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Book Description: Following on the success of the Algebra Survival Guide, the Algebra Survival Guide Workbook presents thousands of practice problems (and their answers) to help children master algebra. The problems are keyed to the pages of the Algebra Survival Guide, so that children can find detailed instructions and then work the sets. Each problem set focuses like a laser beam on a particular algebra skill, then offers ample practice problems. Answers are conveniently displayed in the back. This book is for parents of schooled students, homeschooling parents and teachers. Parents of schooled children find that the problems give their children a "leg up" for mastering all skills presented in the classroom. Homeschoolers use the Workbook - in conjunction with the Guide - as a complete Algebra 1 curriculum. Teachers use the workbook's problem sets to help children sharpen specific skills - or they can use the reproducible pages as tests or quizzes on specific topics. Like the Algebra Survival Guide, the Workbook is adorned with beautiful art and sports a stylish, teen-friendly design. Buyback (Sell directly to one of these merchants and get cash immediately) Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it
VITEEE Syllabus of Mathematics VITEEE Syllabus MATRICES AND DETERMINANTS: Types of matrices, addition and multiplication of matrices-Properties, computation of inverses, solution of system of linear equations by matrix inversion method. Rank of a Matrix – Elementary transformation on a matrix, consistency of a system of linear equations, Cramer's rule, Non-homogeneous equations, homogeneous linear system, rank method.THEORY OF EQUATIONS, SEQUENCE AND SERIES Quadratic equations – Relation between roots and coefficients – Nature of roots – Symmetric functions of roots – Diminishing and Increasing of roots – Reciprocal equations. Arithmetic, Geometric and Harmonic Progressions-Relation between A.M., G. M ., and H.M. Special series: Binomial, Exponential and Logarithmic series – Summation of Series. VECTOR ALGEBRA Scalar Product – Angle between two vectors, properties of scalar product, applications of dot products. Vector Product – Right handed and left handed systems, properties of vector product, applications of cross product. Product of three vectors – Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors. Lines – Equation of a straight line passing through a given point and parallel to a given vector, passing through two given points, angle between two lines. Skew lines – Shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of three points. Planes – Equation of a plane, passing through a given point and perpendicular to a vector, given the distance from the origin and unit normal, passing through a given point and parallel to two given vectors, passing through two given points and parallel to a given vector, passing through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines, angle between two given planes, angle between a line and a plane. Sphere – Equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.COMPLEX NUMBERS & TRIGONOMETRY: Complex number system, conjugate – properties, ordered pair representation. Modulus – properties, geometrical representation meaning, polar form principal value, conjugate, sum, difference, product quotient, vector interpretation, solutions of polynomial equations, De Moivre's theorem and its applications. Roots of a complex number – nth roots, cube roots, fourth roots. Angle measures- Circular function-Trigonometrical ratios of related angles – Addition formula and their applications – Trigonometric equations – Inverse trigonometric functions-Properties and solutions of triangle.ANALYTICAL GEOMETRY Definition of a Conic – General equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Parabola – Standard equation of a parabola tracing of the parabola, other standard parabolas, the process of shifting the origin, general form of the standard equation, some practical problems. Ellipse – Standard equation of the ellipse, tracing of the ellipse (x^2/a^2 )+(y^2/a^2 ) = 1 (a> b). Other standard form of the ellipse, general forms, some practical problems Hyperbola – standard equation, tracing of the hyperbola (x^2/a^2 )-(y^2/a^2 ) = 1 , other form of the hyperbola, parametric forms of a conics, chords, tangents and normals – Cartesian form and parametric form, equation of chord of contact of tangents from a point (x1 ,y1 ) Asymptotes, Rectangular Hyperbola –standard equation of a rectangular hyperbola.DIFFERENTIAL CALCULUS Derivative as a rate measure – rate of change – velocity-acceleration – related rates – Derivative as a measure of slopetangent, normal and angle between curves. Maxima and Minima. Mean value theorem- Rolle's Theorem – Lagrange Mean Value Theorem – Taylor's and Maclaurin's series, L' Hospital's Rule, Stationary Points – Increasing, decreasing, maxima, minima, concavity convexity points of inflexion. Errors and approximations – absolute, relative, percentage errors, curve tracing, partial derivatives – Euler's theorem.INTEGRAL CALCULUS AND ITS APPLICATIONS METHODS OF INTEGRATION STANDARD TYPES Properties of definite integrals, reduction formulae for sin^n (x) and cos^n (x) , Area, length, volume and surface area.DIFFERENTIAL EQUATIONS Formation of differential equations, order and degree, solving differential equations (1st order) – variable separable homogeneous, linear equations. Second order linear equations with constant co-efficient f (x)=e^m(x), sin mx, cos mx,x, x^2.DISCRETE MATHEMATICS Mathematical Logic – Logical statements, connectives, truth tables, tautologies, sets, algebraic properties, relations, functions, permutation, combination, Induction. Binary Operations – Semi groups – monoids, groups (Problems and simple properties only), order of a group, order of an element.PROBABILITY DISTRIBUTIONS: Probability, axioms, theorems on probability, conditional probability, Random Variable, Probability density function, distribution function, mathematical expectation, variance, discrete distributions-Binomial , Poisson, continuous distribution – Normal
... read more Customers who bought this book also bought: Our Editors also recommend: Introduction to Combinatorial Analysis by John Riordan Introductory text surveys the theory of permutations and combinations associated with elementary algebra; the principle of inclusion and exclusion; and the theory of distributions and partitions in cyclic representation. Includes problems. 1958Product Description: specific discrete structure, advancing from elementary (often classical) results to those at research level. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 edition. Foreword by Gian-Carlo Rota. References. Index. Unabridged republication of the edition published by John Wiley & Sons, New York, 1983
Run a Quick Search on "Concepts of Modern Mathematics" by Ian Stewart to Browse Related Products: Short Desription In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math"--groups, sets, subsets, topology, Boolean algebra, and more. By the time readers finish this book, they shall have a much clearer grasp of how modern mathematicians look at figures, function, and formulas, leading them to a better comprehension of the nature of the mathematics itself. If You Enjoy "Concepts of Modern Mathematics (Paperback)", May We Also Recommend:
Course Overview At Stetson, differential equations is an elective math course of the "applied" variety, although there is a good deal of theory in the field. In this course you will be introduced to the field by exploring the basic questions: What is a differential equation? Why is a differential equation? What is a solution to a differential equation? How is a solution to a differential equation found? Text and Software The book is Blanchard, Davaney, & Hall, Differential Equations, 3rd edition, chapters 1-3 and 5. It is both readable and amusing. We will be using Mathematica to support the concepts and calculations. Learning to program is part of the course. Prerequisites The basics of calculus, especially Integration and Complex Numbers. See the reviews posted on Blackboard. Grading Your grade will be based on 3 tests (20% each), a project (10%), homework (5%), and a final exam (25%). The grading scale is A 90-100%, B 80-90%, etc. Policies and Due Dates You must take the major tests during the scheduled class time unless you have a valid excuse cleared with me ahead of time. Test dates are Wednesday 9/17, Wednesday 10/8 (the day before fall break), Friday 11/14, and (final) Tuesday 12/9, 4-6 pm. Tests will include a take-home Mathematica portion that will be 10% of the test grade. Likewise, 10% of the final exam grade will be your total Mathematica portfolio. Please see the grading rubric for the portfolio. The project is individual, and can be a lab from the book or a topic in the book not covered by me. Talks are the week before Thanksgiving, and papers are due the last day of class. Please consult with me well before the due dates to be sure you're on the right track. Also see the Guidelines for Mathematics Papers and the Guidelines for Mathematics Talks on the course web page. Homework should consume about 6 hours per week outside of class. At least one even-numbered problem, more at your option, is collected daily at the beginning of the class period. It must be written neatly on one side of the paper, stapled. You may send assignments with a friend if you miss class. Attendance is expected. Previous students have found that loyal attendance (3 or fewer absences) is required for success in my courses. Assistance All work on in-class tests must be your own: no books, notes, or other people. You may receive help on Mathematica, projects, and homework from me or classmates, but the final product must be your own interpretation in your own words. I support the Stetson University Honor System. This is an upper level course for mature mathematics students. You are responsible for learning the material, reading the text, identifying your questions and difficulties, talking with me inside and outside of class, keeping up with the syllabus, reading your email, and knowing class policies. Visit my web site to find out more about me and about the course. If you have special needs, please don't hesitate to discuss them, either with me or with the Academic Resources Center. Communication I use Blackboard to communicate important information about the class. Also see my contact information above. You are welcome in my office, my voicemail, and my Inbox.
Analysis Studio Analysis ... Math Practice Improve math marks with Math Practice. Get to grips with addition, subtraction, multiplication and your times tables using the Basic Math feature. Use the worksheet feature to practice tons of different types of sums. More than 30 worksheets are provided with Math Mractice as well as help on how to do the sums in the worksheets. The worksheets include worksheets on adding, subtracting, ... word problems 3 v1.0 it is basic introduction to word problems. It is a pre-algebra word problems suitable for children in 5th to 10th grade. It includes the questions as well as their solutions in a simple fashion. The different four operations are involved to expose the child for the variation in solving and translating word problems. About 100 problems are involved. Linear Equation in One Variable v1.0 a program deals with linear equation with one variable . It includes addition and subtraction property of equality. It also includes multiplication and division properties of equality. Strategy to solve linear equation with lots of problems and examples. Finally it gives examples on identity equation, conditional and inconsistent equations. Factoring Polynomials v1.0 a program deals with how to factorization of polynomials. It includes the factorization by GCF, factorization by grouping, other factorization including forms of x^2 + bx + c and ax^2 + bx + c. Factorization of sum and difference of cubes and of difference of squares. Factorization of perfect square trinomial. And finally it includes the strategy how to solve different forms of polynomials with ... Straight Line Equation & Graphing v1.0 a modulus program deals with straight line. It includes how to figure out the lope of a striagt line and x- and y-intercept. How to make equation of a line given certain information.How to graph a line using the slope/intercept form and how you can figure out whether two or more lines are parallel or perpendicular. Quadratic Equaion v1.0 a program deals with quadratic equation. It includes how to create the standard for of quadratic equation. It includes how to solve it by factoring, bu using square root method, by using quadratic formula and to understand the significance of the disciminant. Lots of examples and practices are involved solved step-by-step. Inequalities and Regions A program about inequality but instead of being one-dimensional it is tw-dimential usiung praphs. How to use and draw inequality in two-demensional space, Two-variables inequalities, shading and unshading the required region, coordinates and vertices of a region, how to define which of the regions is required, How to determine greatest and least values.About 100 questions with solutions Formulas v1.0 A program deals with formulas. Formulas are not only important in math but also in science including physics, chemistry, etc. It includes how to construct formulas and its usage in algebra. It includes how to manipulate fomulas by changing its subject and solve questions like these. Solving formulas of square roots and squares are involved with problem solving and exampes. Pre-Algebra 0 v1.0 Very simple review of some topics in pre-algebra. Basic review and introduction about fractions and their manipliulations. Basic review and introduction about decimals. Relative sizes. Basic review and introduction about indices. Standard form (scientific notation). Approximation. Range of values of corrected numbers. Word Problems-1 v1.0 it is basic introduction to word problems. It teaches you how to translare simpe engish into algebraic expressions. It includes keywords to help you on how to translate. More than 75 solved problems are included. Indices 2 v1.0 Ths software provdes to you everything that you have to know about indices. . WhAt is an index. What is zero index. Multiplication of indices with practices & their solutions. Division of indices with practice and their solutions. Power ruke of exponents. Base raise to two exponents with practices & solutions. Quotient raised to an exponent with practices & solutions. Operation with Monomial and Polynomial a program deals with monomials and polynomials. It includes addition and subtraction of polynomials. Also deal with multiplication and division of polynomials. Multiplication of polynomials by a monomial. Multiplication of two binomials and squaring a binomials.Division of monomials and division of a polynomial by a monomial. System of Linear Equations With Two Variables v1.0 it is all about system of linear equations with two variables. It shows how to draw and solve this system y graphing. Step-by-step solving method (along with the practice) on how to solve these systems by both elimination and substituting methods.
working models in mathematics for class 10 Working models in mathematics for class 10 Definition Mathematical model - In analysis, engineers can build a descriptive model of the system as a hypothesis of how the system could work, or ... Mathematics Applied to Deterministic Problems in the Natural ..... Model theory - In mathematics, model theory is the study of (classes of) mathematical structures such as groups, fields, graphs, or even models of set theory, using tools from mathematical logic. Model theory has close ties to algebra and universal algebra. This article focuses on finitary first order categoricity..Glimpses Of A New Mathematical World - ScienceDaily (Mar. 17, 2008) — A new mathematical object was revealed yesterday during a lecture at the American Institute of Mathematics (AIM). Two researchers from the University of Bristol exhibited the first example of a third degree transcendental L-function. These L-functions encode deep underlying connections between many different areas of mathematics. See also: Computers & Math Math Puzzles Mathematics Computer Science Hacking Mathematical Modeling Communications Reference Algebraic geometry Calculus Probability theory Trigonometry The news caused excitement at the AIM workshop attended by 25 of the world's leading analytic number theorists. The work is a joint project between Ce Bian and his adviser, Andrew Booker. Booker commented that, 'This work was made possible by a combination of theoretical advances and the power of modern computers.' During his lecture, Bian reported that it took approximately 10,000 hours of computer time to produce his initial results. 'This break.... "Working models in mathematics for class 10" Videos &nbsp NCSSM Research Experience &nbsp Students from the North Carolina School of Science & Mathematics Research in Chemistry class talk about their experiences working with NASA on a model of the inner ear to study Space Adaptation Syndrome. The model was sent up in the NASA Microgravity Plane. ... NCSSM Education Distance Learning Technology North Carolina School of Science and Math NASA Chemistry Space Adaptation Syndrome
Engineering Computation : An Introduction Using MATLAB and Excel strength of the Engineering Computations text is its combination of the two most important computational programs in the engineering marketplace today, MATLAB and Excel. Engineering students will need to know how to use both programs to solve problems. Howard/Musto/Williams introductory text, Engineering Computations provides an introduction to both programs.While it is important to teach the mechanics of using the relevant tools, those tools can change so the focus of this text is on thefundamentals of engineering computing: algorithm deve... MORElopment, selection of appropriate tools, documentation of solutions, and verification and interpretation of results.This is a new project that will be in a growth phase for the next few editions. Engineering schools continue to struggle with where to fit a computer methods course and Musto/Howard/Williams meets the need for a brief low level introduction to these programs.This book fits into the BEST series and will allow professors to use one book where they used to need two. The strength of Engineering Computation is its combination of the two most important computational programs in the engineering marketplace today, MATLAB® and Excel®. Engineering students will need to know how to use both programs to solve problems. The focus of this text is on the fundamentals of engineering computing: algorithm development, selection of appropriate tools, documentation of solutions, and verification and interpretation of results. To enhance instruction, the companion website includes a detailed set of PowerPoint slides that illustrate important points reinforcing them for students and making class preparation easier.
9780534495015 ISBN: 053449501x Pub Date: 2005 Publisher: Brooks/Cole Summary: An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems. Based on their teaching experiences, the authors offer an accessible text that emphasizes the fundamentals of discrete mathematics and its advanced topics. This text shows how to express precise ideas in clear mathematical language. Students discover the importance of discrete ma...thematics in describing computer science structures and problem solving. They also learn how mastering discrete mathematics will help them develop important reasoning skills that will continue to be useful throughout their careers.[read more] Rating:(0) Ships From:Richmond, TXShipping:Standard, Expedited, Second Day, Next DayComments: 053449501X Purchased as new and in great condition. We cannot guarantee the availability of CD/D... [more] 053449501 [less]
New MAA Book: A Guide to Advanced Real Analysis The second publication in the MAA Guides series, this book is a concise introduction to real analysis, covering the core material of a graduate-level real analysis course. On an abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On a more concrete level, it deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. Highlights: Covers the core material found in a graduate course on real analysis. Gives an overview of the subject so that it can be used as a guide for a beginner or as a refresher for those who have previously studied the subject. Provides essential definitions, major theorems, and key ideas of proofs without the technical details. Excerpt: Metric Spaces (p. 5). The early years of the twentieth century witnessed a great increase in the level of abstraction and generality in mathematical thinking. In particular, mathematicians at that time developed theories that provide a very general setting for studying the circle of ideas related to limits and continuity, which previously had been considered in the context of subsets of Euclidean space or functions of one or several real or complex variables. The most straightforward generalizations of Euclidean space for this purpose is the notion of metric space. About the Author: Gerald B. Folland (University of Washington) has written textbooks and monographs in the areas of real analysis, harmonic analysis, partial differential equations, and mathematical physics.
cl... read moreElements of Pure and Applied Mathematics by Harry Lass This completely self-contained survey explores important topics in pure and applied mathematics. Each chapter can be read independently, and all are unified by cross-references to the complete work. 1957 edition. Product Description: classroom use, self-study, or as a supplementary text. Starting with vector spaces and matrices, the text proceeds to orthogonal functions; the roots of polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Each chapter goes straight to the heart of the matter, developing subjects just far enough so that students can easily make the appropriate applications. Exercises at the end of each chapter, along with solutions at the back of the book, afford further opportunities for reinforcement. Discussions of numerical methods are oriented toward computer use, and they bridge the gap between the "there exists" perspective of pure mathematicians and the "find it to three decimal places" mentality of engineers. Each chapter features a separate
Principles of Calculus Modeling: An Interactive Approach 4 Modeling Accumulations 4.1.1 The Area of a Circle 4.1.2 What is the Area of a Circle? 4.1.3 Another Calculation of the Area of a Circle 4.1.4 The Method of Accumulations 4.1.5 The Circumference of a Circle 4.1.6 The Volume of Water in a River 4.1.7 An Agenda for Future Work
Calculus: Early Transcendental Functions, 4th Edition (Smith) Chapter 0: Preliminaries In this chapter you will find a collection of familiar topics. You need not spend a great deal of time here. Rather, review the material as necessary, until you are comfortable with all of the topics discussed. We have primarily included material that we consider essential for the study of calculus that you are about to begin. We must emphasize that understanding is always built upon a solid foundation. While we do not intend this chapter to be a comprehensive review of precalculus mathematics, we have tried to hit the highlights and provide you with some standard notation and language that we will use throughout the text. As it grows, a chambered nautilus creates a spiral shell. Behind this beautiful geometry is a surprising amount of mathematics. The nautilus grows in such a way that the overall proportions of its shell remain constant. That is, if you draw a rectangle to circumscribe the shell, the ratio of height to width of the rectangle remains nearly constant. There are several ways to represent this property mathematically. In polar coordinates (which we present in Chapter 9), we study logarithmic spirals that have the property that the angle of growth is constant, producing the constant proportions of a nautilus shell. Using basic geometry, you can divide the circumscribing rectangle into a sequence of squares as in the figure. The relative sizes of the squares form the famous Fibonacci sequence 1, 1, 2, 3, 5, 8, . . . , where each number in the sequence is the sum of the preceding two numbers. The Fibonacci sequence has an amazing list of interesting properties. (Search on the Internet to see what we mean!) Numbers in the sequence have a surprising habit of showing up in nature, such as the number of petals on a lily (3), buttercup (5), marigold (13), black-eyed Susan (21) and pyrethrum (34). Although we have a very simple description of how to generate the Fibonacci sequence, think about how you might describe it as an algebraic function. A plot of the first several numbers in the sequence (shown in Figure 0.1) should give you the impression of a graph curving up, perhaps a parabola or an exponential function. In this chapter, we discuss methods for deciding exactly which function provides the best description of these numbers. Two aspects of this problem are important themes throughout the calculus. One of these is the attempt to find patterns to help us better describe the world. The other theme is the interplay between graphs and functions. By connecting the powerful equation-solving techniques of algebra with the visual images provided by graphs, you will significantly improve your ability to make use of your mathematical skills in solving real-world problems.
Microsoft Mathematics 4.0 – now for $0 The new release, Microsoft Mathematics 4.0, comes for free. There are 2 flavors of MS Mathematics 4.0: The standalone version (requires either Windows XP, Vista, Windows 7 or later and .NET framework, which is also a free download). The add-in version, which only works with Microsoft Word 2010, Microsoft OneNote 2010, and Microsoft Office Word 2007. The add-in allows you to easily insert math objects (graphs, equations, etc) into Word or OneNote. The Add-In is invoked from the ribbon in MS Word. It's reasonably well integrated, but there are a few usability gripes, as mentioned below. The current version seems to do everything that Microsoft Math 3.0 did before. As the site says: Microsoft Mathematics can help you with the following tasks: Compute standard mathematical functions, such as roots and logarithms Compute trigonometric functions, such as sine and cosine Find derivatives and integrals, limits, and sums and products of series Perform matrix operations, such as inverses, addition, and multiplication Perform operations on complex numbers Plot 2-D graphs in Cartesian and polar coordinates Plot 3-D graphs in Cartesian, cylindrical, and spherical coordinates Solve equations and inequalities Calculate statistical functions, such as mode and variance, on lists of numbers Factor polynomials or integers Simplify or expand algebraic expressions Like all such software, you need to know what you can ask it to do, and how to ask it. It won't directly solve your word problems – you still need to use your brains for that! So is MS Math 4.0 any good? MS Math does a good job of graphing 2-D and 3-D graphs. For example, here is a paraboloid. You can easily draw a plane intersecting the 3-D surface (the plane is light blue on the left of the diagram below and the intersection of the plane is a parabola, in dark blue). This is quite a useful feature, but only exists in the Add-In version. A paraboloid graphed using MS Math 4 How does MS Math 4 graph arccot(x)? I wrote recently about the fact that different math software disagree on the correct graph for y = arccot(x). (That is, the inverse of the reciprocal of tan(x)). Here's the article: Microsoft Mathematics 4.0 interprets the graph in the following way, the same as Mathematica and Matlab, but not the same as Mathcad's version. MS Math 4′s graph of y = arccot(x), showing the Trace facility In the above graph, you can see the "trace" facility in use. By clicking on the Trace forward arrow on the graph in MS Math, you can move along the graph as x takes values from smaller to larger numbers. Solving Equations You can easily solve equations using Microsoft Math 4.0, as you could earlier in MS MAth 3.0, as the following example shows: Micrsoft's choice of font in MS Math 4 results in quite unreadable text at times. Believe it or not, that's xraised to the power 3 in the above example. Inverse of a Matrix Inverses of matrices are possible, too. One gripe Next I tried out numerical integration, this time using the Word Add-In. This is what I asked Mathematics 4.0 to calculate: What I got was the following error message: No argument with the requirement to change to radians, but I then needed to go back a few steps, and change the setting to radians, as follows: Then I needed to enter the question again, and finally it gave me the answer: How about some usability testing, Microsoft? It doesn't take much to change the warning dialog box to include an option "Would you lilke to change to radians now?". Or even better, it could just change to radians automatically, and alert the reader what happened. (This is what happens in the standalone version, as it should.) Should you get both the standalone and the Add-In for Word and OneNote versions? Personally, I'd stick to the stand-alone MS Mathematics 4.0 application, since you don't need Word or OneNote to use it. You can always copy-paste into Word or OneNote. However, the image you get after pasting from the standalone version is really poor quality and there seems to be more features in the Add-In version. Conclusion This is a very good product, especially for the price ("free" after purchasing Windows and Word). Microsoft has finally figured out that it's good business to give away stuff. Share this page 10 Comments on "Microsoft Mathematics 4.0 – now for $0" I just tested the application and I can say it's a very good one. Very intuitive and friendly. The integration with Word (copy/paste between the apps) is perfect, so the Standalone version do the job well. The fact that it's free is awesome advantage. I think that the best application of that app is when students are writing homeworks. I will give it a try to introduce this app with a Linear Algebra course this semester. [...] 4.0 properly. I refer you instead to the excellent review posted by Murray Bourne on his website, squareCircleZ. Keyboard shortcuts are available for Mathematics 4.0, but I don't know if these are [...] I have installed and now running Microsoft Mathematics 4.0. While it is wonder, especially in graphing capability, I have experiences some problems so far: 1. I can't change the scales on both the x- and y-axes. 2. I plotted the circle x^2+y^2=2 centred at (0,0). However, when I shift the centre elsewhere, e.g. to plot (x-0.2)^2+(y-0.37)^2=2, the graph does not show up. 1. To change scale, you just drag around the graph (left-right or up-down). If you want to zoom in or out, just use the wheel on your mouse (while the cursor is over the graph). If you mean you want to change the upper and lower x- and y-values, click on the "Plotting Range" button near the top and input your values. Your circle will look like a circle then! 2. You're right! I also found it didn't plot that example. However, I did get the desired result by plotting sqrt(2-(x-0.2)^2)+0.37 and -sqrt(2-(x-0.2)^2)+0.37 on the same graph. It did successfully plot their own example (hyperbola) ((x-3)^2 / (a^2)) – ((y-2)^2 / (b^2)) = 1, which contains similar elements to your circle. Oh well, must be a bug. Murray says: "1. To change scale, you just drag around the graph (left-right or up-down)." On my ver 4.0.1108, dragging around the graph just seems to drag around the graph, not change the scales. What am I missing? @Peter: Yes, I have no idea what the MS engineers were on when they came up with those odd scales for the axes. Not only do the major ticks not make sense (like 2.201), but that is divided into 4 divisions, giving 0.55025 per gray division. No, I tried several ways to get a sensible scale, but no luck. I even tried expanding the range bit by bit, hoping it would jump to something decent, but I gave it away. Let me know if you ever figure it out. OK. Ask the program to simultaneously graph these two equations: (1) y=x-2; (2)y=x-3. Enter both, hit Graph and see the two parallel lines on the graph. Then clear the second equation and watch the y-axis scale as you hit the Graph button.
Mathematics Webb's cutting-edge math curriculum offers a unique, student-centric classroom experience, going beyond rote lectures and standardized tests to foster creative thinking and individual initiative. Independent work is balanced with class discussion: students work collaboratively to solve complex problems, while teachers act as coaches and mentors, tying the threads together and relating each lesson to previous work. Throughout, problems are firmly grounded in real-world contexts, so students never have to wonder, "Why are we learning this?" The use of Problem Based Learning (PBL) as a teaching pedagogy is the core of Webb's unique mathematics program. In Algebra 1 through Precalculus, our program focuses on students discovering important mathematical concepts by investigating, conjecturing, predicting, analyzing, and verifying. The department's continuity fosters growth and creativity in students as they progress through the years. In addition, the honors program begins with Honors Integrated Mathematics 2 and includes Honors Precalculus, AP Calculus AB, AP Calculus BC, and AP Statistics. The scheduling of single-gender classes in the early levels (Integrated Mathematics 1 and Integrated Mathematics 2) allows us to best meet the individual needs of our students in environments that our research shows is best suited to their learning styles. That said, appropriate placement of all students is achieved through very careful evaluation of standardized test data, numerical grades, as well as evaluation of a student's progress by their individual teacher. What type of calculator do I need? The Webb Schools' Mathematics Department is phasing in the use of the Texas Instruments TI-Nspire calculator (all models, except see the note regarding CAS calculators below). This calculator is a requirement for all students enrolled in the following courses: Any student may choose to purchase and use this calculator in any course, but it is not required in courses beyond Precalculus for the 2011-2012 school year. Students who will be enrolled in courses beyond Precalculus are required to have either the Texas Instuments TI-83 or 84 graphing calculator (any model, but the TI84 Plus Silver Edition is recommended) or the TI-Nspire calculator. Please note: CAS capable calculators are not allowed for use in testing situations here at Webb at this time. This includes the TI 89 and the TI Nspire CAS.
Your student's problem-solving and reasoning skills will be strengthened, while his or her understanding of math as a tool of commerce, the language of science, and a means for solving everyday problems will be developed. The biblical basis and revelence of math is made evident from beginning to end.
Mathematics AEA The Mathematics AEA is aimed at the top candidates studying the A-level Mathematics course, regardless of examination board and syllabus. The Mathematics AEA is set by Edexcel, with exam code 9801, although all boards participate in forming the paper and questions. It is accessible to all students but is mainly aimed at those who are predicted an A grade for their mathematics A-level. It is only based on the core of A-level mathematics, i.e. C1, C2, C3, C4; there are no applied mathematics questions nor anything from the further mathematics syllabus (unlike STEP). Contents Structure It is one three-hour long paper that consists of about seven questions. Questions may be multi-step with confidence building parts or unstructured. Some may be of an unusual nature that might include topics from GCSE and logic based items. Questions may be open-ended. Seven percent of the marks will be assigned for style and clarity of mathematical presentation. The examiners will seek to reward elegance of solution, insight in reaching a solution, rigour in developing a mathematical argument and excellent use of notation. The use of scientific or graphical calculators will NOT be allowed nor will computer algebra systems. Candidates will be required to remember the same formulae as for GCE Advanced level Mathematics. They will also be expected to be familiar with the Mathematical Notation agreed for GCE Advanced level Mathematics. Grading Assessment materials and mark schemes will lead to awards on a two-point scale: Distinction and Merit, with Distinction being the higher. Candidates who do not reach the minimum standard for Merit will be recorded as ungraded. Performance level descriptors have been developed to indicate the level of attainment that is characteristic of Distinction and Merit. They give a general indication of the required learning outcomes at each level. The grade awarded will depend in practice upon the extent to which the candidate has met the assessment objective overall. Shortcomings in some aspects of the examination may be balanced by better performances in others. Candidates who achieve Distinction will demonstrate understanding and command of most of the topics tested. Candidates who achieve a Merit will demonstrate understanding and command of many of the topics tested. Future The AEA in Mathematics has been extended to June 2015, as confirmed by Edexcel here. It is the sole AEA to be available after June 2009 (when the other AEAs were withdrawn), presumably reflecting the fact that the new Mathematics GCE A-level would not be taught until September 2011, and the first new AS exams would be in the 2012 sessions. It will probably be withdrawn after summer 2015.
Mathematics For Elementary Teachers - 05 edition Summary: The goal of this text is to provide prospective elementary teachers with a deep understanding of the mathematics they will be called on to teach. Through a careful, mathematically precise development of concepts, this text asks that students go beyond simply knowing how to carry out mathematical procedures. Students must also be able to explain why mathematics works the way it does. Being able to explain why is a vital skill for teachers. Through activities, examples...show more and applications, the author expects students to write and solve problems, make sense of the mathematics, and write clear, logical explanations of the mathematical concepts. The accompanying Activities Manual promotes engagement, exploration, and discussion of the material, rather than passive absorption. Both students and instructors should find this material fun, interesting, and rewarding
Ask Dr. Callahan Geometry Instructional DVD For those of you who like help with teaching Geometry, Ask Dr. Callahan has created a teaching DVD that uses Jacobs Geometry, Seeing Doing Understanding, 3rd Edition, 2003. Our daughter used it recently. She says it was extremely helpful and makes the lessons easier to understand. I watched a few lessons. Dr. Callahan is a college professor with a very natural teaching style. His lectures reminds me of the teaching styles of my favorite math teachers. Armed with this Geometry DVD, the Jacobs text, and the Teacher's Guide (includes worked out solutions), you are set to teach Geometry at home! This DVD course assigns problems from the book for the tests. If you wish to purchase the Test Bank and give different tests, it is available separately below. ADCGeoBB List $289.98 Sale Price $259.95 Harold Jacobs Geometry Seeing, Doing, Understanding Text 3rd Edition By Harold R. Jacobs The third edition Jacobs Geometry Text features: more focus on informal and paragraph proofs; streamlined definitions, proofs, and theorems; diverse examples from around the world; a third more exercises than previous editions with 75% of them being new; algebra reviews; SAT problems are included in the exercise sets; updated art program, now in full color; summary and review sections at the end of each chapter; and glossary, postulates and theorems list at the end of the book.
Mathematics Mathematics: Mission statement To develop an appreciation of the intrinsic delights and application of Mathematics in the real world Department introduction / welcome Key Stage 3 Mathematics offers students the opportunities to consolidate and extend their mathematical skills using a wide range of resources. Students are encouraged to stretch the limits of their understanding to ensure the high expectation of their progress is exceeded. This should give students a solid platform for the work they do in the following two Key Stages. Key Stage 4 Students have the opportunity to build on the excellent foundation provided in Key Stage 3 and tackle with confidence the whole Mathematical syllabus. Most Students achieve A* or A grades at GCSE and also take Statistics as an additional GCSE. The coursework for statistics involves new areas of Mathematics not covered previously. Key Stage 5 Both Mathematics and Further Mathematics provide opportunities for learners to enjoy acquiring disciplined logical thinking skills which are, then, applied across a wide range of modelled situations in the Arts and Sciences. The courses prepare students to develop theory independently and provide a firm basis for future study at degree level and beyond. Click here to find out what is being studied and when, in our Curriculum Topics section.
Elementary Statistics (canadian) - 2nd edition Summary: Elementary Statistics: A Step by Step Approach Second Canadian Edition has been updated to help students in the beginning statistics course whose mathematical background is limited to basic algebra. The book follows a non-theoretical approach without formal proofs, explaining concepts intuitively and supporting them with abundant examples. The applications span a broad range of topics certain to appeal to the interests of students of diverse backgrounds and include problems in business, sports, ...show morehealth, architecture, education, entertainment, political science, psychology, history, criminal justice, the environment, transportation, physical sciences, demographics, eating habits, and travel and leisure
Maths from Scratch for Biologists for an Amazon.co.uk gift card of up to £4.21, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more Book Description{"itemData":[{"priceBreaksMAP":null,"buyingPrice":17.59,"ASIN":"0471498351","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":25.51,"ASIN":"0199570876","isPreorder":0}],"shippingId":"0471498351::ugcRuvWR71Ahfi8JGhzWF1GlGNxrVx6k5xMQksuhCRAxrsFEmSJ55du9Gd22il3OyT3y0LwsSIuUSeLgzLuSUXjj6Ugs8nUv,0199570876::XnyeCN9t9R8A2peu%2BT5mA2o3fRdCLn%2Bp6ATA60WJR7mPNjdkbwi2EuVskEs%2FJHhQhVBRD8kellKNuEbRZI1XOs2sKnJRrhNumerical ability is an essential skill for everyone studying the biological sciences, but many students are frightened by the ′perceived′ difficulty of mathematics, and are nervous about applying mathematical skills in their chosen field of study. Having taught introductory maths and statistics for many years, Alan Cann understands these challenges, and is aware just how invaluable an accessible, confidence building, An accessible, jargon–busting approach to help readers master basic mathematical, statistical and data handling techniques in biology. Numerous end of chapter problems to reinforce key concepts, and encourage students to test their newly acquired skills through practise. A handy, time saving glossary. A supplementary website with numerous problems and self–test exercises. Essential reading for all students within the biological sciences, taking core skills and numeracy courses, and an invaluable reference for those working within academia and industry. About the Author Alan Cann has worked in both the UK and USA, and in addition to teaching undergraduate and postgraduate biologists and medical students, he runs an active research laboratory at the University of Leicester, UK, studying the molecular biology and pathogenesis of viruses. He has been awarded numerous grants for educational research and was the inaugural winner of the Society for General Microbiology UK Wildy prize for Education in 2001. I would find it hard to recommend this book. On several occasions, I'm left wondering whether it's me or the author who has misunderstood. For example, the author notes that always rounding numbers like 2.45 up (to 2.5) introduces statistical bias, and prefers a variant of the "round to even" method, which in this case means rounding down to 2.4. Fair enough, but he also rounds down in cases like 2.459, which he would round to 2.4, even though it's clearly closer to 2.5. I'm left wondering what the real justification for this is. Another example: the author gives two methods of calculating percentiles; the first of these seems to assume that the distribution is perfectly flat, yet this isn't explicitly stated. Again, I'm left wondering whether it's me or the author who has misunderstood. 3.0 out of 5 starsA bit overwhelming for those trying to catch up to forgotten math concepts...10 Nov 2008 By Princess Yahm Serna - Published on Amazon.com Format:Paperback\|Amazon Verified Purchase The book is very good, but you have to already have reviewed those forgotten math concepts such as simple algebra and a few other things that the author purposely skipped to get to the details of the book. Unfortunately I ended up returning it after realizing I probably need a book not only to refresh some of the concepts and formulas, but also give me more detailed exercises. I read a few chapters but felt lost without a guide. But the book is a great reference for those already familiar with most mathematical concepts. The author does explain how to apply them very well and the examples are of good use. Before purchasing this book, especially if you're entering the science field or starting college courses in science, make sure to get familiar with algebra, trigonometry, calculus, etc. before diving into this helpful book. Then buy it! Otherwise for those already into it, it's a very small, organized and great book that you can carry in a small purse for those who commute on public transportation. 1 of 2 people found the following review helpful 5.0 out of 5 starsIt was a gift for my daughter24 Oct 2008 By George Winstead - Published on Amazon.com Format:Paperback\|Amazon Verified Purchase I purchased this book as a stocking stuffer for my daughter who is a psychology major and is not particularly fond of math. She tells me that the book was right-on and considerably helped her out in her labs.
Mathematics education is ever becoming an ever-increasing barrier to obtaining a post-secondary education and competing in the job market for many students from all socio-economic backgrounds. Far too often, these are students from diverse cultural backgrounds, students from low socio-economic backgrounds, and students for whom English is a second language. Standardized tests scores, including T.A.K.S., the National Assessment of Educational Progress, and U.S.Census data confirm this. In mathematics, algebra has long been called "The Gatekeeper" however, in terms of student preparation for post-secondary education and the 21st Century job market, we must recognize that algebra is "The Emancipator" opening for students' the gateway for higher level mathematics and complex problem-solving. We live in a country where it has all too frequently been acceptable to be innumerate. Statements like, "I was not good in math", are too frequently the norm. On the contrary, it has never been acceptable to be illiterate. Many students and adults are concrete learners, yet most mathematics instruction is taught in the abstract as a set of rote skills, memorization of disconnected facts and procedures. Students who are concrete learners lose are often left in the dark. The Bill and Melinda Gates Foundation, national political figures, corporate stakeholders, and educational leaders have partnered in an organization called Achieve, acknowledging that high school students with limited access to challenging mathematics instruction are not likely to complete college (see When I refer to algebra, I do not mean the algebra that many of us learned as symbolic manipulation and memorization of formulas, although these processes are still a fundamental part of learning algebra in today's classroom. Algebraic thinking has taken on a new face, which we refer to a function-based algebra. This approach focuses on patterns and relationships and the representation of concepts in multiple forms, i.e. as number, symbols, graphs, verbal descriptions, concrete objects and pictures, as well as the recognition of numerical patterns in tables. Throughout the United States and internationally, the function-based approach to algebra is introduced to students as early as kindergarten in a grade appropriate manner. Effective instructional strategies must be implemented such that we are reaching and teaching all students to comprehend and apply mathematical concepts. Research-based instructional strategies will direct student towards becoming fluent, competent problem-solvers, who are tenacious, creative, and resourcefulness all of which are necessary life skills. It is not possible to escape mathematics in everyday life. I serve as an author with McGraw-Hill Education the Glencoe-McGraw/Hill and MacMillan-McGraw/Hill Division and Co-Authored the high school series of What's Math Got to Do With It? Award-winning video series). I served as the lead-consultant to KERA's Math Can Take You Places video series and curriculum . KERA is the PBS affiliate in Dallas – Fort Worth,Texas and surrounding counties.I have worked on staff at the Charles A. Dana Center at The University of Texas at Austin as the Mathematics Director for the Partnership for High Achievement serving teachers throughout Texas stretching from the bordering states of Louisiana, Oklahoma, New Mexico, Arkansas and the Mexican International border in South and far West Texas. I have also had the pleasure of serving as a Senior Mathematics Consultant for ESC Region X, Richardson, Texas, which encompasses over 83 urban, suburban, and rural school districts in eight counties which includes Dallas Independent School District, the second largest district in the state of Texas. Over the years, I have presented sessions incorporating hands-on mathematics instruction, to tens of thousands of students, teachers, administrators, school board members, parents and others; they often ask, "Why wasn't I taught mathematics this way?"Many have stated, "If I had learned mathematics this way, they would have understood it". I have been blessed to be the author of the vast majority of these professional development and student mathematics materials that I have presented over the years. The Goal: We must work together to improve mathematics instruction for all students through educating and at times, re-educating the public. We must open doors and present choices in mathematics instruction to all students and eliminate the practice of tracking underrepresented student populations into low-level/remedial mathematics courses. We must raise our level of expectation for all student populations, and provide each of them with interesting and challenging instruction.These efforts can be accomplished through ongoing research-based professional development, the establishment of communities of learning, data-driven decision-making and continued commitment to move all students forward.
prove that some of the properties of the groups appearing earlier in the unit are, in fact, general properties shared by all groups. In particular, we prove that in any group the identity element is unique, and that each element has a unique inverse. The modulus function provides us with a measure of distance that turns the set of complex numbers into a metric space in much the same way as does the modulus function defined on R. From the point of view of analysis the importance of this is that we can talk of the closeness of two complex numbers. We can then define the limit of a sequence of complex numbers in a way which is almost identical to the definition of the limit of a real sequence. Another analogue of real analysis arises shall define the complex number system as the set R × R (the Cartesian product of the set of reals, R, with itself) with suitable addition and multiplication operations. We shall define the real and imaginary parts of a complex number and compare the properties of the complex number system with those of the real number system, particularly from the point of view of analysis consider how to sketch the graphs of more complicated functions, sometimes involving trigonometric functions. We look at graphs which are sums, quotients and composites of different functions, and at those which are defined by a different rule for different values of x. The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Once you have completed the workbook and exercises return to this page and watch the video below, 'The arch never sleeps', which discusses a practical application of some of the ideas in workbook. Click 'View document' to open the workbook (PDF, 0.8Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject. An alternative is to see the curriculum
Customers who bought this book also bought: Our Editors also recommend: Introductory Non-Euclidean Geometry by Henry Parker Manning This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901Non-Euclidean Geometry by Stefan Kulczycki This accessible approach features stereometric and planimetric proofs, and elementary proofs employing only the simplest properties of the plane. A short history of geometry precedes the systematic exposition. 1961Product Description: Examines various attempts to prove Euclid's parallel postulate — by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky. Includes 181 diagrams
Product Description Review "Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." — Aimo Hinkkanen, University of Illinois at Urbana "The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." — John Konvalina, University of Nebraska at Omaha From the Publisher A solid presentation of the analysis of functions of a real variable -- with special attention on reading and writing proofs. --This text refers to an alternate Hardcover edition. 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 book covers all that Rudin covers with the exception of Riemann-Stieltjes integration. On the whole, this is a great start! If proof-based math is new to you, then you will appreciate the first chapter on proofs. Would have given five stars, but I would have liked to seen Riemann-Stieltjes integration. That's really only nit picking, though.
Eighth grade students must meet the following criteria in order to take Algebra II at the high school as a freshman and get credit for Algebra I: 1. Pass the class with any grade. 2. Recommendation of the 8th grade math teacher. You must meet the above criteria to be considered to progress to Algebra II as a freshman. All other students in the 8th grade Algebra I class will take Algebra I as a freshman. Being in Algebra I as an 8th grader does not mean that a student has to take Algebra II as a freshman. It is the student's decision to make even if they meet the criteria. Gear up for Algebra Length 1 Semester Credit .5 Per Semester Grades 9 Prerequisite None Students who did not pass at least two years of math at the Junior High are required to take Gear up for Algebra before being placed in Algebra I classes. they will receive an elective credit for passing this class. Intensive Algebra Length 2 Semesters, 2 periods per day Credit .5 Per Semester Grades 9 Prerequisite Students will be placed in this class by test scores and previous math performance. This course will provide an Algebra credit, but will also work on basic skills remediation. Homework will be completed in the class and allows for in-depth hands-on math lessons. Algebra I Length 2 Semesters Credit .5 Per Semester Grades 9-10 Prerequisite None This is designed to be an entry level Algebra course for freshman students. Geometry I Length 2 Semesters Credit .5 Per Semester Grades 9-10 Prerequisite For students who passed Algebra I This course is designed to be the 2nd year of math that introduces geometric skills. Algebra II Length 2 Semesters Credit .5 Per Semester Grades 10-11 Prerequisite Third math course for students who have passed Algebra I and Geometry. This course is designed to provide the 3rd year of math for students. Trigonometry Length 2 Semesters Credit .5 Per Semester Grades 11-12 Prerequisite Fourth math course for students who completed Algebra II. This course continues an advanced course of study in mathematics. It is a continuation of Geometry and is for a 4-year college bound student. Calculus Length 2 Semesters Credit .5 Per Semester Grades 12 Prerequisite Fifth math course for students who complete Trigonometry or may be taken simultaneously with Trigonometry with consent of instructor. This course continues a very advanced course of study in mathematics. It is a continuation of Trigonometry and is for a 4-year college bound student.
This study examined understanding of linear functions held by students with visual impairments. The purpose of this study was to determine students' level of knowledge and type of understanding of linear function and to describe students' abilities in using the four main representational forms of a function: (a) description, equations, tables, and graphs. Other aspects studied were students' preferred representation of function and students' perceived influences in his or her mathematics education. Participants in this study included four high school and four college students who were receiving educational services for a visual impairment and who had completed at least one course in algebra. Data collection and analysis followed a qualitative research design. Three instruments were used for data collection, (a) the Mathematics Education Experiences and Visual Abilities (MEEVA) Interview, (b) the Function Knowledge Assessment (FKA), and (c) the Function Competencies Assessment (FCA). The MEEVA provided demographic information and responses provided information on students' previous educational experiences in mathematics. The FKA and the FCA were mathematics assessments that consisted of problems related to linear functions and their applications. Student responses from the FKA and the FCA provided information on student knowledge of linear functions and student abilities when solving word problems involving linear functions. Instruments were given orally and responses were audio recorded. Each participant met with the researcher one-on-one on two different occasions to complete the three data collection instruments. Data analysis followed the tenets of the Constant Comparative Method (Glaser & Strauss, 1967). Student responses to the MEEVA, FKA, and FCA were transcribed and coded for student understanding in the four function competencies, (a) modeling, (b) interpreting, (c) transcribing, and (d) reifying as described by O'Callaghan (1998). Students' level of knowledge of linear function was further described by students' ability to comprehend and apply knowledge when solving word problems, as described by Wilson (1971). Results indicate that the understanding of modeling and interpreting problems involving linear functions of high school and college students with visual impairments was stronger than that of either translating between representational forms of a function or the ability to reify the function concept. A positive relationship was observed between students' graphing abilities and his or her overall understanding of function. Results also show that students were most comfortable with gaining information on functions through tables and were least comfortable gaining information through graphs. The perceived influences on students' mathematics education were that of individualized education and the use of appropriate materials that allowed for independent access to the
Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing... more...... more... -- including Interface Builder, Xcode, and Objective-C programming... more...
Advanced Level Mathematics This is a set of brief courses aimed at Advanced Level Mathematics students in the United Kingdom. It is structured based on the MEI module system, which is popularly used among exam boards. For A-Level Mathematics material for other countries, please see . Choose one of the following exam boards to see the links to the modules and the relevant topics for the modules: Note: You do not gain a qualification from Wikiversity for taking these courses. However, this course is written to exam standards, so if you contact your local college, you should be able to order the relevant exam papers and sit it under exam conditions.
This well-thought-out program, contained on 2 DVDs, would be a great help to any student. The instructor uses his extensive experience as a tutor to clearly explain the concepts. He works hundreds of examples, with each step fully explained and shown on the board. Perhaps the greatest benefit of the program is that it is not curriculum specific. So if your student is using a particular program and having trouble understanding the concepts, you do not have to change programs! Simply insert Calculus 1 & 2 Tutor, scroll to the concept needed, and watch! The following concepts are covered: What Is a Derivative? The Derivative Defined as a Limit Differentiation Formulas Derivatives of Trigonometric Functions The Chain Rule Higher Order Derivatives Related Rates Curve Sketching Using Derivatives Introduction to Integrals Solving Integrals Integration by Substitution Calculating Volume with Integrals Derivatives and Integrals of Exponentials Derivatives of Logarithms Integration By Parts Integration by Trig Substitution Proper Integrals This program is without bells and whistles; it is just the DVDs. No curriculum or worksheets are used. It simply explains the concept so that the student can continue with the curriculum he or she is already using. This can be quite helpful for the family that doesn't want to switch gears but needs a little help explaining the concepts. Product review by Tamara Dumont, The Old Schoolhouse Magazine, LLC, June 2007
Precalculus (CliffsQuickReview) Precalculus (CliffsQuickReview) : Cl introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as: Arithmetic and algebraic skills; Functions and their graphs; Polynomials, including binomial expansion; Right and oblique angle trigonometry; Equations and graphs of conic sections; Matrices and their application to systems of equations.
Mathematics Mathematics is the common language of the universe. It is an essential tool in the fields of science, engineering, business, and even the social sciences. The application of mathematics has laid the foundation of modern society and continues to push the frontiers of human progress. Mathmathematiceans seek out patterns, and prove (or disprove) conjectures through proofs in order to advance the understanding of this science. The following videos teach the basic principles of math — arithmetic, algebra, calculus, and geometry. There is a course or lecture designed for any level of expertise in the subject. Feel free to explore these lectures in order to build a foundation upon what you already know.
Gardena Precalculus further shows how to use grids, tables, graphs, and charts to record and analyze data. Elementary continues on with the usage of the mean, median, and mode of data sets and how to calculate the range of that data set. It uses the addition and multiplication of fractions to calculate the prob...
Precalculus Dictionary Essential Precalculus Definitions The definitions listed in this Precalculus Dictionary are focused only on the terms that are essential for your understanding of our Precalculus Homework Help Secrets. It is our goal to provide you with just the right amount of critical informaion to put you on the path to better Precalculus Grades without hitting you with the information overload that is so common on the internet. This is not a Precalculus Encyclopedia - No information overload - just the basics. Our Precalculus Dictionary has been organized in an alphabetical listing of the basic terms defined. For your convenience the terms are also divided into three groups (A-I, J-R and S-Z). Many of the precalculus terms listed in our Precalculus Dictionary are also linked to a separate page with examples if you want to know more. Just click on the underlined terms to be taken from the Precalculus Dictonary to specific pages which explain the terms in more detail. An Asymptote is simply a line that a given function y=f(x) approaches but never crosses. y=f(x) gets ever closer and closer to this asymptote line as x gets larger and larger on its way to infinity, but never actually touches the asymptote. The simplest example of an Asymptote is the function y=1/x. As x gets larger and larger, y gets smaller and smaller, in this case closer and closer to 0, but never actually reaches 0. The line y=0 is said to be a horizontal Asymptote of the function y=1/x. In our section on the Real Number System we defined all numbers that are commonly used in arithmetic and general math. In algebra and precalculus we must add one additional type of number which we call Imaginary or Complex Numbers. A Complex or Imaginary Number is defined as any number which contains a multiple of the square root of (-1) which is defined as lower case "i". There are specific rules for carrying out mathematical operations with complex or imaginary numbers. Dividing Polynomials is a common method of finding the zeros or roots of a polynomial. For example the linear polynomial (x-2) can be divided into the polynomial x2-3x+2. The result is (x-1) with no remainder. This means that both x=2 and x=1 are zeros or roots of the polynomial x2-3x+2. Dividing Polynomials is a technique used to carryout this process which is similar to Long Division for numbers. Exponential Functions look very similar to quadratic and polynomial functions such as y=x2 with one very important difference - the variable x is the exponent. Examples of exponential functions include y=2x, y=ex and y=10x. Functions are algebra equations in which there are two variables such as y = 2x + 3. From these equations we see that the variable y changes as x changes. When x = 1 then y = 21 + 3 which is 5. When x = 2 then y = 22 +3 which is 7. Y is said to vary as a function of x and is sometimes written as y = f(x) [read as "y = a function of x"]. A Hyperbola is the general shape of a double quadratic function (one which has both x2 and y2). The simplest hyperbolas have the general formula y2/a2 + x2/b2 = 1. A Hyperbola looks like two "boomerangs" with their tips facing each other and is the result of the intersection of a plane with two cones stacked on top of one another point-to-point. Logarithms, being exponents, follow some specific and unique rules when involved in the standard math operations like addition, subtraction, multiplication and division. These rules are referred to as the Laws of Logarithms. One example of these rules is loga(AB) = loga(A) + loga(B). Logarithms are actually a Code for Exponents. The logarithm of a given number X is the exponent or power to which a specified number "b" called the logarithm base is raised. For example log10(100)=2 because the logarithm base "10" raised to the power 2 (squared) = 100. Polynomials are algebra expressions with more than two terms. Examples of Polynomials include: x2 - 2x + 1 and x3 + 2 x2 + 3 * x + 5. Polynomials are defined by their order or degree, which is the highest power of x present in the polynomial. A polynomial of zero order or degree 0 is simply a constant number. A polynomial of the first order or degree 1 is a linear equation (containing only x to the first power) such as y = ax + b where a and b are constants. A polynomial of the second order or degree 2 is a quadratic equation (containing only x to the first and second powers) such as ax2 + bx + c where a, b and c are constants. Quadratic Functions, sometimes referred to as Quadratic Equations, are polynomials of the second order that contain only x to the first and second power and have a general form of ax2 + bx + c = 0 where a, b and c are constants. All functions y = f(x) can be expressed as a geometric figure in a graph by locating each unique value of x and y of the function and placing a point at that location on the Cartesian Plane. The shape of this geometric figure or graph can be changed by carrying out standard Transformations on the function. These standard transformations include shifting up, down, left or right; stretching or shrinking horizontally or vertically, and reflecting through a straight line usually either the x or y axis. There are specific arithmetic operations that define each of these Transformations. The zero or root of a polynomial y=P(x) is simply a value of x which results in y=0. For example, the two zeros or roots of the polynomial y=x2-3x+2 are x=1 and x=2. This can be shown by substituting 1 and 2 for x which results in y=12-31+2=1-3+2=0 and y=22-32+2=4-6+2=0.
Web Site Webmath.com This is a dynamic math website where students enter problems and where the site's math engine solves the problem. Students in most cases are given a step-by-... Curriculum: Mathematics Grades: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 12. Web Site Prentice Hall Math Textbook Resources This site has middle school and high school lesson quizzes, vocabulary, chapter tests and projects for most chapters in each textbook. In some sections, ther... Curriculum: Mathematics Grades: 6, 7, 8, 9, 10, 11, 12 Web Site Tutorials for the Calculus Phobe Explore a collection of animated calculus tutorials in Flash format. The tutorials that follow explain calculus audio-visually, and are the equivalent of a p... Curriculum: Mathematics Grades: 11, 12, Junior/Community College, University Web Site Calculus Applets Discover the new way of learning Calculus. All manipula applets are visual and animation-oriented. Moving figures on the screen will help students to grasp ... Curriculum: Mathematics Grades: 9, 10, 11, 12, Junior/Community College, University Web Site Online Calculus Tutorials From Algebra Review to Multi-Variable Calculus, this website provides step-by-step tutorials for high school and university students. Curriculum: Mathematics Grades:
Illustrated Maths Dictionary 4th Edition Book with CD or DVD Click on the Google Preview image above to read some pages of this book! This fourth edition of the best-selling Illustrated Maths Dictionary is a comprehensive update of the most thorough mathematics dictionary for primary school students, student teachers and teachers in Australia. It features a new design, new illustrations and the addition of computer terminology in the useful information section. The new edition comes with an electronic version of the dictionary for use on your computer. Features: accurate, clear precise definitions; illustrations that add clarity to definitions where they are needed; a useful information section; new terms; modern, new design; all new illustrations & computer terminology.
Calculus: Early Transcendental Functions, 4th Edition (Smith) Chapter 14: Vector Calculus The Volkswagen Beetle was one of the most beloved and recognizable cars of the 1950s, 1960s and 1970s. So, Volkswagen's decision to release a redesigned Beetle in 1998 created quite a stir in the automotive world. The new Beetle resembles the classic Beetle, but has been modernized to improve gas mileage, safety, handling and overall performance. The calculus that we introduce in this chapter will provide you with some of the basic tools necessary for designing and analyzing automobiles, aircraft and other types of complex machinery. Think about how you might redesign an automobile to improve its aerodynamic performance. Engineers have identified many important principles of aerodynamics, but the design of a complicated structure like a car still has an element of trial and error. Before high-speed computers were available, engineers built small-scale or full-scale models of new designs and tested them in a wind tunnel. Unfortunately, such models don't always provide adequate information and can be prohibitively expensive to build, particularly if you have 20 or 30 new ideas you'd like to try. With modern computers, wind tunnel tests can be accurately simulated by sophisticated programs. Mathematical models give engineers the ability to thoroughly test anything from minor modifications to radical changes. The calculus that goes into a computer simulation of a wind tunnel is beyond what you've seen so far. Such simulations must keep track of the air velocity at each point on and around a car. A function assigning a vector (e.g., a velocity vector) to each point in space is called a vector field, which we introduce in section 14.1. To determine where vortices and turbulence occur in a fluid flow, you must compute line integrals, which are discussed in sections 14.2 and 14.3. The curl and divergence, introduced in section 14.5, allow you to analyze the rotational and linear properties of a fluid flow. Other properties of three-dimensional objects, such as mass and moments of inertia for a thin shell (such as a dome of a building), require the evaluation of surface integrals, which we develop in section 14.6. The relationships among line integrals, surface integrals, double integrals and triple integrals are explored in the remaining sections of the chapter. In the case of the redesigned Volkswagen Beetle, computer simulations resulted in numerous improvements over the original. One measure of a vehicle's aerodynamic efficiency is its drag coefficient. Without getting into the technicalities, the lower its drag coefficient is, the less the velocity of the car is reduced by air resistance. The original Beetle has a drag coefficient of 0.46 (as reported by Robertson and Crowe in Engineering Fluid Mechanics). By comparison, a low-slung (and quite aerodynamic) 1985 Chevrolet Corvette has a drag coefficient of 0.34. Volkswagen's specification sheet for the new Beetle lists a drag coefficient of 0.38, representing a considerable reduction in air drag from the original Beetle. Through careful mathematical analysis, Volkswagen improved the performance of the Beetle while retaining the distinctive shape of the original car.
Mathematics in Education The swiss-army knife for every astronomers, pro or amator. The swiss-army knife for every astronomers, pro or amator. It is intended to provide all necessary informations about stars, observatories, times, telescopes, observing runs, night... Here we have the best Math program. Here we have the best Math program. MATLAB R2008a 7.6 is a language for technical computing that integrates computation, visualization, and programming in an easy to use environment. It can be used in, Math and... Geometric design and strength check of worm gear. Application supports Imperial and Metric units, is based on ANSI/AGMA and ISO/DIN standards and support many 2D and 3D CAD systems Geometric design and strength check of worm gear. Application is... This is an extension to Python library. This is an extension to Python library. It aims to improve the mathematical capabilities using a set of mathematical functions. It includes complex numbers, Taylor series, limits, geometrical algebra, 2D and...….).... Jump Ahead Maths Year 1 is a fantastic garden adventure with counting money, geometry and special relations, subtraction, patterns and sequencing. Jump Ahead Maths Year 1 is a fantastic garden adventure with counting money, geometry and special... Mental Arithmetic has been designed to provide pupils with unlimited practice in the fundamentals of mathematics by teachers David Benjamin and Justin Dodd, the UK's leading experts on the use of software in the classroom. Mental Arithmetic... Now you can create an endless supply of printable math worksheets. Now you can create an endless supply of printable math worksheets. Testing, refresher exercises and homework. Endless educational materials made right now, to your specifications.... The calculation is designed for geometrical design and complex strength check of shafts. Application supports Imperial and Metric units, is based on ANSI, ISO, DIN standards and support many 2D and 3D CAD systems The calculation is designed for... The calculation is intended for... Solutions to dozens of basic formulas from physics, technology and mechanical engineering. Help, pictures as well as many selection tables with values of various coefficients and material properties are available for the formulas. Units... A fast, efficient search tool for scientists, medical professionals and students who rely on the ability to quickly access the millions of research papers indexed in PubMed. A fast, efficient search tool for scientists, medical professionals and... Efofex's FX MathPack contains four of the most powerful and useful mathematical tools available for teachers and students. Efofex's FX MathPack contains four of the most powerful and useful mathematical tools available for teachers and... Makes times tables fun to learn for your kids. Makes times tables fun to learn for your kids. Get a child off to a great start in maths! Keeps them occupied and out of trouble. Times Table Tutor makes an ideal gift for a child at any time of the... Geometric design and strength... Algebrator is one of the most powerful software programs for math education ever developed. Algebrator is one of the most powerful software programs for math education ever developed. It will tackle the most frustrating math problems you throw at... Enables Mac users of the Intel Play QX3, Digital Blue QX3, Digital Blue QX5, and Smithsonian QX5 USB Computer Microscopes to take snapshots and create time-lapse movies of the world around them. Enables Mac users of the Intel Play QX3, Digital... A Math Square is a large square divided into four small squares. A Math Square is a large square divided into four small squares. There are four numbers in a Math Square. Two single digits are placed in the top two boxes, the sum of the two top... Shape and Space 2 an interactive Maths application which can help children better understand the notion of shape in space. Shape and Space 2 an interactive Maths application which can help children better understand the notion of shape in space....
John Carzoli, PhD Mathematica is a software package that does much more than mathematics. Through the 20+ year history of the program it has developed from a text-based mathematics equation-solving and plotting program to a full-fledged graphical user interface front-end resting on top of a kernal that is capable of solving an extremely vast breadth and depth of problems in mathematics, phyiscs, engineering, and most other sciences. In fact, if there is a discipline where data is used in any way, Mathematica can be used to present and/or analyze that data in many different ways. Mathematica can even be used in areas where mathematics is not normally discussed. For example, you can input text from a poem or play and do an analysis on the word count, structure and other possibly interesting things. I've seen some neat examples of this kind of analysis and I will post links to them when I find them. Here is a list of resources for using Mathematica starting from the basics to the more advanced.
Intermediate Algebra MATH 153 All topics of Basic Mathematics and Elementary Algebra plus: Graphing quadratic functions, solving quadratic equations exactly using factoring or quadratic formula, and approximately by graphing; simplifying variable expressions with roots and radicals and fractional exponents, rationalizing the denominator, solving equations with roots and radicals and fractional exponents; distance between two points in the plane, equation of a circle; graphing inequalities in the plane; operations with rational expressions, solving rational equations; solving systems of equations. Functions and Graphs 1 MATH 161 All topics of Basic Mathematics, Elementary Algebra, Intermediate Algebra plus: Functions, rate of change of a function, domain and range of a function from graph and formula; concavity; absolute value functions, piecewise-defined functions; inverse functions; rules for exponents and logarithms, other bases, the number e and interest problems; solving equations involving logarithms and/or exponentials; applications of exponential and logarithmic functions; families of linear, quadratic, power, polynomial, rational, exponential, and logarithmic functions; average rate of change and comparison of rates of growth of these functions; transformations of functions and their graphs, shifts, reflections, symmetry, stretches, compressions. Functions and Graphs 2 MATH 162 All topics of Basic Mathematics, Elementary Algebra, Intermediate Algebra, and Functions and Graphs 1 plus: Measuring angles in degrees and radians, reference angles, special angles; creating sine and cosine functions from circular motion; trigonometric functions and their graphs; trigonometric identities; inverse trigonometric functions and their graphs; solving equations involving trigonometric expressions; solving right triangles; solving general triangles using sine and cosine laws; applications of trigonometry; sums, products, inverses, and composition of functions; power functions; short run and long run behavior of polynomials and rational functions, applications of polynomials and rational functions; comparing power, exponential, and logarithmic functions; vectors in the plane and their components, dot product, applications of vectors. Calculus 1 MATH 281 Limits, continuity. Definition of the derivative; sum, product, and division rules for differentiation; chain rule; graph of a derivative function; equation of a tangent line and local linearization. Definition of the integral in terms of upper and lower sums, fundamental theorem of calculus, average value of a function, mean value theorem.
The present book deals with the theory of computer arithmetic, its implementation on digital computers and applications in applied mathematics to compute highly accurate and mathematically verified results.The aim is to improve the accuracy of numerical computing (by implementing advanced computer arithmetic) and to control the quality of the computed... more...
Elementary Algebra Prepared for students by renowned professors and noted experts, here are the most extensive and proven study aids available, covering all the major areas of study in college curriculums. Each guide features: up-to-date scholarship; an easy-to-follow narrative outline form; specially designed and formatted pages; and much more. Introduction to Calculus Master Your Coursework with Collins College Outlines The Collins College Outline for Introduion to Calculus tackles such topics as funions, limits, continuity, derivatives and their applications, and integrals and their applications. This guide is an indispensable aid to helping make the complex...
This text explains the basics of mathematics and how it can be used in economics. The book is an ideal introduction to mathematics for students of economics, whatever their mathematical background. Th...
This book uses simplified language about mathematics to promote active and independent learning; strengthening critical thinking and writing skills. A "six-step" approach to problem-solving, numerous tips, and clear, concise explanations throughout the book enable users to understand the concepts underlying mathematical processes. Beginning with the foundations of the mathematical process, some of the topics covered are: whole numbers and decimals; integers; fractions; percents; measurement; area and perimeter; interpreting and analyzing data; symbolic representation, linear and nonlinear equations; powers and logarithms; formulas and applications; higher-degree equations; absolute values and inequalities; slope and distance; basic concepts in geometry; and an introduction to trigonometry. This book can serve as a valuable reference handbook for engineering technicians, nurses, dieticians, job trainers, home-schooling professionals, and others who require a basic knowledge of non-calculus mathematics. show more show less Whole Numbers and Decimals Whole Numbers, Decimals, and the Place-Value System Adding Whole Numbers and Decimal Numbers Subtracting Whole Numbers and Decimals Multiplying Whole Numbers and Decimals Dividing Whole Numbers and Decimals Exponents, Roots, and Powers of 10 Order of Operations and Problem Solving Integers Natural Numbers, Whole Numbers, and Integers Adding Integers Subtracting Integers Multiplying Integers Dividing Integers Order of Operations Fractions Fraction Terminology Multiples, Divisibility, and Factor Pairs Prime and Composite Numbers Least Common Multiple and Greatest Common Factor Equivalent Fractions and Decimals Improper Fractions and Mixed Numbers Finding Common Denominators and Comparing Fractions Adding Fractions and Mixed Numbers Subtracting Fractions and Mixed Numbers Multiplying Fractions and Mixed Numbers Dividing Fractions and Mixed Numbers Signed Fractions and Decimals Percents Finding Number and Percent Equivalents Solving Percentage Problems Increases and Decreases Direct Measurement The U.S. Customary System of Measurement Adding and Subtracting U.S. Customary Measures Multiplying and Dividing U.S. Customary Measures Introduction to the Metric System Metric-U.S Customary Comparisons Time Reading Instruments Used to Measure Length Temperature Formulas Area, Perimeter, and Volume Squares, Rectangles, and Parallelograms Perimeter and Area of Circles, Cylinders, and Composite Figures Volume of Prisms and Cylinders Interpreting and Analyzing Data Reading Circle, Bar, and Line Graphs Frequency Distributions, Histograms, and Frequency Polygons Finding Statistical Measures Counting Techniques and Simple Probabilities Linear Equations Rational Numbers Symbolic Representation Solving Linear Equations Applying the Distributive Property in Solving Equations Numerical Procedures for Solving Equations Function Notation Linear Equations with Fractions and Decimals Solving Linear Equations with Fractions by Clearing the Denominators Solving Decimal Equations Using Proportions to Solve Problems Powers and Polynomials Laws of Exponents Polynomials Basic Operations with Polynomials Powers of 10. and Scientific Notation Roots and Radicals Roots and Notation Conventions Simplifying Irrational Expressions Basic Operations with Square-Root Radicals Complex and Imaginary Numbers Equations with Squares and Square Roots Formulas and Applications Formula Evaluation Formula Rearrangement Geometric Formulas Products and Factors The Distributive Property and Common Factors Multiplying and Dividing Polynomials Factoring Special Products Factoring General Trinomials Rational Expressions and Equations Simplifying Rational Expressions Multiplying and Dividing Rational Expressions Adding and Subtracting Rational Expressions Solving Equations with Rational Expressions Solving Quadratic and Higher-Degree Equations Solving Quadratic Equations by the Square-Root Method Solving Quadratic Equations by Factoring Solving Quadratic Equations by Completing the Square Solving Quadratic Equations Using the Quadratic Formula Solving Higher-Degree Equations by Factoring Exponential and Logarithmic Equations Exponential Expressions, Equations, and Formulas Logarithmic Expressions Inequalities and Absolute Values Inequalities and Sets Solving Simple Linear Inequalities Compound Inequalities Solving Quadratic and Rational Inequalities Equations Containing One Absolute-Value Term Absolute-Value Inequalities Graphing Functions Graphical Representation of Equations and Functions Graphing Linear Equations with Two Variables Using Alternative Methods Graphing Linear Inequalities with Two Variables Graphing Quadratic Equations and Inequalities Graphing Other Non-Linear Equations Slope and Distance Slope Point-Slope Form of an Equation Slope-Intercept Form of an Equation Parallel Lines and Perpendicular Lines Distance and Midpoints Systems of Linear Equations and Inequalities Solving Systems of Linear Equations and Inequalities Graphically Solving Systems of Linear Equations Using the Addition Method Solving Systems of Linear Equations Using the Substitution Method Problem Solving Using Systems of Linear Equations Selected Concepts of Geometry Basic Terminology and Notation Angle Calculations Triangles Polygons Sectors and Segments of a Circle Inscribed and Circumscribed Regular Polygons and Circles Introduction to Trigonometry Radians and Degrees Trigonometric Functions Using a Calculator to Find Trigonometric Values Right-Triangle Trigonometry Sine, Cosine, and Tangent Functions Applied Problems Using Right-Triangle Trigonometry Oblique Triangles Vectors Trigonometric Functions for Any Angle Law of Sines Law of Cosines Area of Triangles Symbols Roman Numerals Greek Alphabet Metric Prefixes Business Formulas Using Technology Selected Answers to Student Exercise Material Glossary Index List price: $98.00 Edition: 6th 2004 Publisher: Prentice Hall PTR Binding: Mixed Media Pages: 992 Size: 8.75" wide x 11
Product Information This updated book is a self-teaching brush-up course for students who need more math background before taking calculus, or who are preparing for a standardized exam such as the GRE or GMAT. Set up as a workbook, Forgotten Algebra is divided into 31 units, starting with signed numbers, symbols, and first-degree equations, and progressing to include logarithms and right triangles. Each unit provides explanations and includes numerous examples, problems, and exercises with detailed solutions to facilitate self-study. Optional sections introduce the use of graphing calculators. Units conclude with exercises, their answers given at the back of the book. Systematic presentation of subject matter is easy to follow, but contains all the algebraic information learners need for mastery of this subject.
Jetzt kaufen E-Books sind auch über alle bekannten E-Book Shops erhältlich. Kurzbeschreibung Introduction to Integral Calculus develops an intellectually stimulating level of understanding of the subject while giving numerous applications and incorporating various scientific problems. The authors outline how to find volumes and lengths of curves, anti-differentiation, integration of trigonometric functions, integration by substitution, methods of substitution, the definite integral, methods for evaluating definite integrals, differential equations and their solutions, and ordinary differential equations of first order and first degree. This book is an immensely accessible go-to resource that maintains the highest standards for those in this field. Aus dem Inhalt FOREWORD ix PREFACE xiii BIOGRAPHIES xxi INTRODUCTION xxiii ACKNOWLEDGMENT xxv 1 Antiderivative(s) [or Indefinite Integral(s)] 1 1.1 Introduction 1 1.2 Useful Symbols, Terms, and Phrases Frequently Needed 6 1.3 Table(s) of Derivatives and their corresponding Integrals 7 1.4 Integration of Certain Combinations of Functions 10 1.5 Comparison Between the Operations of Differentiation and Integration 15
MATH ►Rick Geiser ►Jen Lawrence ►Matt Zuercher INTEGRATED MATH II This course is designed for students who took Integrated Math I. Integrated II completes the second year class format. ALGEBRA I Algebra I will provide instruction in the following topics: quadratic equations, linear equations, inequalities, polynomials, factoring, functions and graphs, and coordinate geometry. Algebra I is the first course in the college preparatory program. A scientific calculator (TI 30XIIS), not graphing calculator, is required for this course. GEOMETRY The course embodies the objectives of geometry and the logic upon which it is based. Through definitions, postulates, and theorems, the student will learn direct and indirect methods of finding lengths, angle measures, perimeters, areas, and volumes of geometric figures. Constructions and projects are offered to enhance concepts. Since the course stresses deductive reasoning, it is highly recommended for college preparatory students. A scientific calculator (TI 30XIIS), not a graphing calculator, is required for this course. ALGEBRA II This is the third course in the college preparatory math program. In addition to a more detailed study of Algebra I topics, Algebra II introduces matrices, radicals, complex numbers and quadratic relations and systems. A scientific calculator is required for this course. TRIGONOMETRY Trigonometry is the study of the sine, cosine, tangent, and their reciprocal functions in relation to right triangles. Students will investigate the properties of the trig functions and their inverses, study their graphs and transformations, solve trigonometric equations, and verify/prove identities. Students will also learn techniques to solve both right and non-right triangles. The course is a prerequisite or co-requisite for Pre-Calculus. Students are encouraged to take the course while also taking Algebra II or in the fall while taking Pre-Calculus. A graphing calculator is highly suggested. PRE-CALCULUS This is the 4th course in the college preparatory math program. This course offers a detailed study of circular and trigonometric functions, matrices, theory of education, Polar coordinates, complex numbers, vectors, sequences and series, exponential and logorithmic functions, and intro to calculus. Graphing calculator is strongly suggested! ADVANCED PLACEMENT CALCULUS AB (Calculus AB) This is the fifth course in the college preparatory math program. Topics include limits and their properties, differentiation and its applications, integration, exponential & logarithmic functions, integration techniques & applications, parametric equations, etc. Graphing calculator is strongly suggested! Students may take the AP exam in May with the possibility of testing out of college math classes. The cost is approximately $89.00. ***AP Calculus is offered on a five point grade point average system, requiring the taking of the AP Calculus exam in May. The option of taking this course on a four point grade point system eliminates the AP Calculus exam requirement. TRANSITIONS Transitions to college mathematics is designed to be a mathematics course for seniors who will need to take college courses in mathematics and have completed Algebra I, Geometry, and Algebra II/Algebra II Basic. A commitment to do many problems on a daily basis is essential. Algebra and Geometry concepts are presented in concrete problem settings, approached arithmetically through numerical computation. A scientific calculator is required for this course. BRIDGING THE GAP TO COLLEGE MATH Instead of learning in the traditional classroom, students are pre-tested (COMPASS or ACT) and placed into the course at the level that is right for them. From there, students work through a series of online modules, progressing at their own pace, and practicing skills in class and at home through a combination of online tools and instructor support. This course is designed to help students identify the areas they need to strengthen and develop their skills so they are ready for college algebra and equipped for success in college. Bridging the Gap to College Math is based on the concept of "mastery learning", which involves practicing a skill until it is learned and can be demonstrated. When the student is ready, he/she takes a post-test. With a score of at least 85%, the student demonstrates mastery competence and is ready to progress to the next module. Instructors are available during class time to answer questions and guide the students. Columbus State Community College is our partner for this course. If a student attends CSCC upon high school graduation, they will earn placement into the appropriate credit bearing math course instead of a non-credit remedial course.
Sponsor Links Followers Calculator To our modern world, calculators are basic machines used to measure quantities applied in different field and styles. People used calculator for many purposes where it gives you the calculated amount you were looking for. Student basically used calculators to solve and calculate more accurate solutions and to solve even faster. Just point up the numbers and the desired operation then press the "=" button and there you have the answer. As easy as it is, that is why it is used for a lot in every field were calculation is present. In the history of calculating machines, calculators have come the best and most effective way of solving and calculating digits. Abacus is the oldest calculating device that is still known in some people here in our planet. This calculating machine is manually operated were you can't find digits or buttons but beads sealed linearly set in rows. They place the beads in every row and come with an accurate answer. But when it comes to quality and usage, abacus is far away from calculators. Calculators may come from different kinds and styles. There we have the basic calculator, were it has the number digits from 0 to 9, the basic mathematical operation digits which are the addition (+ sign), subtraction (- sign), multiplication (X sign) and division (sign). This basic calculator also comes with some reset button were it reset back to 0 after the operation. This is commonly used in stores in computing summations of the product's prices and for calculating the change of the customer. Sometimes it is also used in some companies were they summarize all their reference which is written in digits. Scientific calculator is a kind of calculator which has more function than basic calculator. It has its own functional digits designed to calculate angles etc. This goes with some more complicated mathematical operations in some fields of engineering like trigonometry and algebra. It has function keys like tan, cos, sin, x2, nPr, ln, log, etc. which is more complicated than basic calculator keys. This is ever better than basic calculator because if you knew how to operate a scientific calculator, you will benefit every functional keys of it. Scientific calculators have its own mode systems where you can set the calculation like for an equations, graph, fractions, etc. Students in higher years are often use scientific calculators for their own purposes and because of its good features to solve applicable problems and give accurate solutions and answers. If you don't want to become handy and physical when it comes to calculating machines, you can have software calculator. This is software that can be installed on your phones, computers and laptops. Just like the other calculators that I mentioned recently, software calculators offers the same benefits but is more functional than scientific and basic calculators. Unlike the other calculators, this has its specification of problems and can have shown you solutions and graphs how it came with the answer. Software calculators are often used by students out there which are looking for better explanation of works and solutions. You can have written the equation or problem and the let alone the software calculator do it for you. Calculators are designed to help us in calculating things but we must remember that we must still know the basic mathematical operations and much better if we know how to solve problems and equations without the help and aid of calculators. Sometimes it has the bad effect of laziness to some students because calculators just give those answers but not solutions which are confusing in the part of those who don't know the solutions and ways why it came to that answer. Better to study on things and use calculators for answer check not for final answers.
AcademicsCalculus I (NSC2) Course Outline: This course will follow the first five chapters of Calculus by James Stewart, published by Brooks/Cole. Explorations in Calculus, an interactive, multimedia CD program by Joe Mazur et al, published by Springer-Verlag and four videos available through the library, called Views of Calculus, will provide useful extra material. The program will follow a strict schedule that includes drill and practice routines for developing a familiarity with the common tools of calculus alongside discussions surrounding the concepts behind the subject. Thus assignments from Stewart's Calculus, together with additional material from Explorations in Calculus, Views of Calculus and other sources, will prompt class discussion surrounding the concepts, while daily problem sets will reinforce a command of the material. This is a four-credit course and there is much to learn. Please keep in mind that this course requires a daily commitment. The best way to successfully learn the material is to stay ahead of the game and work through the assignments before final class discussion. Grades: Here is the breakdown for how your grade will be calculated: 20% Class participation and attendance; 40% Graded homework assignments; 40% Final exam. Homeworks: Bold numbered problems in the attached homework assignment sheet are to be handed in for grading. Plain text numbered problems are more drill and practice material that should be worked through to keep up with course material. You are expected to complete the current assignment after the topic is introduced in class and before class discussion of the assignment itself. By noon each Friday you are expected to hand in your solutions to the appropriate bold numbered questions (exactly which questions these are will be announced during the previous week); but you may wish to discuss any assignments that you find difficult.
Includes six chapters: Basic Operations, Laws of Indices, Brackets and Factors, Laws of Precedence, Proportionality and Simple Equations. Each chapter contains at least one virtual laboratory, which allows students to input their own examples and produces a step-by-step solution. Main theory is general but the plug-in question books allow for subject- specific, or harder/easier questions and examples to be incorporated. Virtual laboratories address key areas of conceptual difficulty and provide learning models. Over 50 scored questions where the answer needs to be typed in, and a further 75 questions on printable worksheets.
Introduction to Analysis 1 Fall 2004 Course objectives: Topics to be covered include mathematical induction, the axioms of the real number system, sequences, series, functions, continuity of functions, and the intermediate value theorem. Students will solve problems relevant to these topics and students will write proofs of such things as the convergence of sequences and of familiar theorems of calculus. Introduction to Analysis 2 Spring 2005 Course objectives: Topics to be covered include limits of functions, power series, uniform convergence, derivatives, Taylor's theorem, and the Riemann integral. Students will solve problems and will write proofs of theorems relevant to these topics.
Power Maths - A pre-calculus project - Sidney Schuman A pre-calculus investigation designed to enable students to discover each calculus power rule independently (albeit in simplified form), and hence their inverse relationship. Students are required only to do simple arithmetic and some elementary algebra, ...more>> PreCalculus - Trevor Roseborough An introduction to calculus for the student who is about to learn the subject. It makes clear the connection between the integral and the derivative and suggests a more consistent notation before the student becomes hopelessly confused. ...more>> Problem of the Week - Purdue University A panel in the Mathematics Department publishes a challenging problem once a week and invites college and pre-college students, faculty, and staff to submit solutions. Solutions are due within two weeks from the date of publication and should be sent ...more>> The Problem Site - Douglas Twitchell Math puzzles, brainteasers, strategy games, web quizzes, and informational pages. Flash-powered math games include Adders, Zap (slide tiles to move digits and add up to a specified sum), Side By Side (number re-arrangement), One To Ten (given four numbers,Productive Struggle Group blog, with most contributions by secondary math and science teachers, that aims to "push teachers to learn in the same way that we push our students to learn" and "work together to make our struggles productive." Posts, which date back to March, ...more>> Project Based Learning Pathways - David Graser A blog about real life projects suitable for college math courses such as algebra, finite math, and business calculus. Most of these applied math projects include handouts, videos, and other resources for students, as well as a project letter. Graser, ...more>> Public Domain Materials - Mike Jones A collection of public domain instructional and expository materials from a US-born math teacher who teaches in China. Microsoft Word and PDF downloads include a monthly circular consisting of short problems, "The Bow-and-Arrow Problem," and "Twinkle
MERLOT Search - materialType=Collection&category=2513&sort.property=dateCreated A search of MERLOT materialsCopyright 1997-2013 MERLOT. All rights reserved.Sat, 18 May 2013 16:40:39 PDTSat, 18 May 2013 16:40:39 PDTMERLOT Search - materialType=Collection&category=2513&sort.property=dateCreated 4434Rob Beezer's Free Texts From this site there are links to a variety of free math textbooks that can be downloaded in various formats.New York University - Free Textbooks This site has a list of different topics in math and physics. When one clicks on the link, a list of free textbooks is provided along with a link to the book.Math Formulas Reference App for iOS 'Over 100 math formulas at high school level. The covered areas include algebra, geometry, calculus, trigonometry, probability and statistics. Most of the formulas come with examples for better understanding. Use the powerful search function to find what you are looking for and mark your favorites for easier access. A convenient tool for students and teachers and a handy reference for anyone interested in math!'This app costs $0.99The Teacher's Guide Provides free worksheets, printouts, lesson plans, SMARTBoard templates, and more. Also provides free Math Interactive Sites.Ampersand Academic Press Ampersand Academic Press is a section within Free-ebooks.org that offers free educational articles books, and textbooks that you can download to digital devices such as eReaders. Free textbooks are currently offered in Business, Computer Science, Engineering, Law, Mathematics, and Science. You can also submit your own eBook that you have written for review by their staff. Standard Membership is free.The Futures Channel The Futures Channel provides students and educators with an excellent resource collection of inspirational Educational videos about current trends and advancements in Science, Engineering, and Technology. It also showcases conversations with visionaries that are helping to change our future perspectives about the world we live in it by providing viewers with realistic real-world applications of their work within their field of study. An excellent Multimedia resource for K-12 STEM and Science teachers to encourage and inspire their students to pursue careers in Math, Science, and Technology.DNATube Scientific Video Site DnaTube Scientific Video Site is a collection of video-based studies, lectures, seminars, animations, and slide presentations that explain biological concepts. Entries can be easily searched by scientific categories as well by "Recently Added" and "Most Watched" categories. The collection of educational resources is appropriate for middle school, high school, and college classrooms.Elementary Algebra Free Youtube Modules This site is the entry list to a collection of short, engaging text/graphic modules on standard topics in Elementary Algebra. They are available as Youtube videos for free classroom or download by instructors and students. Basic formulas, sample problems and standard applications are included. Format is text, audio and graphics.Sector matemáticas recopilación de variados programas matemáticos que he encontrado en mis paseos por la red y que puedes descargar gratuitamente.ארכיון שווה ארכיון עלון המתמטיקה לבית הספר היסודי מבית מט״ח. כל גיליון עוסק בנושא שונה מהעולם הרחב, אשר מוצג באמצעות קטעי קריאה וחידות.
This is a module framework. It can be viewed online or downloaded as a zip file. It is as taught in 2009-2010. This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the associated theory, with a strong emphasis on rigorous proof. This module is suitable for study at undergraduate level 2. Dr Joel Feinstein, School of Mathematical Sciences Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area
This Advanced Mathematics tutorial course is designed to go with the textbook Geometry with Advanced Algebra, 2nd edition, by John Saxon. The ten DVDs in the set cover the first 90 lessons in the text. (There is a separate set of DVDs for the remaining lessons, ending with lesson 125.) The DVDs come in a sturdy DVD case and can be played on a television or a computer. On the first DVD, Mr. Art Reed gives an overview of the course and a review of Algebra. It would be best to have the textbook Geometry with Advanced Algebra, 2nd edition, to go along with the DVDs (rather than trying to fit this tutorial into another curriculum). Prior to using this tutorial course, students should have completed the Algebra 2 textbook and the Geometry textbook by Saxon. Mr. Reed teaches this Geometry text over the course of four semesters. As mentioned, these DVDs cover lessons 1-90. Mr. Reed's schedule is to complete one lesson every two days. The students watch the DVD on one or both days, completing the odd-numbered problems on one day and the even-numbered problems on the next day. Mr. Reed schedules for one test every four lessons. When the student is ready for a lesson, he or she simply clicks on the lesson number. It states the duration of the DVD lesson. Mr. Reed begins his lecture at his podium. He then uses a white board to teach the lessons. Watching the DVDs is like sitting in a classroom for a math lecture. I found that the teaching was excellent. Mr. Reed did a great job of explaining difficult concepts. He also tied the new material to previous knowledge. He reminds me of my former Trig teacher. If you are looking for instruction to go along with the Geometry with Advanced Algebra book, these are the DVDs for you. There is a sample of the DVD instruction on so that you can view Mr. Reed in action. Product review by Maggi Beardsley, The Old Schoolhouse® Magazine, LLC, June 2010
\input zb-basic \input zb-matheduc \iteman{ZMATH 2011f.00203} \itemau{Putz, Erzs\'ebet} \itemti{Developing mathematical skills. (A matematikai tehets\'eg fejleszt\'ese.)} \itemso{Mat. Tan. 10, No. 5, 4-16 (2002).} \itemab \itemrv{~} \itemcc{C30 C40 C90} \itemut{mathematically gifted persons} \itemli{} \end
Find an Opa Locka SATWhen taking this course, students will develop an understanding not only of basic algebraic principles and techniques, but also of how to model and solve real-world problems. Students will study the writing, graphing, and solving of linear equations and inequalities, both individually and in sys...
The aim of this course is to acquaint the students with applications of calculus in business and economics. The course includes: limits and derivative, Minima and maxima and its applications in business and economics, definite and indefinite integrals, applications of integrals in business and economics. COURSE OBJECTIVES Mathematics intends that students will: Develop mathematical skills and apply them Develop the ability to communicate mathematics with appropriate symbols and language Develop patience and persistence when solving problems Develop and apply business and economics skills in the study of mathematics
Once considered an "unimportant" branch of topology, graph theory has come into its own through many important contributions to a wide range of fields — and is now one of the fastest-growing areas in discrete mathematics and computer science. This new text introduces basic concepts, definitions, theorems, and examples from graph theory. The authors present a collection of interesting results from mathematics that involve key concepts and proof techniques; covers design and analysis of computer algorithms for solving problems in graph theory; and discuss applications of graph theory to the sciences. It is mathematically rigorous, but also practical, intuitive, and algorithmic.
GMTH-1030 - Precalculus Introduction to the principles of trigonometry and possibly some advanced topics in algebra. Coverage includes, but may not be limited to, exponential, logarithmic, trigonometric, and circular functions, triangle problems, and vectors. This course, in conjunction with GMTH-1020 College Algebra, is designed to help prepare the student for calculus. Prerequisites: Proficiency in Mathematics and GMTH-1020 College Algebra or permission of instructor. Dual Enrollment students who do not have credit for GMTH 1020 College Algebra must earn a satisfactory score on a precalculus readiness assessment before registering for this course. Contact the Dual Enrollment coordinator for more details.
Category Archives: Algebra Post navigation Take a free look at the articles from the NCTM middle school journal – Mathematics: Teaching in the Middle School. Explore and share with others. Check out the Reflection Guides. They provide professional development support linked to specific articles for individual, small groups or school use.DigestingThe prospect can sound daunting. You may even feel the need for a refresher in algebra content. If so, you may find these sites helpful. Patterns, Functions, and Algebra This college-level math course explores the "big ideas" in algebraic thinking. Created for elementary and middle school teachers, the online workshop consists of 10 two-and-a-half hour sessions. You begin with a session on algebraic thinking and go on to sessions on such topics as proportional reasoning, solving equations, and nonlinear functions. Each workshop meeting includes video of teachers working together on problems, interactive Web activities, homework exercises, and discussion questions. The final session explores ways to apply the algebraic concepts you've learned to your own K-8 classrooms. Graduate-level semester credits are available through registration at Colorado State University, or the sessions can be completed for free by any interested group of teachers. Algebra in Simplest Terms If you want a basic algebra review, take a look at this video series. Intended for high school classrooms and adult learners, the course offers 26 half-hour video programs and coordinated books—online and free. Offered by Annenberg/CPB: Teacher Professional Development. Navigating through Algebra for Grades 6-8. Written for the middle school teacher, this book outlines the main concepts to be covered in these critical years and presents full activities as teaching samples. Finally, a general resource of ideas for the classroom is Algebraic Thinking: A Basic Skill.Topics range from algebraic expressions to solving equations to understanding graphs. Here you can find online activities at a click. I hope you will find these sites helpful and enjoy next year's classcreator
Quiz on Numbers, Quiz on Integer, Quiz on Fractions and Decimals, Quiz on Rounding and Percentage, Quiz on Absolute value, Quiz on Sets, Quiz on Roots and Radicals, Quiz on Exponents and Powers, Quiz on Function and Their Graphs, Quiz on Polynomials, Quiz on Simultaneous Linear Equations, Quiz on Quadratic Equations, Quiz on Ratio and Proportion, Quiz on Sequences and Series, Quiz on Inequalities, Quiz on Probability, Quiz on Statistics, Quiz on Permutation and Combination, Quiz on Line and Circle Graphs, Quiz on Bar Graph, Quiz on Lines and Angles, Quiz on Triangles, Quiz on Quadrilaterals and Polygons, Quiz on Conic Sections, Quiz on Parabola, Quiz on Ellipse and Hyperbola, Quiz on Circles, Quiz on Area and Perimeter, Quiz on Volume and Surface Area, Quiz on Coordinate Geometry, Quiz on Trignometry, Quiz on Measurement and Conversions, Quiz on Profit, Loss and Average, Quiz on Simple Interest, Quiz on Compound Interest, Quiz on Word Problems, Quiz on Time and Distance, Quiz on Time and Work, Quiz on Data Sufficiency.
Features: first part of book is a dictionary, giving brief and simple explanations of mathematical terms, often with examples and diagrams second part of book contains a detailed reference section, providing an overview of key ideas about a wide range of mathematical topics, including tables, number systems, charts, 2-D shapes, 3-D shapes, measures, conversion tables, equivalences, formulas, rules, explanations and symbols
In math, as in any form of communication, there are rules that are agreed upon so that everyone can understand exactly what is being communicated. Oral and written languages use vocabulary, grammar, and sentence structure to communicate effectively. Mathematics uses its own form of these entities as well. Learning the language of mathematics is a key aspect of understanding the concepts being communicated. Numbers (analogous in some ways to the alphabet in which a language is written) and how these numbers are combined (much as letters are combined in the spelling of words) are the foundation for the study of algebra. This chapter will introduce the basic building blocks of algebra and give you a sturdy foundation for your future study.
Mathematics in Education Turns your Sudden Motion Sensor-equipped laptop into a three-axis seismograph. Turns your Sudden Motion Sensor-equipped laptop into a three-axis seismograph. It shows a scrolling chart of the three axes of acceleration, reading up to five hundred... Terrific Triangles is a math facts drill-and-practice program that teaches fact families for both addition/subtraction and multiplication/division. Terrific Triangles is a math facts drill-and-practice program that teaches fact families for both... The award-winning periodic table of the elements for the Macintosh. The award-winning periodic table of the elements for the Macintosh. In addition to the usual information found in such programs, The Atomic Mac also contains a wealth of nuclear... Solve mathematical models applied to technical problems of various type. Solve mathematical models applied to technical problems of various type. Documents can be realized and used as calculation models for a specific mathematical technical... Do you have a homework assignment that needs the complete working out for a matrix question, and requires that it be neatly typed out? Do you have a homework assignment that needs the complete working out for a matrix question, and requires that... Controls up to 4 USB or Firewire connected cameras during an eclipse so that you can be free to concentrate on observing the event visually. Controls up to 4 USB or Firewire connected cameras during an eclipse so that you can be free to... Visualization tool for the N-body problem. Visualization tool for the N-body problem. The first program of its kind for Mac OS X, it has an intuitive interface, beautiful graphics and an accurate and fast core physics engine. Cavendish is named... A Cocoa application dedicated to the processing of astronomical digital images taken through a telescope. A Cocoa application dedicated to the processing of astronomical digital images taken through a telescope. It is a a€sUniversal binarya€t... Pythagorean Theorem is a text-based program that uses the formula A2 B2 = C2 to calculate the length of any side of a right triangle, provided you enter the other two. Pythagorean Theorem is a text-based program that uses the formula A2 B2 = C2 to... Marketiva specializes in providing traders with high quality online trading services. Marketiva specializes in providing traders with high quality online trading services. With a team of dedicated financial specialists and technical support... AlgeXpansion is an aplication that teaches algebraic expansion. AlgeXpansion is an aplication that teaches algebraic expansion. The program is capable of generating hundreds of sums for drills to ensure that the student masters the skills. It... This program puts a set of problems on the screen. This program puts a set of problems on the screen. Each consists of two digits, and they are to be added or multiplied. There is no penalty for wrong answers. As soon as the user provides the... Control engineers and instrumentation technicians require software tools to test communications both to and from Programmable Logic Controllers (PLCs), Remote Terminal Units (RTUs), and other logic solving devices. Control engineers and... The best matrices calculator there is. The best matrices calculator there is.It is a calculator for real and complex matrices.It is not just a calculator you can write your own programs on it. Can do all manipulations on matrices. It can do add,... A professional numerology decoding program that is easy to use. A professional numerology decoding program that is easy to use. It enables you to enter names, dates, letters, or numbers in any combination. Q-Decode will then break down the data... Teaches the concepts of digital electronic circuits. Teaches the concepts of digital electronic circuits. The integrated schematic entry and simulation software was designed specifically for educational use and can be applied in minutes. Probes,... An easy-to-use utility for backing up and restoring Garmin GPS waypoints and routes. An easy-to-use utility for backing up and restoring Garmin GPS waypoints and routes. All GPS waypoint and route data can be completely restored or you can select... A word-processor-like editor specifically designed for use in high school and college-level algebra-based physics courses. A word-processor-like editor specifically designed for use in high school and college-level algebra-based physics courses....
Pre-Algebra Negative numbers, order of operations, solving for the unknown, and other topics. Essentials Pre-Algebra Instruction Pack The Pre-Algebra Instruction Pack contains the instruction manual with lesson-by-lesson instructions and detailed solutions, and the DVD with lesson-by-lesson video instruction. Additional resource: We offer an Online Co-op Class for this level. To learn more about schedule and pricing or to register, click here. $57.00 QTY: Pre-Algebra Student Pack The Pre-Algebra Student Pack contains the Student Workbook with lesson-by-lesson worksheets, review pages, and honors pages. It also includes the Pre-Algebra Tests. $32.00 QTY: Manipulative Block Set Used in all levels from Primer through Algebra 1 (except Epsilon) Colorful 88-piece base-10 stacking blocks Five each of 2s, 3s, 4s, 6s, 7s, 8s, 9s, and 100s Seven 5s Twenty units Twenty-one 10s Used to teach all aspects of arithmetic Use with Inserts for key algebra and decimal concepts Two sets simplify some lessons by allowing the student to have at least 10 of each piece. We also recommend having two sets of blocks when doing larger problems or when working with more than one student. Each set of Manipulative Blocks includes a two-sided poster featuring Decimal Street and the Block Clock. Decimal Street is a fun and simple way of illustrating place value and regrouping to young learners, and can be used with several of the courses. $38.00 QTY: Algebra/Decimal Inserts Used with Zeta to present decimals Used with Pre Algebra and Algebra 1 to illustrate polynomials Smooth pieces which snap into 10s and 100s blocks Illustrate X, -X, and X2 Decimal pieces represent units, .1s and .01s $22.00 QTY: Recommended Wooden Block Box For those who would like a way to keep their Manipulative Block Sets better organized. This box set will hold two of the Manipulative Blocks sets, which are sold separately. In stock!
A Note on Graphing Calculators by derek As you've probably guessed by now, I am a proud owner of a TI 83 which I affectionately call 'Chuck the Math Monkey'. If you too are a proud owner of one of TI grapher and are trying to learn how to use it, then you've come to the right place. Perhaps you're only considering buying one. Here are a few things to consider: You may not need a graphing calculator. They are not necessary until beyond Alegbra 2 but can be very helpful. I myself made it all the way through Physics with nothing but my trusty TI 25 - the cheapest Scientific calculator. Personally, I recommend waiting until Geometry or later before getting a grapher, unless you want games or you're a geek like me who likes having a pocket computer. :] Which brings up another good point: the different kind of calculators. You have Scientific, which are useful in low to mid level math courses and everyday usage, and then you have Graphing calculators. The graphers are actually split in two groups: those with QWERTY keyboards and those with the traditional number pad. QWERTY keyboards are like what you use with a computer and get their name from the position of the keys (the top left starts with 'q', then 'w'...). You won't see these much at all in High School because that fact they only appear on the TI 92 or higher, which happen to be banned from the SAT. High School academics almost always adopts the SAT standard. You're probably more familar with the number pad graphers: TI 82, 83, 83plus, 85, 86, 89. Don't let the numbers fool you though, they don't go in order! The 82 and 85 are similar in capablities. They differ in slightly different interfaces plus, the 82 is geared more for straight math while the 85 has engineering and world uses more in mind. The 83 is an upgrade to the 82 with some better features and more capablites just as the 86 is an upgrade to the 85. The 83plus is a sup up version of the old 83 with newer technology. This site is centered around the TI 83 since that's what we know best. If you own one the these others, you can still learn how to use it by looking at the 83. The interface and operating systems on all these are very close, though the 82 is much closer than the 85/86. And then came the TI 89. The newest calculator from Texas Instruments, the 89 has the latest technology and a completely different operating system. Actually it has more than one version that can be downloaded (if you have a graphlink) so that even I don't really know how to use on very well. I consider the 89 on par with the 92 (the one that SAT banned) because it has just so many capablities: can work in symbolic as well as numberic, over a meg of memory, 3bit color instead of 2 with a higher resolution, heck the thing has an infinity key! As to date, the SAT board has yet to ban the 89, which suprises me since it is as powerful as the 92, but that may change.
Students should be able: 1. to model simple practical problems which require either discrete decisions or decisions made under uncertainty; 2. to use backward recursion to solve dynamic programming problems; 3. to find optimal and equilibrium strategies for zero- and nonzero-sum 2x2 matrix games; 4. to understand the theory behind the solution methods.
Holt Algebra 2 ... the number of solutions. 7. 1 2x. 6y ... Practice B. Solving Linear Systems in Three Variables. Use elimination to solve each system of equations. Holt Algebra 2 Teachers using ALGEBRA 2 may photocopy complete pages in sufficient ... HOLT and the "Owl Design" are trademarks licensed to Holt, Rinehart and ...... The Ready to Go On? Pre-Test Reports show which students are having difficulty .... Use the result from Exercise 8, to check if your answer to Exercise 7 is reasonable. Specially written for low-level learners, Algebra 2 covers several methods for solving quadratic equations, such as factoring, completing the square, and graphing. The text also introduces trigonometry and exponential functions—vital concepts for real world applications. Filled with full-color illustrations and examples throughout, Algebra 2 motivates students to learn. Overall, this high-interest, low-readability text makes it easy for you to engage students who struggle with reading, language, or a learning disability.
Mathematics for Business, CourseSmart eTextbook, 9th Edition Description For courses in business mathematics at the freshman/sophomore levels, including courses where instructors demand somewhat more rigor than competitive texts permit. Mathematics for Business provides solid, practical, up-to-date coverage of the mathematical techniques students must master to succeed in business today. This Ninth Edition takes a more integrated, holistic approach, and places far greater emphasis on analysis. Business statistics coverage has been moved towards the front, where students are taught to read and interpret graphs and tables; these skills are repeatedly reinforced throughout. Scores of new examples include visual Stop & Think sections that help students understand current events. This text includes algebra where needed to impart real understanding, and covers crucial topics other books ignore, including reading financial statements. Table of Contents PART I. BASIC MATHEMATICS 1. Problem Solving and Operations with Fractions 2. Equations and Formulas 3. Percent 4. Business Statistics PART II. BASIC BUSINESS APPLICATIONS 5. Banking Services 6. Payroll 7. Taxes 8. Risk Management PART III. MATHEMATICS OF RETAILING 9. Mathematics of Buying 10. Markup 11. Markdown and Inventory Control PART IV. MATHEMATICS OF FINANCE 12. Simple Interest 13. Notes and Bank Discount 14. Compound Interest 15. Annuities and Sinking Funds 16. Business and Consumer Loans PART V. ACCOUNTING AND OTHER APPLICATIONS 17. Depreciation 18. Financial Statements and Ratios 19. Securities and Distribution of Profit and Overhead Appendix A: Calculator Basics Appendix B: The Metric System Appendix C: Powers of e Appendix D: Interest Tables Answers to Selected Exercises
Elementary Curves and Surfaces Course description: The course is designed as an informal introduction to the geometry of curves and surfaces in space. This involves the concept of torsion (twisting out of a plane) and curvature (away from a line) of curves, and the curvature (away from a plane) of surfaces. A feature of the course is the use of the computer algebra package Mathematica (for which Manchester University has a site licence and student versions are available for personal use) to do all the calculus and graphics in computer lab sessions. All materials are available on line. Lecture Notes (PDF format). Recommended text: A. Gray. Modern Differential Geometry of Curves and Surfaces. Boca Raton: CRC Press, Second Edition, 1998. Mathematica Packages: Alfred Gray's Mathematica packages for curves and surfaces are free and available locally, together with others that we use, see Beginning Mathematica . Introductory Mathematica Notebook: ==>Download and open in Mathematica Breakdown of Lectures: Lecture Notes 5 Elementary theory of curves, their curvature and torsion 7 Elementary theory of surfaces and their curvature 12 Computer laboratory sessions investigating properties of curves and surfaces. Coursework Assignments: ==>Download and open in Mathematica Assignment 1 Complete and submit by end of Week 4 Assignment 2 Complete and submit by end of Week 8 Assignment 3 Complete and submit by end of Week 11
Several of my colleagues used to teach math in their former lives, and have created some sample lessons covering a variety of math topics. Each includes the NCTM standard which each lesson fulfills. If you're relatively new to Mathematica, these ready-made example lessons can give you a jumping-off point for using Mathematica in your classes...and give you a sneak peak at what's possible with Mathematica.Best regards Stanly Fernandez Hi Stanly, Yes, all of these lessons can be modified as needed, so you're welcome to make changes and use them for your Mathematics and Statistics classes. Although Mathematica does not show the steps it took to find a solution, it is possible to do so with relatively little work. In fact, many users have created functions that allow you to show the steps for solving integrals and equations. e.g.
algebra system "ScienceDaily (Dec. 7, 2007) — Until recently, a student solving a calculus problem, a physicist modeling a galaxy or a mathematician studying a complex equation had to use powerful computer programs that cost hundreds or thousands of dollars. But an open-source tool based at the University of Washington won first prize in the scientific software division of Les Trophées du Libre, an international competition for free software..."
Mathematics Programs K-8 Mathematics Programs: Connected Math Project 2 (CMP2) and Gomath and Glencoe Math High School Mathematics Text Books: Foerster Algebra I & II and Jurgenson Geometry Read below for detailed information about these district programs, district mathematics partnerships, and curriculum maps. Holyoke Public Schools Math Programs Connected Math Project 2 (CMP2) is a researched based program that is being used for middle school mathematics instruction. The overarching goal of the program is that all students be able to reason and communicate proficiently in mathematics. CMP helps students develop an understanding of important concepts, skills, procedures, and ways of thinking and reasoning in number sense, measurement, geometry, algebra, probability and statistics. The concepts are embedded in engaging problems that students explore individually, in a small group, or with a whole class. The problems presented over time give student practice with important concepts, related skills, and algorithms. A three-phased workshop model that support s problem centered instruction is used to deliver the curriculum in these classes. Teachers have had opportunities for training in CMP2 made available to them through district initiatives, America's Choice On-Grade Level Training, and CMP Training from Lesley University and Pearson Learning. The District Math Coaches and Lesley University will continue to provide teachers with training in the mathematical content and implementation of lessons. The Math programs are implemented using the Workshop Model. This three-phase instructional workshop model used to deliver instruction in all math classrooms in grades K - 8. In the initial phase, Launch or Opening – the teacher sets the problem, introduces new ideas, clarifies definitions reviews, old concepts, and connects to past experiences without lowering the challenge of the task. During the second phase, Explore or Work Time – students work independently or in small groups to gather data, share ideas, look for patterns, and make conjectures. In the final phase Summary or Closing – the students present and discuss their solutions as well as the strategies they used as the teacher guides them to reach the mathematical goal of the class and connect their new understanding to prior knowledge. Teachers have had opportunities for training on the workshop model made available to them through district initiatives, America's Choice On-Grade Level Training, CMP Training from Lesley University and Pearson Learning, and Math Investigations Training from Hampshire Educational Collaborative. District Math Coaches will continue to work with teachers to enhance the implementation of the program and help to deepen the understanding and connection of the mathematical strands. Curriculum Maps for K – 8 have been designed to ensure that students are exposed to a rigorous curriculum in every school and every grade, and to have consistent instruction and assessment district wide. The district's expectation is for students to successfully meet the Massachusetts Mathematics Standards and to score at the proficient range on the MCAS test in mathematics. In order to facilitate this, teachers are required to follow the curriculum maps. The successful implementation of these maps requires teachers to work through the project and problems prior to planning their lessons. The math coaches and other district personnel were trained in curriculum mapping by America's Choice, became the principle architects of the documents, and are now providing professional development to the grade level teachers as the first of these maps are available.
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses. Reprint of the Saunders College Publishing, Philadelphia, 1990Proof in Geometry: With "Mistakes in Geometric Proofs" by A. I. Fetisov Ya. S. Dubnov This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions. read more $9.95 read more General Theory of Functions and Integration by Angus E. Taylor Uniting a variety of approaches to the study of integration, a well-known professor presents a single-volume "blend of the particular and the general, of the concrete and the abstract." 1966 edition. read more $22$14.95 Counterexamples in Analysis by Bernard R. Gelbaum John M. H. Olmsted These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition. read more Foundations of Analysis: Second Edition by David F Belding Kevin J Mitchell Unified and highly readable, this introductory approach develops the real number system and the theory of calculus, extending its discussion of the theory to real and complex planes. 1991 edition. read more $24.95 Introduction to Analysis by Maxwell Rosenlicht Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition. read more $14.95 Introduction to Real Analysis by Michael J. Schramm This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition. read more $19.95Problems in Group Theory by John D. Dixon Features 431 problems in group theory involving subgroups, permutation groups, automorphisms and finitely generated Abelian groups, normal series, commutators and derived series, solvable and nilpotent groups, and more. Full solutions. 1967 edition. read more $12.95 read more read more Abstract Algebra by W. E. Deskins Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems. read more $24.95 A Book of Abstract Algebra: Second Edition by Charles C Pinter Accessible but rigorous, this outstanding text encompasses all of elementary abstract algebra's standard topics. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. 1990 edition. read more $16.95 Elements of Abstract Algebra by Allan Clark Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures. read more
Students learn the form and elements of the parabola equation in concept before applying the concepts using a small catapult. Data is collected in a catapult competition and is used to solve the equation in context. Small Catapult with projectile object (contact Sierra College STEM project for assembly of a catapult). Algebra 2 textbook or Pre Calculus textbook to assist student with exploration of parabolic equations. Other materials (need enough for each group in class): ball, long tape measure, yard stick, data collection handout (see attachment), video camera (optional; students could use their phones to video the trajectory if allowed).
Math The mathematics curriculum is designed to provide a rigorous foundation in the basics of mathematics and the tools to foster logical thought and analysis. We want students to appreciate the nature, beauty, and scope of mathematics and to understand its potential in dealing with the world's increasing technological complexities. Critical thinking, collaboration and mathematical modeling are emphasized at all levels. In all mathematics courses, faculty help students develop successful study skills and effective test-preparation techniques. For students whose backgrounds and aptitudes are strong, there are advanced sections of courses in our core curriculum. These include A.P. Calculus BC, Multivariable Calculus with Differential Equations, Advanced Math/Science Research, and A.P. Computer Science. Each of these courses allow students who are passionate about mathematics to pursue excellence in the subject at the highest level
05.0 MATHEMATICS 05.0.1.9.1 -- Students will use real-life experiences, physical materials and technology to construct meanings for rational and irrational numbers, including integers, percents and roots 05.0.1.9.2 -- Students will use number sense and the properties of various subsets of real numbers to solve real-world problems 05.0.2.9.2 -- Students will apply and explain procedures for performing calculations with whole numbers, decimals, factions and integers 04.2 LRIT - COMPUTER TECHNOLOGY 04.2.2.9.1 -- Students will identify capabilities and limitations of contemporary and emerging technology resources and assess the potential of these systems and services to address personal, lifelong learning, and workplace needs What roles do variables play in C++? 2. What roles do data structures play in C++? 3. How do basic math operations perform in C++? 4. How do mixed data types perform in C++? 5. What problems can occur in can occur when performing calculations as a result of the limitations of data types?
For departments of computer science offering Sophomore through Junior-level courses in Algorithms or Design and Analysis of Algorithms. This is an introductory-level algorithm text. It includes worked-out examples and detailed proofs. Presents Algorithms by type rather than application. Designed for use in a variety of courses including Information Visualization, Human—Computer Interaction, Graph Algorithms, Computational Geometry, and Graph Drawing. This book describes fundamental algorithmic techniques for constructing drawings of graphs. Suitable as either a textbook ...
Peer Review Ratings Overall Rating: This subsite of Mathematics Tutorials and Problems (with applets) (see ) is divided into Interactive Tutorials, Calculus Problems, and Calculus Questions, Answers and Solutions. Here the user will find applets with guided exercises and many examples and worked out problems applicable to the first year of Calculus. Learning Goals: To provide tutorials in various areas of mathematics, including pre-calculus, calculus, geometry and statistics. Target Student Population: Undergraduate students taking Calculus. Prerequisite Knowledge or Skills: Basic algebra. Type of Material: This material is designed as tutorials, but many of the applets could also be used as simulations. Recommended Uses: This material is designed as tutorials but many of the applets could also be used in classroom demonstrations. Technical Requirements: A Java-enabled Web browser. Evaluation and Observation Content Quality Rating: Strengths: This site is divided into Interactive Tutorials, Calculus Problems, and Calculus Questions, Answers and Solutions. 1. Interactive Tutorials There are 15 tutorials. Each one consists of an applet accompanied by a brief discussion of the math concept, an explanation of how to use the applet, and a series of guided exercises. The intent of the guided exercises is to provide the student with a more in-depth understanding of the concept rather than to solve a particular problem. For example in the Concavity of Polynomial Functions tutorial, the student is guided to discover that the first derivative is increasing in an interval where the function is concave up, thus explaining why f ''(x) > 0 corresponds to concave up on the graph. Topics covered in the Interactive Tutorials include derivatives, concavity, Mean Value Theorem, Runge Kutta Method, Riemann Sums, the natural logarithm, and Fourier Series. 2. Calculus Problems There are 13 problem areas, but some of areas contain more than one problem. Each of these is a typical calculus textbook problem. For example, one asks for the dimensions of the base of a pyramid that minimizes the surface area for a given volume. Another problem is that of finding all points on a polynomial with horizontal tangent. Graphs, diagrams, and detailed solutions are provided. The problems in this section are limited to differential Calculus. 3. Calculus Questions, Answers and Solutions This section deals with examples that are quite similar to the "Calculus Problems" discussed above. Nearly 50 topics are listed, and each topic contains two or three examples (worked-out exercises). Many are typical textbook problems, like find the derivative of the inverse of a given function or use implicit differentiation to find dy/dx for a given implicitly defined function. The areas of Calculus covered include differential, integral, and ordinary differential equations. Concerns: None. Potential Effectiveness as a Teaching Tool Rating: Strengths: This site should be quite effective for students seeking help in the first year of calculus or introductory ordinary differential equations. While some of the more sophisticated interactive tutorials that use experimentation and discovery may require the aid of an instructor, the majority of the material should be quite accessible to most Calculus students. The math concepts are well-explained, the solutions are quite detailed and thorough, and ample instructions are provided for operating the Java applets. The site should also be quite useful for classroom demonstrations. Concerns: None. Ease of Use for Both Students and Faculty Rating: Strengths: Most of the Java applets are intuitive and easy to use. There is quite adequate instruction provided for the technical aspects throughout the site, and the problems and solutions are well-explained. Even in the non-interactive parts, one finds a great number of illustrative graphs. Concerns: Initially, some of the applets would not work in Firefox. After upgrading Java and then re-installing the upgrade, these difficulties seem to be resolved. Internet Explorer played all the applets without a hitch. There is an apparent font problem in rendering some of the pages in FireFox. In particular, the arrow symbols in limits appear correctly on some pages but not on others. No such difficulties occurred with Internet Explorer. Also, this site would definitely benefit from a hyperlinked subject index that can make navigation a lot easier.
A way of forcing a calculator to perform a calculation in a different order to that given in Section 2.3 is to use the bracket keys. For example the following sequence, on a scientific or graphics calculator: 72 negative or minus sign for the answer −2 maybe slightly smaller and higher than the one used for subtraction in 5 − 7. There maybe two minus keys on your calculator keypad, as there are on the TI-84. The one which means do the operation subtract is calculators, like the TI-84, provide you with several different screens for menus, drawing graphs, writing programs and so on. The most important screen, where calculations are carried out, is called the Home Screen. If you should find yourself trapped on another screen, the 'panic' buttons to return 'home' are usually one or other of the following have been working through this unit, have you thought about how you are studying, and what this process involves? Do you feel confident or concerned about whether you will be able to learn mathematics and use it in the future? Put your study methods under the spotlight now, before moving on with your studies. Learning rarely happens passively. A number of aspects of this unit have been designed to encourage your more active participation and involvement. However, even lays the foundations of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. In particular, this unit – Modelling static problems – considers why objects stay put. Please note that this unit assumes you have a good working knowledge of vectors. This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equation which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and have some familiarity with complex numbers. This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration. Another vector quantity which crops up frequently in applied mathematics is velocity. In everyday English, the words 'speed' and 'velocity' mean much the same as each other, but in scientific parlance there is a significant difference between them. Velocity and speed
Find out more Introduction Mathematics is central to everyday life and to the way we see the world. It is an intellectual adventure in its own right but it is also used to understand the physical world – from black holes to global warming – and to find solutions in business and industry. All of our students take the same core mathematics courses in their early years. In later years you can choose from our wide range of courses in pure mathematics, applied mathematics, statistics, operational research or financial mathematics. What you'll study Year 1 You will take Linear Algebra, Calculus and Proofs & Problem-Solving courses. These are common to all our degree programmes and will take up half of your timetable. You will build on your knowledge of pure mathematics in a more formal way and be introduced to the ways of thinking required at university level. You will also take courses in subjects other than mathematics. You will be able to get support from MathsBase, our popular walk-in help centre. Year 2 You will spend between half and two thirds of your time on mathematics, depending on your degree programme. You will take core courses in pure mathematics, extending your knowledge of calculus and analysis, and be introduced to the abstract ideas of group theory. In most programmes you will also take courses in statistics, probability, computing and applied mathematics. From this year onwards you can use the Maths Hub, our student-run facility that is both a social centre and work space. Year 3 You will focus on the main subjects of your degree. The year will provide you with an excellent grounding in advanced mathematics which prepares you to study courses from the wide selection on offer in the following year. Year 4 In these years there is a wide choice of mathematics courses and you can follow a programme that suits your particular interests and career aspirations. There is a large selection of courses in pure and applied mathematics and statistics as well as options in areas such as mathematical education, financial mathematics, mathematical biology and operational research. Current course titles include Algebraic Coding Theory, Topology and Non-Linear Optimization. You will also do project work which allows you to research a topic independently. Year 5 As Year 4 Learning and assessment You will be taught mainly through lectures and tutorials. In first year you will also have access to the MathsBase help centre. Lecturers always welcome students who come and get help personally, but we also encourage cooperation and learning from each other, both within and between the different years of our programmes. Most courses are assessed by a mixture of coursework and examinations. Careers Mathematics graduates from the University of Edinburgh find a wide range of careers open to them. The logical, analytical and practical, problem-solving skills you gain during your degree are sought after by employers. Many of our recent graduates have been employed by large firms in the financial and business sector, or have gone on to work in aircraft engineering, software engineering, investment analysis, transport logistics and teaching. Our facilities First-year mathematics classes are in the University's Central Area. In subsequent years, teaching will take place within the School of Mathematics, located at the University's King's Buildings campus. You will also have access to the University's Main Library and the Robertson Engineering and Science Library. There are opportunities to study abroad through University-wide programmes. Students have recently completed placements in Berkeley, Melbourne and Singapore. Study abroad Opportunities to study abroad are available in this subject area. In first and second year, along with Maths, I was able to take courses in Psychology, Spanish and Astronomy. In third year I found a wide choice of mathematics courses and a high level of tutor support. The fourth year options gave me a chance to specialise in chosen areas; one course looked at various theories of learning maths and included time teaching at local primary schools. I also had the chance to become involved with the student union EUSA in the capacity of course and School representative. This involved being the communicator between University, staff and students, and increased my communication skills and employment potential.
These activities use the Function Analyzer tool to reveal the connection between symbolic and graphic representations in equation solving. The document includes a series of exercises for single equati... More: lessons, discussions, ratings, reviews,... In these activities, you explore the steps involved in solving systems of linear equations. You'll make observations about the effects of those operations on the solution sets of the systems. In Part ...Winplot is a general-purpose 2D/3D plotting utility, which can draw (and animate) curves and surfaces presented in a variety of formats. It allows for customizing and includes a data table which can bA free web-based function graphing tool. Graph up to three different functions on the same axes. Functions can refer to up to three independent variables controlled by sliders. As you move the...
Description The Bittinger Series changed the face of developmental education with the introduction of objective-based worktexts that presented math one concept at a time. This approach allowed students to understand the rationale behind each concept before practicing the associated skills and then moving on to the next topic. With this revision, Marv Bittinger continues to focus on building success through conceptual understanding, while also supporting students with quality applications, exercises, and new review and study materials to help them apply and retain their knowledge. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book. Table of Contents 1. Introduction to Real Numbers and Algebraic Expressions 1.1 Introduction to Algebra 1.2 The Real Numbers 1.3 Addition of Real Numbers 1.4 Subtraction of Real Numbers 1.5 Multiplication of Real Numbers 1.6 Division of Real Numbers 1.7 Properties of Real Numbers 1.8 Simplifying Expressions; Order of Operations 2. Solving Equations and Inequalities 2.1 Solving Equations: The Addition Principle 2.2 Solving Equations: The Multiplication Principle 2.3 Using the Principles Together 2.4 Formulas 2.5 Applications of Percent 2.6 Applications and Problem Solving 2.7 Solving Inequalities 2.8 Applications and Problem Solving with Inequalities 3. Graphs of Linear Equations 3.1 Graphs and Applications of Linear Equations 3.2 Graphing Linear Equations 3.3 More with Graphing and Intercepts 3.4 Slope and Applications 4. Polynomials: Operations 4.1 Integers as Exponents 4.2 Exponents and Scientific Notation 4.3 Introduction to Polynomials 4.4 Addition and Subtraction of Polynomials 4.5 Multiplication of Polynomials 4.6 Special Products 4.7 Operations with Polynomials in Several Variables 4.8 Division of Polynomials 5. Polynomials: Factoring 5.1 Introduction to Factoring 5.2 Factoring Trinomials of the Type x2 + bx + c 5.3 Factoring ax2+ bx + c, a ≠ 1: The FOIL Method 5.4 Factoring ax2 + bx + c, a ≠ 1: The ac-Method 5.5 Factoring Trinomial Squares and Differences of Squares 5.6 Factoring Sums or Differences of Cubes 5.7 Factoring: A General Strategy 5.8 Solving Quadratic Equations by Factoring 5.9 Applications of Quadratic Equations 6. Rational Expressions and Equations 6.1 Multiplying and Simplifying Rational Expressions 6.2 Division and Reciprocals 6.3 Least Common Multiples and Denominators 6.4 Adding Rational Expressions 6.5 Subtracting Rational Expressions 6.6 Complex Rational Expressions 6.7 Solving Rational Equations 6.8 Applications Using Rational Equations and Proportions 6.9 Variation and Applications 7. Graphs, Functions, and Applications 7.1 Functions and Graphs 7.2 Finding Domain and Range 7.3 Linear Functions: Graphs and Slope 7.4 More on Graphing Linear Equations 7.5 Finding Equations of Lines: Applications 8. Systems of Equations 8.1 Systems of Equations in Two Variables 8.2 Solving by Substitution 8.3 Solving by Elimination 8.4 Solving Applied Problems: Two Equations 8.5 Systems of Equations in Three Variables 8.6 Solving Applied Problems: Three Equations 9. More on Inequalities 9.1 Sets, Inequalities, and Interval Notation 9.2 Intersections, Unions, and Compound Inequalities 9.3 Absolute-Value Equations and Inequalities 9.4 Systems of Inequalities in Two Variables 10. Radical Expressions, Equations, and Functions 10.1 Radical Expressions and Functions 10.2 Rational Numbers as Exponents 10.3 Simplifying Radical Expressions 10.4 Addition, Subtraction, and More Multiplication 10.5 More on Division of Radical Expressions 10.6 Solving Radical Equations 10.7 Applications Involving Powers and Roots 10.8 The Complex Numbers 11. Quadratic Equations and Functions 11.1 The Basics of Solving Quadratic Equations 11.2 The Quadratic Formula 11.3 Applications Involving Quadratic Equations 11.4 More on Quadratic Equations 11.5 Graphing f(x) = a(x - h)2 + k 11.6 Graphing f(x) = ax2 + bx + c 11.7 Mathematical Modeling with Quadratic Functions 11.8 Polynomial and Rational Inequalities 12. Exponential and Logarithmic Functions 12.1 Exponential Functions 12.2 Inverse and Composite Functions 12.3 Logarithmic Functions 12.4 Properties of Logarithmic Functions 12.5 Natural Logarithmic Functions 12.6 Solving Exponential and Logarithmic Equations 12.7 Mathematical Modeling with Exponential and Logarithmic Functions Appendices A: Factoring and LCMs B: Fraction Notation C: Exponential Notation and Order of Operations D: Review of Factoring Polynomials E: Introductory Algebra Review F: Handling Dimension Symbols G: Mean, Median, and Mode H: Synthetic Division I: Determinants and Cramer's Rule J: Elimination Using Matrices K: The Algebra of Functions L: Distance, Midpoints, and Circles
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Main Navigation Whether it is for college or AP Calculus in high school, many of you are just hitting the hard part of this year in calculus. So here are a few tips to get you off on the right foot. Practice the harder problems. Most homework assignments include a mix of easier, medium, and harder problems. Typically, it is best to take an assignment like "1-33 odd" and rework it as "1, 5, 9, 11-21 odd, and 22-33." If you are graded, then it just means that you should do the more difficult even problems as well. Read all of the problems. This means that you should spend a few minutes thinking about how you would approach each and every problem at the end of the chapter. Of course, you will actually write out the ones that are assigned, but take a moment to convince yourself that you at least know how to start all of them. If you have no idea how to start, get out your paper and pencil and give it a few minutes of dedicated thought. If you still can't get anywhere, ask your teacher or tutor. It isn't enough to get the right answer. Calculus is the first time where simply understanding the mechanics is not enough to get an A. Conceptual understanding is crucial. You have to understand why the derivative is what it is, how it relates graphically, etc., not just how to take derivatives. On tests, expect the unexpected. Related to all of the above points is the fact that tests will often throw new types of problems at you. This is why you have to practice problems outside of your homework assignments and understand the concepts behind your answers, not just the steps to get them. Know definitions and theorems precisely. You know those boxes in your textbook that have boldfaced or colored concepts in them? You have to know exactly what those say. Good examples are the limit laws and definitions of continuity. It's not enough to loosely understand them; you have to know exactly why they are exactly as they are. Know examples and counterexamples, meaning know when the definitions and theorems don't apply. Practice every day. Two days in a row, 45 minutes each, is better than every other day for two hours. This is especially important for those of you on odd/even type schedules, or for those of you in college, where you have MWF or TTh classes. Now, more than ever, you need a combination of understanding and performance. It's not enough to understand something, you have to know how to do it. Taking a whole day off sets you back too much. Weekends can erase several days worth of practice. Until next time, hope this helps. I've seen hundreds of students both succeed and fail, and these tips are what I think are most important. So hopefully you take them seriously! Should you take the SAT again? Yes. College counselors, family members, peers, and anyone else you talk to will all try to downplay the SAT's importance. They think that they are doing you a favor by telling you to relax, and that it's not a big deal, and don't forget, you're the vice president of the glee club! There is some truth to all of that. I know a student that just got accepted to Berkeley with a score in the 1900's. While a bad SAT score does not shut any doors, a great SAT score sure can open them. "But I can't get a great score!!" you say. For anyone who is taking precalculus or calculus during their junior year of high school, there is absolutely no reason why you should be getting less than a 700 on each of the math and writing portions of the SAT. You know how to do every single one of the math problems. Every. Single. One. (Notice I also slipped the writing portion in there. That's because it is very formulaic, and you are probably good with formulas, no?) So what is keeping you from scoring well? You probably haven't done at least ten practice tests. What!?! Ten practice tests?? That's crazy!! Well, you don't take them all at once, but one section per day, that's 90 days, at around 20-30 minutes each, seems like a good way to spend a summer vacation, no? "But I already took a class from Revolution!!!" you say. Let's have a Dr. Phil moment then - how's that working out for you? How did sitting through hours of stuff that you already knew, followed by doing homework that was neatly categorized and divided up into little concept nuggets actually prepare you for the test? The SAT is by its very nature unpredictable. That means you practice for it, you don't study for it. Homework assignments that are divided up by subject matter artificially prepare you, because they put you in the frame of mind necessary to solve whatever type of problems they offer. So back to my original suggestion - ten practice tests. One or two sections at a time. No studying, only practice, alternating with review of previous sections. Then take the SAT again. I promise you won't be disappointed. What should you look for in a tutor? If you have read about our tutoring, you'll see that I (and we) firmly believe in private tutoring as a teaching method. That means that, regardless of whether you choose to go with a tutor from us or not, I think that hiring a private tutor is your best avenue for improved grades, raising test scores, and so on. So how do you choose a tutor? In my experience, I have figured out a few things that really matter, and a few that don't. First, a brief list of what doesn't matter: score increase guarantees, the school your tutor graduated from, teaching certification, "proprietary methods," initial assessments, to name a few. So, what does matter? Promptness in communication - You might be surprised to find this seemingly irrelevant trait first on the list. In today's world, there is absolutely no reason not to be on the ball with electronic communication. Look for a tutor that responds promptly, and you'll find a tutor that cares about you or your child. Subject mastery - Especially in the world of mathematics, subject mastery is absolutely crucial to the ability to communicate effectively. It is not enough to have done well in the course. In my tutoring interviews, the first thing that I give is a test. If possible, you should do the same, preferably without warning. Ask your child's teacher or your professor for help in this arena. Rapport - All of the tutoring experience in the world is completely irrelevant to you or your child once the session is underway. What matters is whether the tutor gets along with and communicates well with the student. Ask for a half session meet & greet, and most good tutors will do this for free. After the tutor has left, gauge candidly your or your child's reaction. Long term view - Look for a tutor that mentions ideas that point to long term success, in tandem with the usual strategies to do well on an upcoming test. Building core intellectual skills and concept mastery are worth the investment in tutoring and require a commitment on the part of the tutor and the student. A lack of awareness of this fact will mean that you won't get any lasting results from the tutoring. And, to be honest, that's about it. I'll finish with a few red flags that should send you running in the opposite direction. I've worked for companies of all sorts - some good and others great - and these red flags aren't my opinion, they are what I've gathered from observation. Big companies - Don't get me started here. Places like Kplan, Prnceton Rview, Rvolution, are marketing machines. They invest heavily, heavily, heavily in marketing. What they DON'T invest in is their tutors or their materials. Give me any of their books and I will find a mistake in five minutes. Their good tutors quit readily because their pay structure is so poor. Package requirements - Offering discounts is one thing (we do that), but requiring the purchase of a package? Use your imagination and you'll be right as to how this can go wrong. Initial questionnaire - If the very first thing that a tutoring company has you do is fill out a census style questionnaire, it means that the person assigning and managing the tutors is probably underqualified as an education professional. I'll probably think of some things to add to this, I always do. Until next time, happy schooling. New Year's (re)Solutions Some of you are done with final exams, and some of you have them upcoming after break. Most of you, no doubt, are resolving to study harder, get better grades, all that stuff. So, I thought I would list a few promises that you can make to yourself and really keep. As always, you'll get no fluff from me. And this time, you might get more than a few objections if you actually follow through. But this is good advice. Seriously. You can blame me if it goes wrong. But make sure you read the explanations that follow. Stop copying everything the teacher writes. How many times have you missed something and then been completely lost during class? Rather than furiously trying to keep up with everything the teacher writes, how about trying instead to listen to everything and follow conceptually. It's okay if you miss the details, you can always look in your book. And it's way better than wasting a whole day trying to catch up to something you don't understand anyway. Stop doing your homework. Okay, not exactly. Stop doing exactly what you are assigned. Instead, start your homework by reading each and every problem at the end of the chapter. I'll repeat that, louder, because it is so important: READ EACH AND EVERY PROBLEM AT THE END OF THE CHAPTER. Think about how you would start each one. Work on the ones that you don't know how to do. Of course, you'll still do (most) of what you are assigned, but your real goal should be to prep yourself for the more difficult problems, the ones that might trip you up on the test. Stop working so hard on the same problem. Problems in textbooks and on tests are meant to be solved in an efficient manner. If you are encountering some impossible algebra, chances are that you made a mistake somewhere. Starting over is almost always better than continuing to push along what may be an impossible path. Stop writing between the lines. Don't write math the same way that you write everything else. Give active thought to how you organize symbols on the page: how you use parentheses, how you space the numerator and denominator of a fraction, how you carefully keep track of negatives. This piece of advice, if followed correctly, is probably worth more than any other, in terms of increased grades. Stop being so fancy with your graphs. With graphs, one of two things can go wrong. The first is that you try to use some fancy method for translating and reshaping a graph, and you forget to check that it goes through the right points. Seriously, PLUG IN POINTS!!! Never underestimate the method that a seventh grader uses for graphing. The second is that you take forever carefully labeling a graph, making sure it looks pretty. It's just a waste of time. Just label the key points, and get on with life. Stop checking over your work. There is a saying in business: "Build in quality control from the start." In other words, do something right the first time, and you don't have to pay an inspector to fix the mistakes. Incorporate this lesson into your test taking. Slow down and do it right the first time. Also, instead of checking over your work by rereading, try solving the problem a different way. Check your answer by plugging in some simple numbers. If you simply reread your solution, chances are you will simply make the same mistake(s) again. Stop reviewing your homework/notes. Instead, get out a blank sheet of paper, open up your book, and start working problems. Even if they are problems you have already done. Until next year, happy holidays, and be sure to keep up with the YouTube videos. A New Toy EDIT: I've realized that, in my efforts to go slowly in the videos, I sound totally boring and even might put you to sleep. I'll fix that. EDIT: Okay now I sound less dull, at least in the first one below. Just a quick post to point out that I just got a stylus for my iPad, and also got the app ScreenChomp, which allows me to make math videos, Khan Academy style. Right now I'm peppering the site with video content, so if you have a question, send it to me, and I'll answer it in a video! Check out the GRE problems below. Word Problems, Part 1 At every level of abstract math, from algebra 1 to multivariable calculus, there is a common complaint from students: "I hate word problems." (After multivariable calculus, no one wants to look stupid, so they stop complaining.) So there you are, stuck on your last homework problem, and it is a word problem. You aren't even confused by the math, or so it seems: you've mastered fractions, or factoring, or asymptotes, or the chain rule, or polar coordinates, or Green's theorem, or whatever it is that you happen to be studying between the ages of 12 and 65. You ask your tutor, and the tutor begins "Well, you just have to break it down...write out what you know...draw a picture...blah blah blah." It makes perfect sense when the tutor works it out like that. You tell yourself that word problems are easy, and you kind of feel silly for not getting it. Then the next day there is a word problem on the quiz. And you stare at it and don't get it. What happened? Math is a language. So, to be fair to math, let's call a word problem what it really is - a math problem written in a foreign language. And let's suppose that math is your native language. So, all you need to do is translate the word problem - which is written in a foreign language - into math, which is your native language. The trouble is, you don't really speak the foreign language that well. What do you do when you have to translate a foreign language into your native language? You certainly don't stare at a whole passage and try to just "get it" all of a sudden. You go sentence by sentence, phrase by phrase, maybe even word by word. You break it up into whatever chunks are necessary. For each chunk, you go to your dictionary. You don't think about the other chunks while you are focusing on each particular chunk, you rely on the dictionary. When you are done with every chunk, you will have an awkwardly written passage, but it will be in your native language. Now you can sort out what it means. For now, I've got some more tutor stuff to do, but I'll work through an example in the next post. Until then...well, for most of you it is summer, and you probably aren't reading this, so you'll just see both posts at once. The Math of Khan Just a quick post to point you to one of the most valuable math tutoring sites on the net: Khan Academy. I guess it proves that I'm not much of a salesman if I show you a place where they are giving math instruction away for free! In all honesty, for those times when you are stuck and there isn't a tutor, teacher, or a classmate to turn to, try watching some videos of Sal Khan. He's done something truly remarkable, and more power to him. In the fall, a number of schools are going to pilot for software based on the site, and my fingers are crossed for Renaissance Arts Academy to get the nod. Of course, I'm biased, since I've been a math adviser there for the past few months, and I plan to continue into next year. Good luck on final exams, or on your summer courses, whatever the case may be. Metatesting Lately, whether it be prepping for the AP test that has come and gone, or prepping for California state testing which is about to start, I've been thinking and tutoring a lot with test prep strategies. I thought I would share a few. Once again, no filler material. And if you think you are too fancy for some of these, like you are in BC calc or something, then you have a lot to learn: The answers are part of the question on a multiple choice math test. Read the answers before you start working on the problem. It can save you work when you can immediately rule out wrong answers, and it can also save you frustration by preventing a trip down the wrong problem solving path. Read the question, read the answers, read the question. Do this routine every time. Plug in 0. Plug in 1. Plug in -1. Plug in 1/2. Plug in -1/2. Plug in 2. Plug in -2. In that order. Did you forget to plug in numbers to the answers as well? The answers are part of the question! Go back and reread the previous three bullet points. The first thing you should look at when you see a graph is the y-intercept. The next is the x-intercept. The next is the slope, or whether it is increasing or decreasing. Check your work in a different way than the way that you did the problem. Generally, that means testing out your answer by plugging in numbers if you found the answer algebraically or abstractly, and trying to do algebra or differentiate or whatever if you found the answer with numbers. Until next time, always use parentheses, write big and clear, and always get your negatives right. Advanced Placement Anyone in AP Calculus knows that the test is coming up in May. So I thought I would share some tips. And this isn't going to be a useless "top 10 best ways to eat a good breakfast and make sure you study every night" list. You'll only get the actual useful stuff, and only serious readers need continue. Here goes: (1/x)' = -1/x2 and (x½)' = 1/2x½. These derivatives come up over and over, and you don't want to have to use the power rule every time. Memorize them and it will save you valuable minutes. The second one also tells you that if a square root is in the denominator of an integral, it will be in the numerator of the answer. (arctan(x))' = 1/(1+x2). This knowledge alone is worth one or two multiple choice questions, and you probably have forgotten it from first semester. While you are at it, go look up the derivatives of all of the trig and inverse trig functions. That means csc(x) and sec(x). These obviously will also show up in integrals. PRACTICE. Don't study. Do lots of problems. Only do problems. If you are tempted to lazily read over your notes, take a nap instead, until you are rested enough to do problems. Don't buy a book. If you are unsure how to find practice problems, you can get a step by step guide here. "Linearization" means using the tangent line. The formula for the tangent line is best remembered in point-slope form. That means f'(a) = [y-f(a)]/(x-a), or slope = rise/run. For those of you in BC calc, have your basic Taylor series memorized. That means knowing that sin(x) = x - x3/6 + ... WITHOUT going through the tedium of the Taylor series formula. There will be a numerical integration question among the open ended problems. Learn to find volumes geometrically; DON'T memorize the formula for "rotating around the y-axis" and so on. The AP test loves to ask you to find volumes involving cross sections that are triangles and rectangles, instead of circles. That's enough for today. It's been a hectic month, and my posts are lagging a bit, in true blog fashion. But I promise more study tips soon. Motivation So far, I've written about practice, and that's about it. The New York Times even wrote an article that let me off the hook for a whole blog entry, since they wrote about a study that "demonstrated" that practicing test taking was the most effective means to do better on tests. The last angle in our approach we call "Motivation." It doesn't mean the desire to get up at 6:14am and set aside 3 hours and 32 minutes per weekday evening for homework, although those things are nice. What it means is that behind every mathematical concept, every problem and every problem solution, there is a motivation behind why anyone ever thought of it in the first place. And if you really want to understand an idea, to understand it to the point that it is a part of you, so that you can apply it in ways that you yourself haven't even considered yet, you absolutely must learn the motivation behind the idea. One of my favorite pseudo-layman's books regarding this angle is Einstein's Clocks and Poincare's Maps. The theory of relativity is some pretty fancy stuff, but setting that aside for a moment, the author shows the reader the reason why Einstein was led to consider the ideas in the first place: he wanted to know how to coordinate the times between train stations that were far apart. This was during the turn of the previous century, before routine conveniences like telephones and wireless internet on transatlantic flights. Ultimately, this got Einstein thinking about relativistic time, a paradigm shift that led him to his now famous theory. To learn more, I invite you to check out the book, which is not for the mathematically faint at heart, but hopefully you have a better idea of how a practical consideration can motivate an idea. For something more accessible, we can turn to high school geometry, when students must learn to make things like right angles and parallel lines using only a ruler and compass. In Euclid's time, this was the way that engineers, architects, and construction teams actually did things! When they were building the walls of some huge thing that we now know as ruins, they literally had huge compasses and rulers to guide them towards precise angles and measurements. When they had to construct congruent shapes, they had to get it right, or things literally collapsed. Euclid was a revolutionary in publishing his work on plane geometry, and it became an indispensable reference. (He also pioneered the domain of intellectual property rights, because the knowledge became carefully guarded and fought over, but that is a history lesson, and far from my domain of expertise.) Whenever you have the question in math class of "Why should we have to know this?", you probably should rephrase it as "Why did anyone ever think of this in the first place?" Put that way, it is a fair and even crucial question to answer. We consider it part of learning mathematics, beyond interesting historical tidbits. So ask your teacher next time, and don't take "Because it's on the test!" as an answer. Something Scientific? The New York Times recently published an article about test taking as a method for learning, and the study goes as far as to claim it is better than "studying." Far be it from me to gloat, but the timing of this article couldn't be better for me to say "I told you so." It also prompts me to clarify what constitutes practicing a math problem: it means starting from scratch, without your book or notes, and struggling through the points of confusion without giving in to the temptation of going to your book or notes. So if you'll scroll a few entries down, you'll see that I once had no idea if our method works better than others. Well, at least now I've got a scientific study to back me up. Of course, those can always be wrought with logical fallacies and statistical errors, but that is a different discussion altogether. So, if you want to really learn, keep practicing. And you don't have to take my word for it. "You Want to Know Geometrical Problems" The title of this post is the title of a book on geometry that I came across in college. It had been translated from Japanese, which explains the weirdness. It does manage to highlight why we actually learn math and what it means to DO math: it means solving problems. Although it is listed second on the tutoring approach, I believe practice is the most important component to improvement in math. (The reason that I list confidence first is because confidence makes people feel good, and I'd like potential customers to feel good while they read the site.) I mention the analogy between math and music. If you've ever been my personal tutoring client, you are probably sick of me and my analogies between math and music. The basics: songs ~ problems, performances ~ tests, chords/scales ~ concepts, song recordings ~ textbook. Suppose that you were practicing for a piano recital. Would you rehearse a song enough times until you finally played it perfectly, all the way through, one time? If you did that, there would still be a good chance that your recital went fine. Let's be generous and say that 75% of the time you would perform just fine. That rehearsal scheme is exactly how most students go about their math homework. They work each problem until they get it right, then they move on. If they do look back at the problem, then they read over it to "make sure that they still get it." Reading over the problem is about as useful as listening to a recording of yourself playing a song perfectly. Supposing you screwed up the recital, would you try to explain it to the audience? "But I totally understood the song. I knew how to play every note and every chord perfectly. So you should be satisfied." (What's truly funny is, if you are familiar with American Idol and similar shows, you'll hear contestants try to do exactly that.) Of course, that sounds ridiculous, but the same justification is attempted with math tests all the time. Hopefully by now you have a better idea of the role that practice plays in learning to DO math. So I'll get off my soapbox for now, until next time... Practice vs. Study vs. Confidence vs. Motivation On the left you'll see my explanation of our Tutoring Approach, and if you explore a bit further, you'll see that I've broken it down into four categories: confidence, practice, study, and motivation. For these first few blog entries, I'd like to explain that a bit further, if not to you, then to myself. First off, a confession: for a long time, I had never actually written down my approach to tutoring. A few years back, there came a time when my tutoring requests exceeded what I could personally handle. So I began referring clients to colleagues of mine in the math department at Berkeley. Before I passed any torches, I had to tell each of them how I went about doing things. Lo and behold, my tutoring business was born, and with it, my tutoring method. Later, when I taught a course to new graduate students on how to teach, I refined my methods further. (To this day I'm proud to say that I've personally influenced more than a few parts of the "how to teach" syllabus.) More recently, I launched this website, polished my methods a bit further, and laid them out for all to see. (I'll probably revise them further after I write this entry.) Another confession: I have no idea how unique or groundbreaking my approach is. In fact, I used to call it unique, right here on this site, but I just revised that. But if you can forgive the shameless plug, I will tell you why I have an overwhelming hunch that I'm doing something right, something different from what other people are doing. Over and over my clients are shocked at the progress they make. Heck, I'm shocked. It's awesome; it's a thrill; it's why I do what I do. Okay, enough with the self-promotion. Last confession: I have absolutely no formal training in education. What I dohave is a lot, and I mean A LOT, of formal training in mathematics. My credentials are that of a professional mathematician, not a professional educator. That means that I know how to DO math. And that's what I do my best to teach clients: how to do math. Not how to understand it, not how to memorize it, how to DO it.
MAK offers a very vigorous and interactive math program. Students are challenged with critical thinking, story problems and real-life applications. Our program uses the McDougal Littel series of middle school and high school courses. The 6th and 7th grade courses cover the five major strands of mathematics; Numerical and Proportional Reasoning, Algebraic Reasoning, Geometry and Measurement, Statistics, Data Analysis and Probability, and Problem Solving and Reasoning. Beginning in the 8th grade, students may take Pre-Algebra or can test into an advanced track of high school Algebra followed by Geometry in the 9th grade. The 7th and 8th grade students will be competing in AMC, an American Math Competition in November, 2010. In the spring, they will then compete in the Gauss Contest, while the 9th grade students compete in the Pascal Contest, which are Canadian Mathematics Competitions.
About Scott Steketee Scott Steketee taught secondary math and computer science in Philadelphia for 18 years and received the district's Teacher of Excellence award. Since 1992 he has worked on Sketchpad software, curriculum, and professional development for Key Curriculum Press and KCP Technologies. He also teaches Secondary Math Methods in the graduate teacher education program at the University of Pennsylvania. After writing yesterday's post on the connections between polar and Cartesian graphs, I realized that I hadn't said anything about how easy it is to start from scratch and create a polar graph in Sketchpad, so I decided to write … Continue reading → The May 2013 Mathematics Teacher has an excellent article by Jonathan F. Lawes ("Graphing Polar Curves") on the value of plotting the same function in both polar and rectangular coordinates. Doing so not only helps students understand how polar coordinates … Continue reading → I had the immense good fortune this year to attend ICME, the International Congress on Mathematical Education. The Congress is held every year divisible by 4, and this iteration (the twelfth) was held in Seoul, Korea. It is quite something … Continue reading → Not long ago, I conducted a Saturday morning PD session for some Texas teachers participating in an NSF research project. (The research is a controlled study of the relationship between students' use of Sketchpad and their conjecturing and proving behavior. … Continue reading → Functions are hard for students. Students seem to master various families of functions – linear, polynomial, exponential, trigonometric, and so forth. They can graph them, evaluate them, transform them, and answer a variety of questions about them. But ask evenI am troubled. Today is the first day of teaching my spring semester course, "Advanced Methods in Secondary Mathematics," for my preservice master's students. The mission of the Teacher Education Program at Penn is to prepare "reflective, collaborative, visionary teacher-leaders" … Continue reading →
OCR Mathematics for GCSE Specification B - Foundation Silver and Gold, and Higher Initial and Bronze Homework Book has been published to support students and teachers of the OCR course. The resource has been written and edited by experienced examiners and authors, combining their teaching and examining expertise to deliver relevant and meaningful coverage of the course. Each homework book provides complete coverage of relevant Specification B units at Foundation and Higher respectively. The structure and content of the resources allow teachers to prepare students for the final exams in an incremental way as well as across the entire tier. The content also supports delivery of the revised Assessment Objectives including Problem Solving. - Endorsed by OCR for use with Mathematics GCSE Specification B - Full coverage of the topics required by the tiers of the course - Appropriate practice questions - Dedicated student books, teacher's resources, homework books, and online digital assessment and resources.
Mathematics For Business - 8th edition Summary: The Eighth Edition of Mathematics for Business continues to provide solid, practical, and current coverage of the mathematical topics students must master to succeed in business today. The text begins with a review of basic mathematics and goes on to introduce key business topics in an algebra-based context. Chapter 1, Problem Solving and Operations with Fractions, starts off with a section devoted to helping students become better problem solvers and critical...show more thinker while reviewing basic math skills. Optional scientific calculator boxes are integrated throughout and financial calculator boxes are presented in later chapters to help students become more comfortable with technology as they enter the business world. The text incorporates applications pertaining to a wide variety of careers so students from all disciplines can relate to the material. Each chapter opener features a real-world application. Features Current financial data used throughout the text. Real-world applications within exercise sets are now called out by topical headings for each problem so that students immediately see the relevance of the problems to their lives. Introduction to problem solving in Section 1.1 helps students learn how to think through solving common problems. The emphasis on problem-solving skills is carried through the text so that students can enter the business world with critical thinking skills and apply what they have learned. Chapter openers now incorporate an application with a real-world graph or figure so students can understand how the chapter content pertains to actual business situations. Financial calculator boxes that explain how to solve examples using a financial calculator are now integrated into later chapters to familiarize students with the technology they will be using in the business world. A Metric System Appendix, complete with examples and exercises, explains the metric system and teaches students to convert between US and metric units of measurement. 'Net Assets emphasize the World Wide Web and keep students current on how businesses adapt to technology. Cumulative Reviews help students review groups of related chapter topics and reinforce their understanding of the
Vineland ACT explain it all simply so that students understand. Calculus can be a difficult topic at first. Like most math classes it has a few elementary parts that once grasped lend incite to the rest of the topic.
updated guide to the newest graphing calculator from Texas Instruments The TI-Nspire graphing calculator is popular among high school and college students as a valuable tool for calculus, AP calculus, and college-level algebra courses. Its use is allowed on the major college entrance exams. This book is a nuts-and-bolts guide to working with the TI-Nspire, providing everything you need to get up and running and helping you get the most out of this high-powered math tool. Texas Instruments' TI-Nspire graphing calculator is perfect for high school and college students in advanced algebra and calculus classes as well as students taking the SAT, PSAT, and ACT exams This fully updated guide covers all enhancements to the TI-Nspire, including the touchpad and the updated software that can be purchased along with the device Shows how to get maximum value from this versatile math tool With updated screenshots and examples, TI-Nspire For Dummies provides practical, hands-on instruction to help students make the most of this revolutionary graphing calculator.
Klappentext Developments in computer algebra systems will help shape the way mathematical models and techniques will be used in future applications of mathematics in science and engineering. At the forefront of these developments, MuPAD is a powerful computer algebra system designed to handle mathematical problems and computations of a new order of magnitude. The MuPAD User's Maunal provides a detailed survey of the system's capabilities and contains:A complete description of the MuPAD progreamming language.Guidelines on how to produce graphics with MuPAD.A survey of the functions of the MuPAD standard libary.Designed as a parallel system it will also run on sequential computers, from small size machines to more powerful workstations. The advantages over other computer algebra systems are thatMuPAD is a system that offers a windowbased userinterface (hypertext online help, graphics and a source code debugger) on all platforms.MuPAD is the first system that provides native parallel instructions to the user.MuPAD offers tools for the dynamical linking of binary code objects.Students, researchers and professionals in all quantitative disciplines will find MuPAD to be userfriendly and invaluable aid to their work. The accompanying CDs include a hypertext version of the manual and the full MuPAD system following platforms:PC (Linux)Sun 4Apple MacintoshSilicon GraphicsHewlett-PackardDECstation
Questions About This Book? The Used copy of this book is not guaranteed to inclue any supplemental materials. Typically, only the book itself is included. Summary The Graphing Calculator Manual by Judith A. Penna contains keystroke level instruction for the Texas Instruments TI-83/83+, TI-84, and TI-86. Bundled with every copy of the text, the Graphing Calculator Manual uses actual examples and exercises from Elementary and Intermediate Algebra: Graphs and Models, Third Edition, to help teach students to use their graphing calculator. The order of topics in the Graphing Calculator Manual mirrors that of the text, providing a just-in-time mode of instruction.
By: gorav.saini98@yahoo.com \| 2011-09-29 \| Homeschooling What do you understand by the terminology absolute value? The absolute value of a real number p is denoted by p or notion is p and is defined as read more By: yagvendra \| 2012-02-05 \| Online education A key element is to take little techniques. For example understand one algebra formula, exercise it for a week, then switch on to the next. Progress only if you understand what you've acquired. Every time switch on to the next algebra concept improve the issues of the equations or the workouts you're trying to fix. By: \| 2011-02-17 \| Business Pre Algebra is required to study higher level of mathematics and develop quick algebraic skills. It is also helpful in planning and executing day-to-day activities efficiently. read more By: iTech Troubleshooter \| 2010-12-09 \| Software In the algebraic specification technique an object class or type is specified in terms of relationships existing between the operations defined on that type. It was first brought into prominence by Guttag [1980, 1985] in specification of abstract data types. Various notations of algebraic specifications have evolved, including those based on OBJ and Larch languages. Representation of algebraic specification Essentially, algebraic specifications define a system as a heterogeneous algebra. A het read more By: nelson carlin \| 2011-02-18 \| Business Algebra 1 is the stepping-stone to the next level of algebra. Since acquiring higher level of algebraic skill is important, one should focus on the middle school algebra to reach there. read more By: Nelson Carlin \| 2011-02-17 \| Business Algebra 1 is the stepping-stone to the next level of algebra. Since acquiring higher level of algebraic skill is important, one should focus on the middle school algebra to reach there. read more By: Timcy Hood \| 2010-12-22 \| Business Algebra 1, a difficult stream of mathematics, has been made easy with the help of online excellent masters. They make beautiful strategies to crack the problems in a simpler way .
West New York Calculus begins with learning to translate verbal phrases into symbols. This leads to the topic of formulas and equations. In particular, proportions are solved and linear and quadratic equations are solved and graphed
Calculus I MAT 149 or both MAT 140 and MAT 122, with minimum grade of C or appropriate score on the Mathematics Placement Test. III. Course (Catalog) Description Course is first in calculus and analytic geometry. Content focuses on limits, continuity, derivatives, indefinite integrals and definite integrals, applied to algebraic, trigonometric, exponential and logarithmic functions, and applications ofdifferentiation and integration. Technology integrated throughout course. IV. Learning Objectives 1. Understand the concept of limit. 2. Understand the concept of continuity. 3. Understand the concept of derivative. 4. Evaluate derivatives of algebraic, trigonometric, exponential, and logarithmic functions. 5. Use derivatives to solve optimization problems, motion problems, and problems involving rates of change. 6. Use derivatives to analyze functions and their graphs. 7. Understand the concepts of indefinite integral and definite integral. 8. Evaluate indefinite and definite integrals. 9. Use definite integrals to find area, average functional value, distance traveled, and total change. 10. Use of technology for finding limits, derivatives, and integralsMethods of presentation can include lectures, discussion, demonstration, experimentation, audio-visual aids, group work, and regularly assigned homework. Calculators/computers will be used when appropriate. Use of a computer algebra system is recommended. Mathematica, Derive and TI-92 calculators are available for use at the College at no charge. Course may be taught as face-to-face, media-based, hybrid or online course. VIII. Course Practices Required (To be completed by instructor.) IX. Instructional Materials Textbook information for each course and section is available on Oakton's Schedule of Classes. Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information". Textbooks can also be found at our Mathematics Textbooks page. A graphics calculator is required. A TI-83 or higher numbered model will be used for instructional purposes. X. Methods of Evaluating Student Progress (To be determined and announced by the instructor) Evaluation methods can include graded homework, chapter or major tests, quizzes, individual or group projects, computer/calculator projects, and a final examination
Final Unit (PDF) - Charlotte Teachers Institute Mtrujillo unit 2012.pdf. Final Unit (PDF) - Charlotte Teachers Institute. language acquisition (which usually takes five to seven years), and that having. 8. In ESL- English classes content and language are integrated and students are taught. theories have failed to explain and answer all the questions related to language. textbook Holt McDougal literature, Common Core Edition, unit 9.ΗΤΤΡ://CΗΑRLΟΤΤΕΤΕΑCΗΕRS.ΟRG/WΡ-CΟΝΤΕΝΤ/UΡLΟΑDS/2013/03/ΜΤRUJΙLLΟ_UΝΙΤ_2012.ΡDF Holt McDougal Florida Larson Geometry - Marion County Public Are you ready.pdf. Holt McDougal Florida Larson Geometry - Marion County Public. Holt McDougal Florida Larson Geometry should check each other's answers. Have students continue this exercise until each student has graphed 5 numbers.ΗΤΤΡ:// Alignment of Common Core Geometry Standards and Alaska Grade MathAlignment Geometry.pdf. Alignment of Common Core Geometry Standards and Alaska Grade. rotations, reflections, or dilations) to figures on a coordinate plane L]. Common Core does not. and the proportionality of all corresponding pairs of sides.ΗΤΤΡ:// Algebra 1, Geometry, and Algebra 2 PearsonSchool.com 2012CCFlyer.pdf. Algebra 1, Geometry, and Algebra 2 PearsonSchool.com. Algebra 2. Common Core. Geometry. Common Core. Algebra 1. Common Core. Get to the Core Cumulative Test Prep after every chapter Answers at point of use on the same page Answer Keys Quarter, Mid-Course, and Final TestsΗΤΤΡ://ΑSSΕΤS.ΡΕΑRSΟΝSCΗΟΟL.CΟΜ/ΑSSΕΤ_ΜGR/CURRΕΝΤ/201153/2012CCFLΥΕR.ΡDF
Additional product details Best-selling authors, James Stewart, Lothar Redlin, and Saleem Watson refine their focus on problem solving and mathematical modeling to provide students with a solid foundation in the principles of mathematical thinking. The authors explain critical concepts simply and clearly, without glossing over difficult points to provide complete coverage of the function concept, and integrate a significant amount of graphing calculator material to help students develop insight into mathematical ideas.

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