angles and improve your knowledge about trigonometry calculating the trigonometric functions of related angles: complementary angles, supplementary and opposite angles. Solve right triangles using trigonometry and solve all triangles using the law of sines and the law of cosines. Provides problems, explanations, and solutions.
Chapter 7 Animations are demonstrations of selected Key Concepts and topics from your textbook. Similar Polygons BrainPOPS are 3- to 5-minute animated movies that provide a clear and concise explanation of a particular topic in an engaging manner. Using Proportions Interactive Labs are problem-based learning opportunities that provide additional practice on a variety of topics. Cartography and Similarity Chapter 8 Animations are demonstrations of selected Key Concepts and topics from your textbook. Multiply Matrices Interactive Labs are problem-based learning opportunities that provide additional practice on a variety of topics. Using Matrices
Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics. It has applications in many fields of the natural sciences. Curvature is the central concept in Riemann?Finsler geometry. This invaluable textbook presents detailed discussions on important curvatures such as the Cartan torsion, the S-curvature,... more...
Book Description: Susanna Epp's DISCRETE MATHEMATICS: AN INTRODUCTION TO MATHEMATICAL REASONING provides a clear introduction to discrete mathematics and mathematical reasoning in a compact form that focuses on core topics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students develop the ability to think abstractly as they study each topic. In doing so, the book provides students with a strong foundation both for computer science and for other upper-level mathematics courses.
Applied Calculus (looseleaf) - 4th edition Summary: APPLIED CALCULUS, 4/E exhibits the same strengths from earlier editions including the "Rule of Four", an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students. The fourth edition gives readers the skills to apply calculus on the job. It highlights the appl...show moreications' connection with real-world concerns. The problems take advantage of computers and graphing calculators to help them think mathematically. The applied exercises challenge them to apply the math they have learned in new ways. This develops their capacity for modeling in a way that the usual exercises patterned after similar solved examples cannot do. The material is also presented in a way to help business professionals decide when to use technology, which empowers them to learn what calculators/computers can and cannot do
Calculus A, the first of a two-semester course, centers on limits, differentiation, and applications of differentiation. Topics in this course apply to many problems studied in physics and engineering. Students review algebra concepts and learn fundamental calculus concepts, along with working problems for limits and derivatives. Students apply rules for finding different derivatives as well as learn the applications of the derivative. After finding the area under a curve using several different methods, students will complete an essay assignment that applies this to a real-world problem. Students conclude the course by applying theorems and demonstrating knowledge of basic rules for anti-derivatives. After successful completion of this course, students will have a fundamental understanding of the principles of calculus.
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MATLAB: An Introduction with Applications MATLAB: An Introduction with Applications 4th Edition walks readers through the ins and outs of this powerful software for technical computing. The first chapter describes basic features of the program and shows how to use it in simple arithmetic operations with scalars. The next two chapters focus on the topic of arrays (the basis of MATLAB), while the remaining text covers a wide range of other applications. MATLAB: An Introduction with Applications 4th Edition is presented gradually and in great detail, generously illustrated through computer screen shots and step-by-step tutorials, and applied in problems in mathematics, science, and engineering. This training guide introduces development practitioners, policy analysts, and students to social accounting matrices (SAMs) and their use in policy analysis. There are already a number of books that ...
Algebra 2 Polynomials review was created using smart notebook software. This review covers simplifying using rules of exponents, adding polynomials, subtracting polynomials, multiplying polynomials, dividing polynomials by a monomial and polynomials by binomials, and expanding binomials. I use this review with student response boards for my students to work out the problem and show me their answers. This review is a great way for my students as well as for myself to see how ready they are for the assessment. Elizabeth Welch NOTEBOOK (SMARTboard) File Be sure that you have an application to open this file type before downloading and/or purchasing. 164.81
Differentiation practicing materials? Differentiation practicing materials? Hello, I`m studying 1st year physics and I would really like to improve my basic maths. The thing is I don`t want to sit and first make up a random expression and then calculate the derivative, I would like to be able to print out hundreds and hundreds of small expressions with varying difficulty (possibly with solutions) and train until I`m at least as good as in the multiplication table.... So any such sources for practice materials?
Quick Graph: Your Scientific Graphing Calculator It is a powerful, high quality, graphic calculator that takes full advantage of the multitouch display and the powerful graphic capabilities of the iPad and iPhone, both in 2D and 3D. A simple, yet intuitive interface that makes it easy to enter and/or edit equations and visualize them in mathematical notation. It's capable of displaying explicit and implicit (opt) equations as well as inequalities (opt) in both 2D and 3D, in all standard coordinate systems: cartesian, polar, spherical and cylindrical, all with amazing speed and beautiful results, which can be copied, emailed or saved to the photo library. "It's ok to write yet another graphing app, so long as it is the best one. And this is" -- Review by RightyC1 Please keep in mind that in this version, you now have to specify y=, x=, z= and so on, whenever you want to plot an equation. The advanced feature set gives you access to some of the new features, such as implicit graphs and tracing. You need to specify the dependent variable now, since just typing "x^2" without the y=, will assume the expression to be "x^2=0" and will try to plot it as an implicit graph. Up to 6 equations can be visualized simultaneously, in both 2D and 3D modes, this limitation can be removed by purchasing the advanced feature set. All the features from the original application are present and will remain free. It also includes an evaluate feature, to evaluate equations at specific points, as well as a library where you can store commonly used equations. Last year our school district was fortunate to receive a $12,000 grant to fund a handheld computing project. We chose the iPod touch (a.k.a., "iTouch") as our handheld solution for a variety of reasons. The iTouch is fast and portable. The students stay on task because we can control the apps they are using. There are apps available in all subject areas that focus on specific classroom objectives. We purchased 18 iTouch units for our high school and 30 units for our middle school, grades 5-8. They were implemented as "portable labs" (15 to 20 units in a small bag that can be used by any of the classroom teachers). With many different teachers using the iTouch sets, we learned a lot about using them in the classroom.
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Site is in Italian and English, with links to the author's homepage ...more>>
What should one teach to liberal-arts students who will take only one math course, and that because it's required of them? The conventional answer: partialPartial What should one teach to liberal-arts students who will take only one math course, and that because it's required of them? The conventional answer: partial
The focus of the study was to identify secondary school students' difficulties with aspects of linearity and linear functions, and to assess their teachers' understanding of the nature of the difficulties experienced by their students. A cross-sectional study with 1561 Grades 8–10 students enrolled in mathematics courses from Pre-Algebra to Algebra II, and their 26 mathematics teachers was employed. All participants completed the Mini-Diagnostic Test (MDT) on aspects of linearity and linear functions, ranked the MDT problems by perceived difficulty, and commented on the nature of the difficulties. Interviews were conducted with 40 students and 20 teachers. A cluster analysis revealed the existence of two groups of students, Group 0 enrolled in courses below or at their grade level, and Group 1 enrolled in courses above their grade level. A factor analysis confirmed the importance of slope and the Cartesian connection for student understanding of linearity and linear functions. There was little variation in student performance on the MDT across grades. Student performance on the MDT increased with more advanced courses, mainly due to Group 1 student performance. The most difficult problems were those requiring identification of slope from the graph of a line. That difficulty persisted across grades, mathematics courses, and performance groups (Group 0, and 1). A comparison of student ranking of MDT problems by difficulty and their performance on the MDT, showed that students correctly identified the problems with the highest MDT mean scores as being least difficult for them. Only Group 1 students could identify some of the problems with lower MDT mean scores as being difficult. Teachers did not identify MDT problems that posed the greatest difficulty for their students. Student interviews confirmed difficulties with slope and the Cartesian connection. Teachers' descriptions of problem difficulty identified factors such as lack of familiarity with problem content or context, problem format and length. Teachers did not identify student difficulties with slope in a geometric
The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary. Text:Mathematics for Elementary Teachers , first edition, and the accompanying Class Activities manual by Sybilla Beckmann, published by Addison-Wesley. These can be purchased from the UGA bookstore and other bookstores. Please bring the activity manual to class. Course topics: Visualization. Angles. Geometric shapes and their properties. Constructions with straightedge and compass. Transformation geometry: reflections, translations, rotations. Symmetry. Congruence. Similarity. Measurement, especially length, area, and volume. Converting measurements. Principles underlying calculations of areas and volumes. Why various area and volume formulas are valid. Area versus perimeter. The behavior of area and volume under scaling. Course objectives: To strengthen and deepen knowledge and understanding of measurement and basic geometry and how they are used to solve a wide variety of problems. In particular, to strengthen the understanding of and the ability to explain why various procedures and formulas in mathematics work. To strengthen the ability to communicate clearly about mathematics, both orally and in writing. To promote the exploration and explanation of mathematical phenomena. To show that many problems can be solved in a variety of ways. Class work: This class is part of your preparation as a professional. As a professional, you should engage in collegial discussions about professional practice and you should constantly seek to enhance and refine your professional knowledge. To receive a full participation score, your work in class must consistently exhibit several or all of the following: interest in mathematical ideas interest in different ways of approaching mathematical ideas careful listening to different ways of solving a problem careful evaluation of proposed methods of solution attempts to connect the course material to your experiences with children and teachers at schools There will be regular homework assignments. I encourage you to work on homework assignments with your classmates. Of course, you should always write your homework up on your own, using your own words to express the ideas you have discussed with others. Do not allow anyone to copy your work. When you discuss assignments with others, all partners should "give and take" ideas. Late homework will not be accepted. Please consult with me as soon as possible if you are unable to hand in an assignment due to an illness or emergency. Writing Intensive Program: This section of MATH 5030 is part of the Writing Intensive Program. The Writing Intensive Program is designed to help courses teach the writing process within various disciplines. Although you have taken English courses on writing, and although these courses will help you with all your writing, mathematical writing has its own special features. In mathematics, we seek coherent, logical explanations, in which the desired conclusion is deduced from starting assumptions. Our graduate assistant, Peter Petrov, has been trained by the Writing Intensive Program to help you learn to write good mathematical explanations. By participating in the Writing Intensive Program we have also learned about ways to use writing to deepen your understanding of the course concepts. How your grade will be calculated: We will grade all your work on a 5.25 point scale, and we will assign points as follows: # of points description characteristics 5.25 points exemplary work that could serve as a model for other students 5 points very good correct work that is careful and thorough 4 points competent good, solid work that is largely correct 3 points basic work that has merit but also has significant shortcomings 2 points emerging work that shows effort but is seriously flawed 0 points no credit no work submitted, or no serious effort shown Grading criteria: We will determine your score on assignments and tests by the extent to which your work meets the following criteria: The work is factually correct, or nearly so, with only minor, inconsequential flaws. The work addresses the specific question or problem that was posed. It is focused, detailed, and precise. Key points are emphasized. There are no irrelevant or distracting points. The work could be used to teach a student: either a child or another college student, whichever is most appropriate. The work is clear, convincing, and logical. An explanation should be convincing to a skeptic and should not require the reader to make a leap of faith. Clear, complete sentences are used. Mathematical terms and symbols are used correctly. If applicable, supporting pictures, diagrams, and/or equations are used appropriately and as needed. The work is coherent. Your grade will be based on tests, homework, and a comprehensive final exam. I expect to give 2 tests and 2 announced quizes during the semester. I will calculate your course score using the following percentages. term tests, 20% each 40% quizzes, 7% each 14% class participation (please see criteria above under class work) 3% homework 15% final exam 28% Makeup exams or quizzes will not be given. If an exam or quiz is missed due to an illness or emergency, I will calculate a grade for the exam or quiz using a relevant portion of the final exam. I expect to assign letter grades as follows. for scores from up to letter grade 4.6 5.25 A 4 4.6 B 3.5 4 C 2.5 3.5 D below 2.5 F Materials needed: Please have a calculator available. Please bring your activity manual to class. You may wish to have colored pencils or markers on hand since we will frequently solve problems with the aid of pictures.
Measure theory is a classical area of mathematics born more than two thousand years ago. Nowadays it continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics. This book gives an exposition of the foundations of modern measure theory and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and, finally, more specialized topics partly covered by more than 850 exercises. Volume 1 (Chapters 1-5) is devoted to the classical theory of measure and integral. Whereas the first volume presents the ideas that go back mainly to Lebesgue, the second volume (Chapters 6-10) is to a large extent the result of the later development up to the recent years. The central subjects of Volume 2 are: transformations of measures, conditional measures, and weak convergence of measures. These three topics are closely interwoven and form the heart of modern measure theory. less
Delphi For Fun - Gary Darby; Intellitech Systems Inc. Delphi is based on the Pascal programming language developed in the early 1970s by Niklaus Wirth and named after mathematician Blaise Pascal. This site explores the use of programming as a tool in math problem solving, discussing interesting problems, ...more>> Delta Blocks - Hop David A way to model different 3-D tessellations and a tool for studying geometry, crystallography, and polyhedra. Delta blocks were inspired by M. C. Escher's print "Flatworms," which he said demonstrates that one can build a house not only with the usualDennis Stanton Dennis Stanton is a professor at the University of Minnesota studying combinatorics and hypergeometric functions. Many of his papers are available online in PostScript and PDF formats. There are also exams and solutions from previous classes, and a complete ...more>> Design Science - Design Science, Inc. Math publishing and presentation tools for the web: MathType, the professional version of Equation Editor, for Windows or Mac; WebEQ, for building interactive math web pages; MathFlow, math publishing for the enterprise; and MathPlayer, to display MathML ...more>>
The differences between the two types of convergence are illustrated with several examples. Some standard facts are also discussed: a uniform Author(s): The University of Nottingham License information Related content No related items provided in this feed How and why we do mathematical proofs This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Autumn Semester 2009/10 The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing proofs. In particular, the student will learn the following: * proofs can help you to really see why a result is true; * problems that are easy to state can be Author(s): Feinstein Joel F. DrMathematics for Chemistry Workbook A workbook for chemists on the underlying mathematics needed to study chemistry at beginning undergraduate level. Videos of worked solutions to many of the problems in this workbook can be also found in JORUM Author(s): Patrick J O\'Malley
This course is designed to strengthen basic math skills. Topics include properties, rounding, estimating, comparing, converting, and computing whole numbers, fractions, and decimals. Upon completion, students should be able to perform basic computations and solve relevant mathematical problems.
Concrete Mathematics A Foundation for Computer Science 9780201558029 ISBN: 0201558025 Edition: 2 Pub Date: 1994 Publisher: Addison-Wesley Summary: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the auth...ors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. 0201558025B04062001
A Beginner's Guide to Finite Mathematics For Business, Management, and the Social Sciences This second edition of A Beginner's Guide to Finite Mathematics takes a distinctly applied approach to finite mathematics at the freshman and sophomore level. Topics are presented sequentially: the book opens with a brief review of sets and numbers, followed by an introduction to data sets, histograms, means and medians. Counting techniques and the Binomial Theorem are covered, which provides the foundation for elementary probability theory; this, in turn, leads to basic statistics. This new edition includes chapters on game theory and financial mathematics. Requiring little mathematical background beyond high school algebra, the text will be especially useful for business and liberal arts majors. show more show less Edition: 2nd 2012 Publisher: Springer London, Limited Binding: Trade Cloth Pages: 483 Size: 6.25" wide x 9.00" long x 1.25 Beginner's Guide to Finite Mathematics For Business, Management, and the Social Sciences - 9780817683184 at TextbooksRus.com.
COURSE SYLLABUS Advance Placement Calculus AB Syllabus (27072000) Druid Hills High School Teacher: Paul Johnson Phone Number: 678-874-6411 Room Number: 510C Email: Paul_D_Johnson@fc.dekalb.k12.ga.us Semester: Fall 2011 Tutorial Days: Monday, Thursday, and by appointment Textbook: Calculus James Stewart Tutorial Hours: 3:20-4:00 Textbook Price: replacement cost Tutorial Location: Room 510C Department Philosophy: We believe that by creating an environment conducive to learning, building positive rapport with students, and employing differentiated instructional strategies, we can promote student success. Furthermore we believe that each student can be successful in learning to: value mathematics, become a mathematical problem solver, communicate and reason mathematically. We expect that every student will be successful in this course. Course Description: Our emphasis is on students truly understanding calculus and its application to the real world. Student discussions and explorations are a big part of the class. Students should be able to calculate, write about the content, along with the discussions that take place. The first semester begins with an in depth look at functions, then the limits and continuity of those functions are explored. Next, the concepts of the derivative are covered. Finally, applications of the derivative are studied. In the last part of the semester, antiderivatives are investigated. The first semester concludes with calculating areas below and between curves. Each student has a graphing calculator, either a TI-83, TI-84, or TI-89. We use our calculators to explore and reinforce concepts. Assessments are given with calculator required and others without a calculator. Note that students may continue on with the BC portion of the AP Calculus curriculum in the spring semester. Course Prerequisites: Permission of instructor and successful completion of Analysis, Math 4, or Accelerated Math 3. Rough Course Outline: Week 1 Trigonometry Review Week 2 Limits and Rates of Change Week 3 Graphical interpretation of first and second derivatives Week 4 Limit definition of derivative, Power Rule Week 5 Equations of tangents and normals Week 6 Product and Quotient Rules Week 8 Derivatives of trigonometric functions Week 9 Chain Rule, Implicit differentiation Week 11 Optimization, Derivatives of exponential and logarithmic functions Week 12 Curve sketching (graphical look at antiderivatives) Week 13 Fundamental Theorem of Calculus, Riemann Sums Week 14 Area beneath/between curves, Volumes of revolution Weeks 15-16 Differential Equations Week 17 Wrap-up/Review Week 18 Review/Exam Grading Scale: Category Percent of grade Homework /classwork 15% Quizzes 20% Tests 45% Final exam 20% Total 100% A - 90-100, B - 80-89, C - 71-79, D - 70, F - 69 and below Required Materials: Notebook with lined paper, dividers, graph paper Pencils and erasers Ruler Graphing calculator (TI-83 or equivalent. To be provided by school or student) Textbook (provided by school) To achieve an "A" or "B" in this class, the student must: 1. Attend class regularly and be on time. 2. Do all assignments following the specific guidelines given for each assignment making few errors. 3. Turn in all assignments on time and keep up with make up work when absent. 4. Ask questions when puzzled. 5. Have an organized notebook and take legible notes regularly. 6. Be prepared for and achieve above average scores on exams (including quizzes, tests, midterm, and final). 7. Seek help when faced with difficulty (personal or school related). Late Assignments (Department-wide policy): Homework and class work may be redone in the current 4½ -week grading period only. The grades on these assignments will be discounted by 10% per day late. Make-up Policy (Department-wide policy): Students will have two days for each day excused absence to make up work without penalty. Absence must be excused by the attendance office. Make up tests and quizzes may be different. Re-do Policy: A low score on a quiz or test may be mitigated by the following procedure: 1. Review each problem on the quiz/test. Understand what went wrong. Come in for at least one day of tutoring. 2. Write a similar (but different) quiz or test. You can take problems from the textbook or other sources (or write them yourself), but make sure they require you to demonstrate the same skills as the original required. This new quiz/test must be approved by the teacher. This may take one or two revisions. Suggestions will be made to ensure that the rigor of your questions is on a par with the original. 3. Come take your quiz/test in a proctored environment. (Note that you can work every problem ahead of time.) 4. Your final grade will be the average of the original and the grade you earn on the retest. Parents: Please email or call to let me know that you have seen this syllabus and to give me a way to contact you if we need to discuss your child's progress in this course. Thank you!

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