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An introduction and a guide to trigonometry, with hints and answers to exercises, and Java applets as illustrations. Contents include applications of trigonometry, angle measurement, chords, sines, cosines, tangents and slope, the trigonometry of right triangles, the trigonometric functions and their inverses, oblique triangles, and a summary of trigonometric identities.This field guide contains a quick look at the functions commonly encountered in single variable calculus, with exercises for each topic: linear, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise functions. Also algebraic operations on functions, function composition, and general types of functions.
This unit consists of two computer programs. The first teaches X,Y plotting; the second is a demonstration of coordinate transformations, matrices, vector equations of lines and perspective and will draw a picture of any geometric solid whose coordinates it has been given. These pictures will be stereograms and may be viewed in three dimensions. | 677.169 | 1 |
...The expression of these principles, however, is a little different. The hurdles people usually confront with Algebra 2 come mainly from their relying on memorizing procedures and rules. The only problem with that is as you memorize more and more material, you'll eventually come to a point where you'll have trouble distinguishing one formula from another and even when to apply them.
...Linguistic competence, the knowledge of forms and meanings is, however, just one part of communicative competence. Therefore the learner needs knowledge of forms, and meanings, and functions. For example, when teaching kids their first Arabic lessons, I start with the alphabets by writing it in shapes of animals this way it becomes easier for kids to memorize. | 677.169 | 1 |
Informatique pédagogique et intelligence artificielle, un example concret en géometrie. Initiation, support de cours, discussion.
Software in French for Windows. Hypothèses means "proofs"; the software can solve Euclidean geometry problems (construction and demonstration) and correct a student interactively. Articles about the software showing some screens are provided in French and English, and a demo version is available.
From the Ministere de l'Education Nationale, de l'Enseignement Superieur et de la Recherche. A French site that lists different types of software products categorized as 1) "Les didacticiels," which provide individualized exercises or activities which students can use by themselves; 2) "Les imagiciels," interactive computer programs that students can manipulate by defining different parameters; and 3) "Les logiciels outils": constructions geometriques, tableurs, grapheurs, traceurs de courbes, logiciels de calcul formel, et traitements de textes. Many examples of problems and illustrations are provided.
Mathematics programs designed to facilitate learning in destreamed classes as well as in home study and distance learning. Interactive programs for: algebra, equations, exponents, fractions, geometry, and integers. Understanding exponents and algebra are also available in French. Free demos for all programs. An on-line lesson database provides outcome-based lesson plans in several areas of mathematics and is updated weekly. Also workshop information. | 677.169 | 1 |
Math: Functions to your Bookmark Collection or Course ePortfolio
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Discussion
Discussion for Visual Math: Functions
Alison Benke
(Student)
This is an amazing site if you need help with linear comparisons and linear equalities and inequalities. I learned about graph transformation operations which change a function by changing it's graph. There can be one function or more than one function, the site calls it a family function. The site described the 10 parts of quadratic functions and then explained each of the 10 in detail. There was an exercise on how to write an essay on transformations which I didn't do but I looked at the steps and it seemed very applicable. For example,it gavefeatures of quadratic equations like symmetry, intersections with the axes, and vertexes. I liked learning about linear and non linear comparisons since that is what we are studying in math class right now.
Technical Remarks:
This site is set up really clever. There is a total of 10 parts to the quadratic functions. Within each part there are sets of activities tools, tasks and exercises that help navigate you around the site. At the bottom of each page there is a suggested activity that can help you apply what you have learned. It is either in the form of writting a report or writing an essay. I think out of all the sites I have visited so far, this one looks like it would be most helpful to students and teachers.
Time spent reviewing site:
I spent about 30- 40 minutes looking at the site. I enjoyed looking at the polynomial forms and the addition to functions. | 677.169 | 1 |
Tagged Questions
For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.
I have just started teaching a very elementary class for 1st year students on introductory pure mathematics. ( classes at my institution are groups up to 20 students and supplement the lectures. The ...
Are there any resources that show how are the various proofs of important theorems in mathematics are invented? I don't understand how can anyone come up with this method for proof for example. I want ...
How or where does one express work they've done to others?
What does it mean formally to 'publish' mathematical work you've done?
How do you know if your work is any good?
Or if someone has already ...
Can you please tell me what is ((stochastic modelling and statistical analysis of spatio-temporal data)) related to?
I mean Mathematics or statistics? Is it good subject for student who interested in ...
I'm interested in movies about or related with mathematics or physics, I mean not documentaries which I also consider movies, but artistic or mainstream films about math. Now I have the following in ...
How to learn about interesting topics in a small group of people?It seems very useful to broaden your mathematical background and get to know topics that are away from your field of specialization.
...
Let $P$ be a mathematical statement or a mathematical problem. I am looking for a couple of nice examples for $P$ that satisfy the following criteria:
Given two (or more) mathematical points of view ...
I'm not sure that this is the appropriate forum for this question but the snooping around that I've don of the site makes me feel as if I'll get solid advice. I'm currently finishing an introductory ...
I have experience in Abstract algebra (up to Galois theory), Real Analysis(baby Rudin except for the measure integral) and probability theory up to Brownian motion(non-rigorous treatment). Is there a ...
Why would we want to transform a vector in our normal basis (xyz axes) to another basis? The only situation I can recall is when we are looking at a force applied on an inclined plane. Are there any ...
Does anyone know where I could find a book or resource of very simple intuitive proofs of the basic results in Geometry? I tutor geometry to middle schoolers, and find that due to shoddy mathematical ...
In a presentation I will have to give an account of Hilbert's concept of real and ideal mathematics. Hilbert wrote in his treatise "Über das Unendliche" (page 14, second paragraph. Here is an English ...
I have a high schooler who I need to get energized about math. She excels in other sciences, but does not in math. The issue, I learned after some discussion, is that she doesn't find math interesting ...
I am currently relearning basic math - including; fractions, decimals and percentages. I am learning from various different sources, and what gets me is that they only teach math in forms of methods. ...
Let me begin with some background: I used to enjoy mathematics immensely in school, and wanted to pursue higher studies. However, everyone around me at that time told me it was a stupid area (that I ...
So we had a quiz in math a couple of days ago and I had gotten none of the questions wrong on the quiz. I was very angered to find out that I had been marked down 5 points for not checking my work and ...
I searched this community upon proofs and found some interesting topics. Yet I would like to know how you guys achieved to write your own proofs. What I mean is, my course describes proof as something ...
I am a second year physics undergrad. After spending about an year exploring mathematical physics (QFT,solitons, etc), I have realized that maybe theoretical physics isnt my passion after all, and I ...
Tomorrow is a very special day for both my students and I: we will be starting a calculus course. I'm looking for some nice quotes to read to them to convey just what a complete game changer calculus ...
After reading several books on distribution theory, I got a strange feeling. Why do they all begin with the theory of distributions and then move on to tempered distributions? Why can't we just start ...
$$
\binom{12}6 = \frac{12\cdot11\cdot10\cdot9\cdot8\cdot7}{6\cdot5\cdot4\cdot3\cdot2\cdot1} = 924.
$$
Sometimes it's hard to talk students out of computing both the numerator and the denominator in ... | 677.169 | 1 |
This textbook for the second year undergraduate linear algebra course
presents a unified treatment of linear algebra and geometric algebra,
while covering most of the usual linear algebra topics.
Geometric algebra and its extension to geometric calculus simplify, unify,
and generalize vast areas of mathematics that involve geometric ideas.
Geometric algebra is an extension of linear algebra.
The treatment of many linear algebra topics is enhanced by geometric algebra,
for example, determinants and orthogonal transformations.
And geometric algebra does much more, as it incorporates the complex, quaternion,
and exterior algebras, among others.
This book can be used as a linear algebra text, without geometric algebra, as outlined in the preface. Thus an instructor can include geometric algebra as time permits, or teach a two track course, with some students studying geometric algebra and some not.
Videos
I have created a six video YouTube playlist
Geometric Algebra, about 72 minutes in all, taken from the book. Unlike the book, some knowledge of linear algebra is a prerequisite for the videos. The geometric algebra starts at the beginning.
Third Printing
The third printing has no major changes.
It corrects all errors known to me in the first printing.
There are many improvements in wording. The numbering of equations, theorems, etc.
is unchanged from the first printing.
What People Are Saying
From a review of Linear and Geometric Algebra:
"I commend Alan Macdonald for his excellent book! His exposition is clean and spare. He has done a fine job of engineering a gradual tran sition from standard views of linear algebra to the perspective of geometric algebra. The book is sufficiently conventional to be adopted as a textbook by an adventurous teacher without getting flack from colleagues. Yet it leads to gems of geometric algebra that are likely to delight thoughtful students and surprise even the most experienced instructors."
— David Hestenes, Distinguished Research Professor, Arizona State University
Available at Amazon
Computer Exercises
GAlgebra. The computer exercises in the book use GAlgebra,
a Python module written by Alan Bromborsky.
GAlgebra is cross-platform (Linux, PC, Mac), with all components freely available on the web.
The software is no longer available at this page.
Notebook. GAlgebra is available in a jupyter (formerly IPython) notebook.
Output is typeset in beautiful LaTeX.
GAlgebraPrimer.pdf
contains instructions for installing and using GAlgebra.
The file also downloads with the module. It will be updated as necessary.
Appendix B of the book also contains instructions for installing and using the module.
But the information there will become dated as GAlgebra evolves.
So I recommend that you use GAlgebraPrimer. | 677.169 | 1 |
mathscard GCSE
Screenshots
Details
Description
Developed by Loughborough University, the mathscard GCSE app contains hundreds of examples of maths formulae, graphs and diagrams. The GCSE app is based on the hugely successful Loughborough A-level app and is designed to help students with their exam revision when at home or on the move. Number and Arithmetic, Algebra, Graphs, Statistics and Probability, Geometry and Measurement and much more are all covered in this handy resource | 677.169 | 1 |
The subject of real analysis is concerned with studying the behavior and properties of functions, sequences, and sets on the real number line, which we denote as the mathematically familiar R. Concepts that we wish to examine through real analysis include properties like Limits, Continuity, Derivatives (rates of change), and Integration (amount of change over time). Many of these ideas are, on a conceptual or practical level, dealt with at lower levels of mathematics, including a regular First-Year Calculus course, and so, to the uninitiated reader, the subject of Real Analysis may seem rather senseless and trivial. However, Real Analysis is at a depth, complexity, and arguably beauty, that it is because under the surface of everyday mathematics, there is an assurance of correctness, that we call rigor, that permeates the whole of mathematics. Thus, Real Analysis can, to some degree, be viewed as a development of a rigorous, well-proven framework to support the intuitive ideas that we frequently take for granted.
Real Analysis is a very straightforward subject, in that it is simply a nearly linear development of mathematical ideas you have come across throughout your story of mathematics. However, instead of relying on sometimes uncertain intuition (which we have all felt when we were solving a problem we did not understand), we will anchor it to a rigorous set of mathematical theorems. Throughout this book, we will begin to see that we do not need intuition to understand mathematics - we need a manual.
The overarching thesis of this book is how to define the real numbers axiomatically. How would that work? This book will read in this manner: we set down the properties which we think define the real numbers. We then prove from these properties - and these properties only - that the real numbers behave in the way which we have always imagined them to behave. We will then rework all our elementary theorems and facts we collected over our mathematical lives so that it all comes together, almost as if it always has been true before we analyzed it; that it was in fact rigorous all along - except that now we will know how it came to be.
Do not believe that once you have completed this book, mathematics is over. In other fields of academic study, there are glimpses of a strange realm of mathematics increasingly brought to the forefront of standard thought. After understanding this book, mathematics will now seem as though it is incomplete and lacking in concepts that maybe you have wondered before. In this book, we will provide glimpses of something more to mathematics than the real numbers and real analysis. After all, the mathematics we talk about here always seems to only involve one variable in a sea of numbers and operations and comparisons.
Note: A table of the math symbols used below and their definitions is available here.
This part of the book formalizes the various types of numbers we use in mathematics, up to the real numbers. This part focuses on the axiomatic properties (what we have defined to be true for the sake of analysis) of not just the numbers themselves but the arithmetic operations and the inequality comparators as well.
This part of the book formalizes sequences of numbers bound by arithmetic, set, or logical relationships. This part focuses on concepts such as mathematical induction and the properties associated with sets that are enumerable with natural numbers as well as a limit set of integers.
This part of the book formalizes the concept of limits and continuity and how they form a logical relationship between elementary and higher mathematics. This part focuses on the epsilon-delta definition, how proofs following epsilon-delta operate on, and the implications of limits. It also discusses other topics such as continuity, a special case of limits.
This part of the book formalizes differentiation and how they are used to describe the nature of functions. This part focuses on proving how derivatives study the nature of change of a function and how derivatives can provide properties to functions. | 677.169 | 1 |
...
Show More concentrate on models involving differential equations, the ideas used can be applied to many other areas. The book carefully details the process of constructing a model, including the conversion of a seemingly complex problem into a much simpler one. It uses flow diagrams and word equations to aid in the model building process and to develop the mathematical equations. Employing theoretical, graphical, and computational tools, the authors analyze the behavior of the models under changing conditions. They discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model. Through applications and the tools of Maple™ and MATLAB®, this textbook provides hands-on model building skills. It develops, extends, and improves simple models as well as interprets the results | 677.169 | 1 |
Intermediate Algebra Everyday ExplorAlice Kaseberg's respected Intermediate Algebra: Everyday Explorations, Fourth Edition, helps students build confidence in algebra. This text's popularity is attributable to the author's use of guided discovery, explorations, and problem solving, all of which help students learn new concepts and strengthen their skill retention. Known for an informal, interactive style that makes algebra more accessible to students while maintaining a high level of mathematical accuracy, Intermediate Algebra includes a host of teaching and learning tools that work together for maximum flexibility and a high student success rate. With the Fourth Edition, instructors have access to an Instructor's Annotated Edition that provides additional examples, as well as a robust Instructor's Resource Manual, algorithmic computerized testing, and an extensive online homework system.
Problem Solving, Expressions, and Equations
Mathematical Thinking: Problem Solving
Number Sense
Numeric and Symbolic Representations
Problem Solving and Verbal Representations
Visual Representations: Rectangular Coordinate Graphs
Solving Equations with a Table and Graph
Solving Equations and Formulas
Inequalities, Functions, and Linear Functions
Inequalities, Line Graphs, and Intervals
Functions
Linear Functions
Modeling with a Linear Function
Special Lines
Special Functions
Systems of Equations and Inequalities
Solving Systems of Two Linear Equations by Substitution or Elimination
Solving Systems of Two Linear Equations by Graphing
Solving Equations Involving Quantity and Rate
Solving Systems of Three or More Linear Equations
Solving Linear and Absolute Value Inequalities
Quadratic and Polynomial Functions
Quadratic Functions
Modeling Quadratic Functions
Polynomial Functions and Operations
Special Products and Completing the Square
Solving Quadratic Equations with Tables, Graphs, and Factors
The Role of a, b, c, and Binomial Squares in Graphing Quadratic Functions | 677.169 | 1 |
The resource contains many Flash physics animations covering topics such as chaos, mechanics, vectors, waves, relativity;...
see more
The resource contains many Flash physics animations covering topics such as chaos, mechanics, vectors, waves, relativity; includes a tutorial on using Flash with mathematical equations to create controlled Animations for Physics to your Bookmark Collection or Course ePortfolio
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GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets,...
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GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package. GeoGebra is a rapidly expanding community of millions of users located in just about every country. GeoGebra has become the leading provider of dynamic mathematics software, supporting science, technology, engineering and mathematics (STEM) education and innovations in teaching and learning GeoGebra to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material GeoGebra
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Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material ICT Games
Select this link to open drop down to add material ICT Microsoft Excel as a Visual [Basic] Teaching and Learning Tool to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Microsoft Excel as a Visual [Basic] Teaching and Learning Tool
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The Probability/Statistics Object Library is a virtual library of objects for use by teachers and students of probability and...
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The Probability/Statistics Object Library is a virtual library of objects for use by teachers and students of probability and statistics. The library contains objects of two basic types, applets and components.An applet is a small, self-contained program that runs in a web page. Applets are intended to illustrate concepts and techniques in an interactive, dynamic way. A teacher or student can download an applet, drop it in a web page, and then add other elements of her own choice (such as expository text, data sets, and graphics). The applets in the library contain essentially no mathematical theory and thus can be used by students at various levels. The applets are intended to be small "micro worlds" where students can run virtual versions of random experiments and play virtual versions of statistical games.Components are the building blocks of applets and of other components. The Java objects are of three basic types: virtual versions of physical objects, such as coins, dice, cards, and sampling objects; virtual versions of mathematical objects, such as probability distributions, data structures, and random variables; user-interface objects such as custom graphs and tables. The Java objects can be used by teachers and students with some programming experience to create custom applets or components without having to program every detail from scratch, and thus in a fraction of the usual time. In addition, the components are extensively documented through a formal object model that specifies how the components relate to each other.Each object can be downloaded as a Java "bean" that includes all class and resource files needed for the object. An object in the form of a Java bean can be dropped into a builder tool (such as JBuilder or Visual Cafe) to expose the properties and methods of the object. Each object can also be downloaded in the form of a zip file that includes the source files and resource files for the object/Statistics Object Library to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Probability/Statistics Object Library
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This applet is a web based lab that explores the properties of quadratic functions. It is one in a series of other...
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This applet is a web based lab that explores the properties of quadratic functionsah's Home Page to your Bookmark Collection or Course ePortfolio
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This applet is a web based lab that explores the properties of cartesian coordinates. It is one in a series of other...
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This applet is a web based lab that explores the properties of cartesian coordinates Cartesian Coordinates to your Bookmark Collection or Course ePortfolio
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This site is the mathematics area of the larger Wolfram Alpha project – described as a computational knowledge engine to make...
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This site is the mathematics area of the larger Wolfram Alpha project – described as a computational knowledge engine to make the world's knowledge computable. In response to natural language questions it provides direct answers, explanations, related information and comparisons. In addition to mathematics the main site offers, for example, chemistry, engineering, places and geography, money and finance. Mathematica is used as the underlying software engine.From the point of view of mathematics education it poses advantages and disadvantages in the way of most technology – but the free availability of a powerful mathematical tool opens up vast new possibilities for students and teachers to explore. For the professional mathematician it's not clear if it solves anything that their stand alone version of Mathematica could Alpha Mathematics Examples to your Bookmark Collection or Course ePortfolio
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General Education Mathematics
MAT 110 with minimum grade of C or appropriate score on the Mathematics Placement Test, and MAT 080 or geometry proficiency.
III. Course (Catalog) Description
Course focuses on mathematical reasoning and the solving of real-life problems. Topics include: counting techniques and probability, logic, set theory, and mathematics of finance. Calculators/computers used when appropriate.
IV. Learning Objectives
1. Develop and justify problem solving strategies for cases involving personal decision-making, and apply problem solving techniques to propose solutions in these cases. 2. Demonstrate logical equivalence of propositions and identify common logical fallacies. 3. Construct deductive logical arguments. 4. Apply techniques of the mathematics of finance to common personal financial situations found in everyday life. 5. Calculate probabilities and use them to analyze situations arising in everyday life. 6. Use calculators and/or computer software to solve applied problems1. Problem Solving Strategies and Basic Set theory
Problem Solving Strategies
Basic Set Concepts
Subsets
Venn Diagrams and Set Operations
Set Operations and Venn Diagrams with Three Sets
Survey problems
2. Logic
Statements, Negations, and Quantified Statements
Compound Statements and Connectives
Truth Tables for Negations, Conjunction, and Disjunction
Truth Tables for the Conditional and Biconditonal
Negations of Conditional Statements and De Morgan's Laws
Arguments and Truth Tables
Arguments and Euler Diagrams
3. Consumer Mathematics and Financial Management
Percent, Sales Tax, and Income Tax
Simple Interest
Compound Interest
Annuities, Stocks and Bonds
Installment Loans, Amortization, and Credit Cards
4. Counting Methods and Probability Theory
The Fundamental Counting Principle
Permutations
Combinations
Fundamentals of Probability
Probability with the Fundamental Counting Pronciple, Permutations, and Combinations
Events involving Not and Or; Odds
Events Involving And; Conditional Probability
Expected Value
VII. Methods of Instruction
Methods of presentation include lecture, discussion, demonstration, group work, and regularly assigned homework. Techniques will emphasize critical thinking and applications. Calculators/computers will be used where appropriate. Course may be taught as face-to-face, media-based, hybrid or online course.
VIII. Course Practices Required
Homework, Study Plans, Chapter Quizzes, In-Class Activities
IX. Instructional Materials
Note: Current 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.
X. Methods of Evaluating Student Progress
(To be completed by instructor.)
Evaluation methods can include assignments, quizzes, chapter or major tests, individual or group projects, computer assignments and/or a final examination | 677.169 | 1 |
Course Section Information
Seeing Math™: Linear Functions
Course Section Description:
Discover a fresh approach to teaching linear functions through the use of real-world problems that generate varied approaches and solutions. Learn how multiple representations and solutions strengthen students' understanding of functions, equations, and problem solving.
Note: This is a facilitated course. Learners submit coursework and
participate in asynchronous discussions throughout the course term, and
receive graded feedback.
The number of hours identified for each course reflects time spent online, but does not
reflect the total time spent completing offline coursework and assignments. All learners
are different and you will likely spend double the indicated number of hours completing all
coursework depending on your learning style and work habits.
Graduate Credit Information:
Graduate credit may be obtained from the provider(s) listed below, for an additional fee after the course begins. | 677.169 | 1 |
07506038Introduction to the Mathematics of Finance: Published in association with the Institute of Actuaries and Faculty of Actuaries Author(s): J J McCutcheon, W F Scott
ISBN: 0750603887
ISBN-13: 9780750603881
Book Description
Introduction to the Mathematics of Finance: Published in association with the Institute of Actuaries and Faculty of Actuaries
In today's money markets interest rates are all-important. This book, which is intended as a successor to D.W.A Donald's Compound Interest and Annuities-certain, develops the classical theory of compound interest (in which the force of interest is constant) as a special case of a more general model.
There is a concise but thorough treatment of the basic compound interest functions, nominal rate of interest, and the yield (or internal rate of return) and there are many examples on discounted cash flow. Also discussed are applications of the theory to capital redemption policies (with allowance for income tax, capital gains tax and index-linking), and consumer credit calculations. The final chapter provides a simple introduction to stochastic interest rate models.
Concise and thorough Extensive use of examples Endorsed by the Institute of Actuaries and the Faculty of Actuaries | 677.169 | 1 |
Graphing
Author:
Unknown
ISBN-13:
9780768202380
ISBN:
0768202388
Publisher: Schaffer Publications, Frank
Summary: Help students succeed in math! Math Minders provide students with the self-confidence they need to succeed in math. Students learn one step at a time, reviewing skills learned in earlier grades, then moving to skills appropriate for their grade level. They progress gradually, giving them the constant feeling of success! Vocabulary is kept at a level appropriate for each grade level to help ensure success. Fun and sim...ple formats help maintain a high level of student interest. Perfect for home or school, or to reinforce any existing math program | 677.169 | 1 |
42 Answers
42
I like the idea of promoting mathematics to students, i.e. more explanation of the contribution of mathematics to civilization, so that students have some language and background to justify their subject. See other articles on my web page.
On specific subjects, I have enjoyed showing first year UK students the power of the symbolic algebra packages on dealing with Grobner bases, i.e. solving polynomial equations in more than one variable. To more advanced students one can give exercises like:
Find a polynomial in x,y which has more than 5 critical points, classify them as max, min, saddle, and use the computer algebra package to draw your function and display or indicate the critical points. Verify with the package that the points you find are critical points.
(The last part gives useful lessons in rounding accuracy.) The whole exercise gives students a nice sense of power, as the machine manipulates vast expressions!
Computing with Feynman diagrams in zero dimension, i.e., a graphical calculus
for tensor contractions. It is very elementary yet can lead quickly into rather deep
mathematics. It would make later studies in say mathematical physics or low dimensional
topology much more congenial.
Possible applications could be
Once students have been exposed to linear algebra and vector calculus, build calculus on manifolds using many examples; i.e. go from real $\mathbb{R}$-abstract multilinear to the de Rham complex, illustrating in $\mathbb{R}^3$. All that easen differential geometry, differential topology Riemannian geometry, etc.
But, please, with motivation. Understanding manifolds is THE hardest part of "elementary" advanced mathematics. Just introducing them by an abstract definition and then doing proofs by "local-global" handwaving doesn't do the job; the students will neither have an idea what the definition signifies, nor why the handwaving is allowed. Maybe some non-Euclidean geometry as a nontrivial motivating example would be useful...
– darij grinbergMar 15 '10 at 11:18
2
I actually would love to see non-euclidean geometry (from a more elementary perspective) and differential geometry unified into one course. You always see elementary books which give you bits and pieces of the idea that there are other geometries, and that the sophisticated way of doing this is differential geometry - then much later in life you get thrown into a course where you pick up from multivariable calculus and define manifolds, tangent spaces, tensor fields, etc... There should be an attempt to show the connection between the two.
– David CorwinJun 16 '10 at 8:12
What should one teach to liberal-arts students who will take only one math course, and that because it's required of them?
The conventional answer: Partial fractions. And various useless clerical skills that they'll need if they take second-year calculus, although they'll never take first-year calculus. Et cetera.
My answer: the truth.
E.g. in third grade you were told that
$$
3+3+3+3+3 = 5+5+5
$$
and so on. Why should that be true? Assign that as a homework problem. At this point they may think that means there's some formula to plug this information into to get the answer. They've been taught that memorizing algorithms and applying them is what math is. That's a lie. We should stop lying and level with them.
I posed the question and asked for a course, not a rant on the substance of mathematics education for non-mathematicians: -1
– Michael HoffmanJun 15 '10 at 23:48
4
There is no "the truth". It's much easier to blindly criticize than to offer constructive answers: -1.
– André HenriquesMay 11 '11 at 18:02
1
+1, if only for displaying the eternal problem about why is $3+3+3+3+3=5+5+5$. I've asked that of many bright undergrad before, and rarely got and answer better than "that's the law" (the commutative law, they mean, which we all abide by except when we do powers).
– Dror Bar-NatanMay 11 '11 at 18:56
2
Michael: answering the questions you want to pose is surely something better done on a blog. Redefining the original question to one you can then be righteous about does not strike me as very courteous
– Yemon ChoiMay 12 '11 at 23:37
First, statistics, indeed, is not taught enough. I studied statistics in a good school, but when it came to actually using it, found that I don't understand it. Second, motivation: they have to show the student how much and how urgently (s)he will need these concepts while on the workplace, with good real examples.
Quantum mechanics, as in understanding the mathematics behind its foundational issues, and not just as in computing the spectrum of the Hydrogen atom (though that's good too).
It's hard to think of a topic that shakes one's image of the physical world harder than quantum mechanics. General relativity is easy to digest once you are not scared of things like manifolds. Quantum mechanics remains a challenge to one's worldview no matter how hard one tries to get used to it. You cannot count yourself scientifically literate if you were not exposed to the foundational issues of quantum mechanics.
And it's a math course at least as much as a physics course. The pre-requisites are basic probability and logic and complex numbers and basic Hilbert space theory, and the content is philosophy and non-commutative probability theory and (may as well, at the end) some spectra of some differential operators.
Mermin article "Is the moon there when nobody looks? Reality and the quantum theory" was an eye opener for me, the year after I finished my undergraduate studies.
I would love to see more differential geometry offered in undergrad. The course I envision would start with a review of vector calculus, move to studying hypersurfaces in $\mathbb{R}^n$, and then move into a study of manifolds. You could tie all these subjects together via the Fundamental Theorem of Curves, the Fundamental Theorem of Hypersurfaces, and the Fundamental Theorem of Riemannian Geometry. I feel such a course would help bridge the gap between undergrad and grad school; simultaneously reviewing the key ideas of calculus at a high level while also giving a solid foundation from which to study manifolds in grad school.
P.S. I am not a differential geometer. I study homotopy theory. I just thought a course like this was missing from the curriculum. Any feedback on other topics that could be covered or tangents that could be mentioned leading off from this material would be welcome.
Personally, I think the answer to this question is largely going to depend on one's particularly interests (whether they lie in algebra, analysis, topology, or whatever). This can be seen from many of the previous posts.
That being said, I do think that more number theory would be a great addition to the undergraduate curriculum. Many students take an introductory number theory course (or skip it because they learned it all in high school) and then don't do any more. There are lots of great areas of number theory which don't require too much background. P-adics would be great (Gouvea even laments in his book that p-adics aren't taught earlier - so maybe such a course should use his book). One could teach a basic semester of algebraic number theory, or a course in elliptic curves (following Silverman and Tate, for example). Both of these require no more than a basic course in undergraduate algebra. You can probably find these courses at many top universities, but they usually aren't emphasized as much to undergraduates. The reason why I think that these would be good is because number theory is a particularly beautiful area of math, and by getting glimpses of modern number theory early on, students get to see how beautiful is the math that's ahead of them.
(Another possibility is to have a course on Ireland and Rosen's book A Classical Introduction to Modern Number Theory. Princeton had a junior seminar on this book, for example.)
I also think Riemann surfaces are a very beautiful topic which should be taught early on and aren't too complicated in their most basic form. For, you get to see the deep geometrical theory lying behind the $e^{2 i \pi}=1$ and the ambiguity of complex square roots which you learned about when you were younger. It shows the student that there can be very deep ideas lying behind a simple observation, and it shows the beauty and deep understanding that modern mathematics can lead you to.
"What's one class that mathematics that should be offered to undergraduates that isn't usually?"
OK, I'll rephrase my earlier answer. A class that should be offered to undergraduates that usually isn't is a "what is mathematics" course for those liberal-arts majors who will take only one math course in their post-secondary schooling. It would be a truthful course that would avoid telling them that mathematics consists memorizing algorithms whose utility can be seen only by taking later courses that they won't take. It would acquaint them with the fact that mathematics, like physics, is a subject in which new discoveries are constantly being made. It would tell them that one doesn't generally do math by taking a problem and feeding it into an algorithm that was given to one by a prophet who came down from Mount Sinai. It would tell them that mathematics is a subject that, like music, relies heavily on technical skills but does not consist of those alone. Among the goals would be that a student who takes only that course and becomes a professor of some liberal arts subject would not be among the many such professors who don't suspect the existence of such a field as mathematics.
Combinatorics seems like one of those subjects that you really have to have a natural affinity for.
– Harry GindiDec 7 '09 at 10:15
4
IMHO there is already too much unmotivated analysis in undergrad education. I rarely meet undergrads who think categories are the pinnacle of math, but I do meet more than enough undergrads who think that two-lines bounds involving epsilons, deltas, absolute values (as commonly seen in stochastics, diff. equations and asymptotics) are the pinnacle of maths.
– darij grinbergMar 15 '10 at 11:06
1
@Harry: I used to think so too. But then I saw analytic combinatorics, 'done right', and I learned to really enjoy it, while I hated my 2nd year combinatorics class.
– Jacques CaretteMay 20 '10 at 2:31
2
@Jacques, which book did you use? or did you go from lecture notes? It always seems that combinatorics is almost never taught in an understandable way...
– Michael HoffmanMay 20 '10 at 21:14
Computer Science. I know programming has been said already, but computer science isn't programming. (There's the famous Dijkstra quote: "Computer science is no more about computers than astronomy is about telescopes.")
There is a vast and beautiful field of computer science out there that draws on algebra, category theory, topology, order theory, logic and other areas and that doesn't get much of a mention in mathematics courses (AFAIK). Example subjects are areas like F-(co)algebras for (co)recursive data structures, the Curry-Howard isomorphism and intuitionistic logic and computable analysis.
When I did programming as part of my mathematics course I gave it up. It was merely error analysis for a bunch of numerical methods. I had no idea that concepts I learnt in algebraic topology could help me reason about lists and trees (eg. functors), or that transfinite ordinals aren't just playthings for set theorists and can be immediately applied to termination proofs for programs, or that if my proof didn't use the law of the excluded middle then maybe I could automatically extract a program from it, or that there's a deep connection between computability and continuity, and so on.
Numerical methods should be considered a very advanced topic, even though it was historically 'early'. The beauty of computer science, as far as I am concerned, generally lies in those parts where everything is exact. The connections between a multitude of areas of mathematics and computer science seem to be exploding in the last few years - and generally with no numbers in sight!
– Jacques CaretteMay 20 '10 at 2:23
3
I'm one of a very large and growing number of graduate students whose training didn't require any serious computer science-and who deeply regrets it now. In many ways,computer science is one vast interrelated set of applications of mathematics to engineering.It DEFINITELY should be required of mathematics students and as early as possible in thier training.There's very good reason to unite the CS and mathematics departments as many universities do.
– The MathemagicianJun 12 '10 at 1:57
3
I agree wholeheartedly. I feel that Pure Maths is more relevant to, and has more in common with, CS than Stats, and yet my department is in the middle of combining with the Stats school.
– ADLJun 14 '10 at 13:36
1
@Alan Stats will make the joint department a lot more money then theoretical computer science will. It's all about the bottom line.
– The MathemagicianJun 14 '10 at 18:11
I was a graduate student at Yale, and all but a few courses had single digit enrollment. I distinctly remember a course where I was the other student, and a course where our exchange student from Germany got stuck, being the only one attending and not wishing to offend the professor by dropping.
– Victor ProtsakMay 20 '10 at 7:39
What about "Mathematics with Computers"? Having modern computer algebra and symbolic computation tools available, one can use them to present and explore nontrivial examples in various fields of mathematics. Part of the course could also present basic algorithms and other techniques used.
Caveat: My undergraduate & graduate studies were both not in Math but in Engineering. But I would love to have taken a course on the history of mathematics and I think this isn't a commonly offered course. There are lots of compelling stories here and it also gives a great perspective on how the different areas of math came to be born (non-Euclidean geometry from work on the parallel postulate to name one). Knowing how a subject evolved historically can give a nice perspective on the subject especially when a formal course on the subject might not necessarily follow the same order of ideas.
With the proviso that much of the older "folk history" is, I'm told, not accurate, or is misleading. I went to several entertaining history of mathematics lectures where this was pointed out vehemently. Also, the history of ideas is really tricky, because we have to try and understand how e.g. the Greeks thought, not how we would think about what they appear to describe.
– Yemon ChoiMar 15 '10 at 6:40
I have seen many students dropping out of math because they didn't get an answer to the question "why should I learn this?". Of course, one could say, a good student should have intrinsic motivation and/or figure out the motivations by himself, but this seems to me like wasting potential.
I don't want to say that mathematics courses don't provide any motivation, but in undergraduate courses (and even textbooks), especially in linear algebra and calculus (when there isn't so much time), I haven't seen enough motivation.
This motivation should go beyond "we want to model the physical world" and/or "with this theorem you can calculate the Eigenvalues". Students need the story between these two extremal answers, they need to know how calculation of Eigenvalues is really applied in modelling the physical world. (This is just an example, I would appreciate to see more motivation for abstract, non-applied mathematics, too)
When teaching eigenvalues the textbook I used gave a simple predator prey example and then looked at the diagrams of the phase space . (I think it was woodrats and spotted owls (oops that is a prey-predator problem!)) The oscillations in population levels could be seen to be interesting as a simple explanation of things students have heard about. That lead o to how on earth can you calculate these eigenvalues and eigen vectors and to some numerical methods. The point was that the example chosen was simple enough to comprehend without knowing a whole lot of some other subject area.
– Tim PorterMar 14 '10 at 19:38
A course that just attempts to define the current research areas of maths. If the landscape is so complex, why can't undergraduates be provided with a map, so to speak, in order to begin to decipher this subject?
I was never offered a geometry course as an undergraduate, and there's so much lovely geometry, from Euclidean and non-Euclidean geometries, to algebraic and differential geometry, and the rest. So...geometry.
Courses aimed towards applied, rather than pure, mathematics. Like a modeling course related to environmental sciences, perhaps. Most math majors prepare the students for graduate school in pure mathematics, but offer less support for applied tracks, and there be some good careers there.
I did a course with Atomic and Nuclear Physics making up a third of the time. Apart from beautiful functional analysis and topology courses, one of my favorite courses was in Quantum Mechanics taught by an excellent Physics prof. I there understood about orthogonal functions, etc. He talked sense! The earlier courses on these subjects went straight past me. I could do the problems but did not grok them.
– Tim PorterMar 14 '10 at 18:27
Blackboards are threatened in many places (I'm aware of Oxford, and some places in Australia). The mathematicians I know in those places are very unhappy with this situation.
– André HenriquesMay 11 '11 at 18:05
Following Greg's lead, I wish that undergrads who want to become math majors didn't "skip out" of differential equations classes (in their eagerness to get to the good stuff like Drinfeld chtoukas, or whatever). I can't think of a more important foundational subject that tends to be systematically avoided by the "best" undergraduate mathematics students.
I completely agree!!! Lots of places have "rigorous linear algebra" type classes (I'm teaching one right now) -- I wonder why more places don't have a differential equations class geared for math majors. There are even nice books available (like Hurewitz's beautiful little book, or Arnold's).
– Andy PutmanNov 12 '09 at 19:35
3
I think part of the problem here is the types of course offerings universities have. For example, when I was an undergrad at U.Alberta, there was an honours intro ODEs course, but it was taught like a service course and was largely non-rigorous. It's difficult to attract students to material when the curricula is presented in such an unflattering light.
– Ryan BudneyAug 31 '11 at 15:21
When I was in my first year, I always missed order theory. I teached it to myself then and thought many times "Why didn't they teach us this - we would understand everything so much better!"
And I still think so today. Order theory starts off easy, when you lern about relations, preorders, lattices and so on, and then you get into Zorns Lemma, Schörder-Bernstein Theorem and stuff like that.
But I'm also on the category theory track. I think the notion of category will become, just like the notion of a group, more common sense, not just in mathematics but also in computer science, physics, chemistry and maybe even more.
I'm going to change the question slightly. What topics do we all think are taught in undergraduate mathematics, but often leak out of the curriculum so that students see too little of them? I have in mind the standard situation at large research universities, where there is a mix of good and not-so-good students.
My pet peeves:
Complex numbers as they should appear in standard calculus and linear algebra. They tend to be postponed to upper division courses. Complex numbers greatly simplify both trig identities and partial fractions, but calculus students aren't told.
Complex analysis. It tends to float to the top of upper division and disappear.
Full multivariate calculus: The Jacobian of a general change of coordinates, the derivative of a multivariate inverse function, maybe also the multivariate Newton's method. The calculus sequence often chickens out and just does special cases of the first of these.
Higher-dimensional Euclidean geometry. Like, the definition of an n-cube and the fact that it has 2n vertices.
Multivariate probability, especially with both discrete and continuous features.
Linear algebra. At least, it's not taught to math majors. They tend to see little bits of it in the calculus sequence (in order to solve systems of ODEs, for example) and then again in an abstract algebra class (matrices being a nice source of examples of groups) but never see a coherent treatment of it. At least this is true at the universities I'm familiar with. In both cases there is a linear algebra course mostly taken by nonmajors, but it's not possible for majors to get credit for both linear algebra and first-semester abstract algebra (basically the group theory course).
– Michael LugoNov 4 '09 at 13:31
3
Adding emphasis to your comment (3), I find especially in the States there's a rather artificial distinction between "analysis" and "calculus". To the point that calculus is seen as mindless symbol manipulation, but in analysis thought is allowed. John Hubbard's textbook does a great job of blurring those boundaries, especially when it comes to things like the inverse function theorem and Newton's method.
– Ryan BudneyNov 6 '09 at 22:32
2
My son took a really good AP calculus course at the local high school, using the most standard textbook and in some sense the most standard syllabus. So I've seen it from the other side. I don't think it's fair to call it "mindless symbol manipulation". But it is true that American universities sell calculus short in various ways. One reflection of that is that a good AP calculus course can be harder than the university product.
– Greg KuperbergNov 6 '09 at 22:59
5
In Germany, linear algebra is emphasized very much. Every university I know has a compulsory one-year linear algebra course along with the one-year analysis course (whose second semester is devoted to multivariate calculus) in the first year. Complex numbers are usually one of the first things which are introduced. Sometimes, they are even introduced in the first week of both courses since the professors talk less to each other than they should ;). But then, in most courses in analysis one is not really told what to do to solve an integral.
– Lennart MeierJun 16 '10 at 8:35
I think a great class for undergrads (in particular, for seniors planning on grad school) would be a capstone "Comparative Mathematics" course. In my imagining, this would be a mix of math history, the "greatest hits", contrasting the fundamental objects of study and proof techniques, and an introduction to the map of modern mathematics. Think the Princeton Companion to Mathematics distilled into a semester.
Maybe this is an overbroad answer, but I'd like to see more specialized subjects that are just really fun. Computational geometry (in the classical/Euclidean sense, not the computational algebraic geometry sense) is the example that leaps to mind -- I'm not aware of anywhere that offers it as an explicitly undergrad-level course, despite the fact that it's amazingly fun, quite simple (I suspect that bright undergrads could get to Arora's PTAS for Euclidean TSP within a semester, and certainly Christofides' algorithm is within the reach of anyone who's taken basic algorithms), and practically useful, although I guess this is more (T)CS than straight math...
I would have loved a class on how to write mathematical papers and what goes into mathematics research. Everything from neat Latex tricks to how to organize and structure ideas, theorems, etc, going over bad vs good papers, even perhaps discussing what makes good math books. As well, an overview of what goes into a PhD thesis would have been extremely useful. It's a shame that one usually has to pick up these various bits of info on their own. The class could coincide with a current undergraduate senior project for example and act as a supplement. I took a similar class like this in the physics department and it helped me immensely with my work.
There's not a whole lot of magic when it comes to writing good papers or books. Usually the magic is an immense amount of hidden effort. Allen Hatcher's "Algebraic Topology" is considered a pretty good book. I have dot-matrix printouts of some of the first versions, dating back to about when Hatcher arrived at Cornell. So the book represents about 30 years of teaching algebraic topology, and many iterates of revising the lecture notes.
– Ryan BudneyNov 6 '09 at 22:43
2
I now wish I had such a class as an undergrad, incidentally, although I think some of the undergrads actually in the class view it (incorrectly!) as "fluff." (Many students take 18.100B, which gives the analysis without the writing.) I disagree with Ryan Budney: just like giving presentations, or teaching, or even conducting research, there are lots of specific, teachable skills that can improve one's writing. Before helping to teach this class, I could diagnose a paragraph as unclear, and with enough work I could fix it. ...
– JBLMar 18 '10 at 15:50
1
The content of this class includes both a language to describe certain types of bad writing, and tools for quickly identifying and correcting what about it loses the reader. In other words, there are techniques to make good writing easier, and people who are good writers typically either know these techniques or have a strong intuitive feel for them. Just as is the case with any other endeavor, teaching the techniques makes it easier to do it well, and having really good heuristics lets one write better without having to work any harder at it.
– JBLMar 18 '10 at 15:58 | 677.169 | 1 |
The goal of Advanced level Developmental Mathematics is to provide students with sufficient algebra, geometry, and trigonometry to satisfy grade 11 prerequisites for some vocational, career, technical, and/or further academic programs. This course satisfies the mathematics requirement for the BC Adult Graduation Diploma.
Course Content:
Operations with Real Numbers
- Writing fractions as decimals and repeating decimals as fractions
- Adding, subtracting, multiplying and dividing rational numbers
- Evaluating powers with rational bases and integer exponents
- Order of operations with rational numbers
- Evaluating radicals with rational radicals and distinguishing between exact answer and approximate answers
- Simplifying, adding, subtracting, multiplying and dividing square roots
First Degree Equations and Inequalities
- First degree equations, including those involving parentheses
- formulas for a given variable when other variables are known
- formulas for given variable
- first degree inequalities in one variable
Polynomials
- monomials, binomials, trinomials, and other polynomials
- the laws of exponents to variable expressions with integral exponents
- adding, subtracting, and multiplying polynomials
- factoring polynomials by removing the largest common factor
- factoring binomials of the form a2x2 - b2y2 and trinomials of the form x2 + bx + c
- quadratic equations using the law of zero products
Optional: factoring trinomials of the form ax2 + bc + c
Rational Expressions
- simplifying, by factoring, rational expressions
- determining values for which a rational expression is undefined
- multiplying and dividing rational expressions
- adding and subtracting rational expressions consisting of monomial and/or binomial denominators
- solving simple rational equations and check solutions
Linear Equations
- graphing linear equations including the forms x = a and y = b
- determining slope and x and y intercepts when given a linear equation or its graph
- determining the equation of a line, y = mx + b, given its graph, given its slope and a point on the line, and given two points on the line
Systems of Linear Equations
- solving a system of first degree equations in two unknowns by graphing, substitution and elimination methods
- using a system of equations to solve practical problems
Radical Expressions
- simplifying, adding, subtracting, multiplying and dividing square roots with variable radicand
- solving equations with one square root containing a polynomial radicand and check for extraneous solutions
Trigonometry
- solving right triangles using one or more of the:
sine ratio
cosine ratio
tangent ratio
Pythagorean theorem
Angle sum property of triangles
Optional: evaluating sine and cosine for angles from 0 degrees to 180 degrees
Optional: solving triangles using the Law of Cosines or the Law of Sines, excluding the ambiguous case
Optional Course Content (one of the following must be completed):
The Quadratic Equation
- solving quadratic equations by factoring
- solving equations of the form x2 = bx = c = 0 by completing the square
- solving quadratic equations by using the quadratic formula
- graphing y = ax2 + bx + c and determining its x/y intercepts and vertex
- solving practical problems that can be solved using a quadratic equation
Statistics
- determining the mean, median, mode, range and standard deviation of a set of data
- representing data graphically using broken line graphs and bar graphs
- how the normal curve can be used to describe a normally distributed population
- calculating Z - scores and determine areas under the normal curve
- using areas under the normal curve to analyze data in terms of the probability of various events
Financial Mathematics
- simple interest problems
- compound interest problems
- calculating interest rates
- annuity problems
- periodic payment problems
- determining the finance charge on a loan
- determining the interest rate on a loan using tables or appropriate technology
Geometry
- classification of triangles according to angles and sides
- using the properties of triangles to determine the measure of sides and angles
- determining the measure and/or congruence of angles given a transversal and two parallel lines
- triangle congruence theorems in simple guided proofs
Learning Outcomes:
Operations with Real Numbers
- Write fractions as decimals and repeating decimals as fractions
- Add, subtract, multiply and divide rational numbers
- Evaluate powers with rational bases and integer exponents
- Demonstrate order of operations with rational numbers
- Evaluate radicals with rational radicands and distinguish between exact answer and approximate answers
- Simplify, add, subtract, multiply and divide square roots
First Degree Equations and Inequalities
- Solve first degree equations, in one variable, including those involving parentheses
- Solve formulas for a given variable when other variables are known
- Solve formulas for a given variable
- Solve first degree inequalities in one variable
- Solve practical problems that can be solved using a first degree equation
Polynomials
- Distinguish between monomials, binomials, trinomials, and other polynomials (in one variable only)
- Apply the laws of exponents to variable expressions with integral exponents
- Evaluate polynomials by substitution
- Add, subtract, and multiply polynomials
- Factor polynomials by removing the largest common factor
- Factor binomials of the form a2x2 - b2y2 and trinomials of the form x2 + bx + c
- Solve quadratic equations using the law of zero products
Optional: factor trinomials of the form ax2 + bc + c
Rational Expressions
- Simplify, by factoring, rational expressions consisting of polynomial numerators and either monomial, binomial or trinomial denominators
- Determine values for which a rational expression is undefined
- Multiply and divide rational expressions
- Add and subtract rational expressions consisting of monomial and/or binomial denominators
- Solve simple rational equations and check solutions
Linear Equations
- Graph a linear equations including the forms x = a and y = b
- Given a linear equation or its graph, determining its slope and x and y intercepts
- Determine the equation of a line, y = mx + b, given its graph, given its slope and a point on the line, and given two points on the line
Systems of Linear Equations
- Solve a system of first degree equations in two unknowns by graphing, substitution and elimination methods
- Solve practical problems that can be solved using a system of equations
Radical Expressions
- Simplify square roots with variable radicand
- Add, subtract, multiply and divide square roots with variable radicands
- Solve equations with one square root containing a polynomial radicand and check for extraneous solutions
Trigonometry
- Solve right triangles using one or more of the:
sine ratio
cosine ratio
tangent ratio
Pythagorean theorem
Angle sum property of triangles
Optional: evaluate sine and cosine for angles from 0 degrees to 180 degrees
Optional: solve triangles using the Law of Cosines or the Law of Sines, excluding the ambiguous case
Optional Learning Outcome (one of the following must be completed):
The Quadratic Equation
- Solve quadratic equations by factoring
- Solve equations of the form x2 = bx = c = 0 by completing the square
- Solve quadratic equations by using the quadratic formula
- Graph y = ax2 + bx + c and determining its x/y intercepts and vertex
- Solve practical problems that can be solved using a quadratic equation
Statistics
- Determine the mean, median, mode, range and standard deviation of a set of data
- Represent data graphically using broken line graphs and bar graphs
- Understand how the normal curve can be used to describe a normally distributed population
- Calculate Z - scores and determine areas under the normal curve
- Use areas under the normal curve to analyze data in terms of the probability of various events
Financial Mathematics
- Solve simple interest problems
- Solve compound interest problems
- Find the effective interest rate using E.R. = (1 + r/n)n-1
- Solve annuity problems
- Find periodic payment
- Determine the finance charge on a loan
- Determine the interest rate on a loan using tables or appropriate technology
Geometry
- Classify triangles according to angles and sides
- Use the properties of triangles to determine the measure of sides and angles
- Determine the measure and/or congruence of angles given a transversal and two parallel lines
- Use triangle congruence theorems in simple guided proofs
Grading System: Letters
Passing Grade: D (50%)
Percentage of Individual Work: 100
Textbooks: Textbooks are subject to change. Please contact the bookstore at your local campus for current book lists. | 677.169 | 1 |
Math 42 for iPhone and iPad not only solves math problems but helps you better understand them
Math 42 is an amazing little app for iPhone and iPad that functions both as an all-in-one calculator and as a learning tool. Aimed at 5th to 12th grade level students, you can get the help you need solving problems in many different categories. When you get stuck, Math 42 can even take you step by step through how to solve a particular problem.
Whenever you get stuck on a math problem, it doesn't typically help to just stare at the solution and wait for it to click. This is where Math 42 really stands out and actually helps students understand different types of math including the following -
Simplifying expressions
Binomial decomposition
Fractions
Equations (linear and quadratic)
Polynomial long division
Derivation
Not only can students practice these topics in Math 42, they can also input their own problems and have them solved. Each solution can also be explained step by step which makes for a great learning aid when you get stuck.
Whether you're a student studying math or a parent who really just doesn't remember enough of this kind of stuff to be of much help, Math 42 is a great option to have on handMath 42 for iPhone and iPad not only solves math problems but helps you better understand them | 677.169 | 1 |
Includes test and answer key booklets. 758 pages, hardcover.
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This set of additional tests is perfect for siblings or co-ops! Accompanying Saxon Math's Calculus curriculum, these test forms will easily let extra students get the practice they need! 37 Tests with Test solutions are included, with work shown for the test solutions.
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The DIVE software teaches each Saxon lesson concept step-by-step on a digital whiteboard, averaging about 10-15 minutes in length; because each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. DIVE teaches the same concepts as Saxon, but does not use the problems given in the text; it cannot be used as a solutions guide.
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This set of DVDs is to be used with Saxon Math Calculus, 1st Edition. Please Note: this set is not compatible with Saxon's Calculus, 2nd Edition.
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Cite This Source
Squares and Square Roots Introduction
In this section, we'll cover squares and square roots, also known as radicals.
This is not because of their extreme political views, although it might
explain why none of them have ever been elected to public office. We've
talked a little about squares and square roots here and there; now
we'll dive deeper into what they are and how they make geometrical
sense. (We'll also talk about what it means to make geometrical sense,
in case you were wondering.) Finally, we'll practice manipulating
expressions and solving equations that involve radicals. We'll get to
the root of these squares if it's the last thing we do.
We'll
introduce a few more ways to solve quadratic equations. We already know
how to solve quadratic equations that can be factored, but now we'll
turn our attention to solving any quadratic equation with real-number
solutions. And they thought they could hide from us because they
couldn't be factored. Joke's on them.
Finally, we'll do some word
problems and get friendly with the Pythagorean Theorem. Not too
friendly, of course; we hear it's seeing Euclid's proof of the
infinitude of primes, and it's getting kind of serious. Here's a
preview: If you're the kind of person who who hisses and recoils at the
sight of word problems (bet that makes math class super fun), we've got
the perfect rule to help you beat them. We hope you're ready for this
jelly, because here it is: | 677.169 | 1 |
Geometry Guide illustrates every geometric principle, formula, and problem type tested on the GMAT to help you understand and master the intricacies of shapes, planes, lines, angles, and objects.
Each chapter builds comprehensive content understanding by providing rules, strategies, and in-depth examples of how the GMAT tests a given topic and how you can respond accurately and quickly. The Guide contains a total of 83 Geometry question bank.
Includes separate chapter on numerous Advanced Geometry topics, as well as additional practice problems.
AboutTop Customer Reviews
I love most of the MGMAT books but this one just does not feel right. The book is realistically 95 pages and covers all important concepts: from lines to coordinate geometry. Does not go over the top and gives enough material, seems like the writers covered all the bases. However, I have an issue with it - it is not laid out very well. I am a visual learner and felt it would have been a better book if it was spread out more, included more illustrations, and did not have so much verbiage everywhere. Even larger all-in-one books dedicate close to 100 pages for Geometry.
Another issue is that all of the problems in the book are in a non-gmat format (meaning you only get a question, not the 5 answer choices). That is OK for some sections, but not having a single gmat-like question in the entire book is a "no-no". GMAT is heavily about basics and good framework, but there are other ways to solve questions such as backsolving, picking numbers, etc and those skills are honed only when questions are in the GMAT format. Important to point out that the book comes with access to the Geometry quiz bank online, which does have GMAT-style questions, so there is hope.
The big redeeming factors are 6 online tests that are included with every MGMAT book ($39 value), additional online practice materials, and coverage of Coordinate Geometry (a harder topic often omitted in larger textbooks).
***Bottom line: this is a solid geometry book that was crammed in 95 pages but is still a worthy buy for the sake of tests and the coordinate geometry section.
Questions about the book? Post them here - i will respond. BB, Founder of GMAT Club Community.
When i started GMAT preparation everybody told me that maths is easy and you don't need to work hard on it. But soon i realized that though its not hard, but its really tricky. Specially DS questions would leave you frustrated. But after doing part 1 - 3 of manhattan, i really imporved on DS. Problem Solving is also good. Overall i was really satisfied with manhattan, except Reading Comprehension book - don't buy it, its worth less.
I didn't take a class, but I have alot of friends who have and have used the Kaplan book and practice tests in addition to the Manhattan. Manhattan prep material and tests are head and shoulders above Kaplan. My only wish is that I had started with the Manhattan series and not even worried about Kaplan. Kaplan may have the brand name, but the fact that Manhattan focuses only on the GMAT shines through. The material goes wayyy more in depth, and it really leverages the other best source of practice material you have, the Official Guide (it has a great feature called rephrasing that references the OG problems directly to give data sufficiency help. It almost makes so much sense that it seems obvious but ingenious at the same time. Why not use the actual old test problems provided by the GMAC as much as you can?).
I wasn't going to buy the whole series but was so impressed by the first book I used (Sentence Correction), that I bought a couple of the quantitative prep books. I was so impressed by those, that I ended up buying all the rest of them. I can not stress enough how much more focused and useful this material is than Kaplan. When used in conjunction with the Official Guide, you have everything you need to break 700.
The things these books provide make so much sense as the best way to prepare, that it makes you wonder why everyone else doesn't do it. My guess is that Manhattan benefits from a focused business model of limiting itself to the GMAT. If you're not looking to score that well and only need to practice some and get used to the questions, the Official Guide is enough. But the Manhattan series is also nice in that it allows you to pick and choose the certain topics you need extra help with.Read more ›
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I have purchased other GMAT strategy guides, but this is my favorite series. This item is very helpful, particularly if you have been away from geometry for several years. It organizes re-learning the topic into areas of focus for the exam. I appreciate the section on Data Sufficiency. | 677.169 | 1 |
en.wikipedia.org/wiki/Complex_analysisComplex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex ...
en.wikipedia.org/wiki/Several_complex_variablesThe theory of functions of several complex variables is the branch of mathematics dealing with complex valued functions. on the space C n of n-tuples of complex numbers.
variable, In mathematics, a variable that can take on the value of a complex number. In basic algebra, the variables x and y generally stand for values of ...
Variables In the calculus of functions of a complex variable there are three fundamental tools, the same funda-mental tools as for real variables.
the delivery contract of 160 units from the functional helyu Complex Variable Traffic Control Point Design, manufacture, supply, installation, and Adapting to ... | 677.169 | 1 |
Summary: Math 5B List of Prerequisite Topics
Summer Session B, 2011
This list is NOT exhaustive and might have additions as the course progresses. If
you find yourself using prerequisite material that is not on this list, please send me
an email and I will add it on for the others. As you begin the class, make sure you
have a thorough knowledge of the following topics:
Trigonometry and Algebra
· Quadratic Formula
· Unit Circle (radians and degrees)
· Trig formulas (Pythagorean Identities, inverses, double angle formulas,
even-odd identities. Other sum-difference identities might be required on
homework.)
· Volume/area formulas
Math 3A, Derivative Calculus You should be very good at derivation.
· calculating limits
· definition of derivative
· interpreting the "derivative" in word problems as rate of change
· derivative rules (trig, chain rule, product, and quotient rules)
· related rates
Math 3B, Integral Calculus You should be very good at integration. | 677.169 | 1 |
Basic Information
Course Webpage:
The main resource for this course. You will find there announcements,
a class log, links to handouts, worksheets, homework assignments, and
other resources. Bookmark this page and check it frequently.
Instructor: A.J. Hildebrand, office 241 Illini Hall, phone
244-7721, email ajh@illinois.edu. I will be available daily in the hour
after class (in the regular classroom or one of the neighboring classrooms).
If there is interest, I will set aside additional time slots later in the
day.
Text and syllabus:
The official Math 347 text is "Mathematical Thinking" by D'Angelo
and West (2nd edition). We will cover Chapters 1-4, 13-14, and selected
topics from the other chapters depending on audience preferences. I
will supplement this text with handouts summarizing the key concepts,
definitions, and theorems on a given topic, and with worksheets
providing additional, carefully selected practice problems.
Note on purchasing the text. The class handouts are intended to
complement the text, not to replace it. You will still need
access to the text for the assigned reading and for the homework,
though you don't necessarily have to purchase a copy. The Math Library
has several copies of the D'Angelo/West text on course reserve that you
can check out for 2 hours to makes copies. It also has some other texts
that are useful as supplementary references; in particular,
Rosen's "Discrete Mathematics" (which is the official text for Math 213
and CS 173) is an excellent source for practice problems on most of the
topics covered in Chapters 1-4.
Grading
Grading summary:
Your course grade will be based on homework, midterms and the final exam, weighted
as follows:
Homework: 30%
Midterms: 40%
Final Exam: 30%
Curving: Each grade component will be individually curved, depending
on the distribution of raw scores. For example, a raw score of 88/100 on an
exam (which would be a B+ on a standard 100/90/80/70 curve) may convert to a
score of 90/100 (an A- on the standard curve) as a result of such curving.
The curving will always be "up"; it will never lead to a lowering of the
score.
Course grade:
The average of the curved grade components, computed with the above weights,
will determine your course grade. It will be translated into a letter grade
(with plusses and minuses) in the usual way: 96.67% - 100% corresponds to an
A+, 93.34% - 96.66% corresponds to an A, 90% - 93.33% corresponds to an A-,
etc. No additional curving will be done, except possibly for some minor
adjustments to avoid close calls.
Homework:
There will be twice weekly graded HW assignments, usually due on Thursdays
and Mondays. Late assignments will not be accepted, but if you have a
legitimate, documented excuse for missing an assignment (e.g., illness), I
will mark the assignment as excused (see the section "Missed/late homework"
below). At the end of the semester, the lowest HW score will be dropped; the
remaining HW scores will determine your HW grade. Homework accounts for 30%
of the course grade.
Midterm exams: There will be three midterm exams,
spread out evenly over the semester. The midterm dates are
Wednesday, July 2, 16, 30.
All midterms will be given in-class, in the regular classroom. At the end of
the semester, the lowest of the three midterm scores will be dropped. Midterm
exams contribute 40% to the course grade.
Final Exam: The Final Exam will cumulative and will
account for 30% of the course grade.
It will be held on the official final exam slot for this class,
Friday, August 8, 2014, 8 am - 10 am.Please keep the above date in mind when making your travel plans.
The University is strict about enforcing final exam dates, and
instructors do not have the authority to let a student take the
final at a different date.
Policies
Group work policy:Group work on regular homework problems (excluding bonus/extracredit
problems) is fine and, indeed, encouraged.
If you work with others on the homework, put the names of the other group
members on the problem sheet. You must write up solutions yourself,
using your own words. Group work should not be a one-sided affair,
and it also should not be a division of labor, with each group member doing
only a subset of the problems and passing out solutions to the rest of the
group. Everybody should contribute, and the goal should be for everyone in
the group to end up understanding all of the problems.
Missed/late homework:
Late homework will not be accepted. Since the lowest homework
score will be dropped, you can afford to miss one homework assignment
and still end up with a perfect homework average.
If you cannot turn in an assignment due to illness or some other valid excuse,
and have obtained an "absence letter" from the Dean's office (see below),
I will mark the assignment as excused.
In this case, the homework will not count towards the homework average,
and will also not affect your drop score.
To get an absence letter, call the
Dean's office at 217-333-0050 or come to the office at 300 Turner Student
Services Building, 610 East John Street, Champaign.
For more information about absence letters, see
the Dean of
Students website.
Missed midterm exams:
Missed midterm exams will normally be treated in the same way as missed homework
assignments: if you have a valid excuse, documented by an "absence letter" from the
Dean, the exam will be counted as "excused" and not taken into account in the
computation of your grade. In exceptional cases, I may give you the option
to take a make-up exam instead of counting the exam as excused.
Missed final:
Final exams must be taken at the regular final exam date and time. The
University is very strict in enforcing this rule; exceptions can only be
granted by the Dean (not the instructor). If you are sick on the date of the
final, the Deam can issue an "Incomplete" grade that allows you to make up the
final at a later date. In this case, contact the Emergency Dean (see above)
as soon as possible to start the process.
Attendance. I expect you to attend class. Skipping classes shows
a lack of commitment and disrespect. The same goes for chatting, texting,
or websurfing during classtime. I take my duties as instructor seriously
and put a lot of effort into preparing lectures, and I expect students to
be respectful of this effort. While in large lecture/discussion format
classes you may get away skipping the lectures without anyone noticing,
in a small class like this one, absences do get noticed. If you have to
miss the class for a legitimate reasons such as illness, send me an email so
that I know why you are not there. When you are back, I'd be happy to meet
with you to help you catch up with what you missed. | 677.169 | 1 |
A basic math course focusing on the four operations of whole numbers and decimals as well as the critical thinking skills to solve these problems. The content also includes an understanding of fractions and geometry in relation to perimeter and area. (1.7) Proficiency Credit Not Available Pass/No Credit Available | 677.169 | 1 |
Laguna Beach ChemistryJason H.
...Calculus presents a lot of abstract ideas and the logic needed to do things like evaluating limits, improper integrals and divergence vs convergence is difficult to follow; textbooks and lectures sometimes skip steps when explaining these ideas. I have done a lot of calculus over the years and h...
Alexander Z. | 677.169 | 1 |
Before the first day of instruction, email your instructor that you have registered for the course. The starting point for the class is
<
Course Prerequisites:
Prerequisite: "C" or higher in MATH 25 OR placement in MATH 103
Course Description:
An extension of the elementary algebra sequence designed to prepare students for precalculus. Topics include simplification of algebraic and radical expressions, factoring, solution of linear, quadratic, absolute value and literal equations and inequalities, complex numbers, solution of linear and quadratic systems, logarithms and an introduction to functions and their graphs. | 677.169 | 1 |
Penn Wynne, PA ACT Math used Microsoft Publisher as my platform of choice for all of my desktop publishing applications. I have published several downloadable books. Additionally, I have prepared several monthly newsletters about various subjects such as the college admissions process, study abroad, and building a home-based business.
Amelia E | 677.169 | 1 |
You are here
Linda Boxley
Courses:
MTE 3 - Algebra Basics
Includes basic operations with algebraic expressions and solving simple algebraic equations using signed numbers. Emphasis will be placed on applications throughout the unit. Prerequisite Competency in Math Essentials MTE 1 through 2 as demonstrated through the placement and diagnostic tests, or by satisfactorily completing the required MTE units or equivalent. Lecture 1 hour.
MTE 6 - Exponents, Factoring, and Polynomial Equations
Includes factoring polynomials and solving polynomial equations. Emphasis will be placed on learning all the different factoring methods, and solving application problems using polynomial equations. Prerequisite: Competency in Math Essentials MTE 1 through 5 as demonstrated through the placement and diagnostic tests, or by satisfactorily completing the required MTE units or equivalent. Lecture 1 hour.
MTE 4 - First Degree Equations and Inequalities in One Variable
Includes the solution of first degree equations and inequalities containing one variable, and using them to solve application problems. Emphasis will be placed on learning the steps to solving the equations and inequalities, applications and problem solving. Prerequisite Competency in Math Essentials MTE 1 through 3 as demonstrated through the placement and diagnostic tests, or by satisfactorily completing the required MTE units or equivalent. Lecture 1 hour.
MTE 5 - Linear Equations, Inequalities and Systems of Linear Equatio
Includes determining the equation of a line, graphing linear equations and inequalities in two variables and solving a system of two linear equations. Emphasis will be placed on writing and graphing equations using the slope of the line and points on the line, and applications. Prerequisite Competency in Math Essentials MTE 1 through 4 as demonstrated through the placement and diagnostic tests, or by satisfactorily completing the required MTE units or equivalent. Lecture 1 hour.
MTH 163 - Precalculus I
Presents college algebra, matrices, and algebraic, exponential, and logarithmic functions. Equations and inequalities, graphing and functions, and systems of equations are included. Prerequisite Competency in MTE 1 though 9 as demonstrated through the placement and diagnostic tests or equivalent or SAT score greater than or equal to 520 or ACT greater than or equal to 22 . Lecture 3 hours per week.
MTE 7 - Rational Expressions and Equations
Includes simplifying rational algebraic expressions, solving rational algebraic equations and using them to solve application problems. Prerequisite Competency in Math Essentials MTE 1 through 6 as demonstrated through the placement and diagnostic tests, or by satisfactorily completing the required MTE units or equivalent. Lecture 1 hour. | 677.169 | 1 |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more | 677.169 | 1 |
Math Department
About
The Yakima Valley Community College Mathematics Department is committed to serving the diverse student population of the Yakima Valley by providing a positive learning atmosphere with the highest quality of instruction enabling our students to pursue further studies in Mathematics, Engineering, and Science, as well as general and vocational education.
The Math Center
The Math Center located on the first floor of Glenn-Anthon Hall in Room 101, provides drop-in instructional support for classes from arithmetic through calculus. No appointment is needed, this service is free of charge to our students.
Math instructors provide individualized assistance to students about their math courses as well as other math related courses.
Focused on your Success
Help is also provided though computer / CD instruction focusing on concept development and guided practice. Resources such as calculators, textbooks, manipulatives, math-related materials and supplemental written materials are available to students in the study areas of the center. | 677.169 | 1 |
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Read More effective tool for teachers and students. 25 Just-In-Time review topics are placed throughout the text and MyMathLab to help students right when they need it most. This, along with the existing Mid-chapter Mixed Review exercises, Study Guide summaries, and the new MyMathLab with Integrated Review course, students have an unparalleled amount of review resources to help them be successful in the course. Also available with MyMathLab(R) MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. With this edition, the authors focused on developing MyMathLab features that help better prepare students and get them thinking more visually and conceptually. NOTE: This is the standalone book, if you would like the book/with Access Code order the ISBN below: 0321970055 / 9780321970053 Precalculus: A Right Triangle Approach plus MyMathLab with Pearson eText,1969553 / 9780321969552 Precalculus: A Right Triangle Approach
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Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780321970084-2Hardcover. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 9780321970084PLEASE READ** INSTRUCTOR'S EDITION** which is the same as the student edition with additional notes and answers. Marked not for sale with disclaimer. (5th edition). SHRINKWRAPPED! ! ! TEXT ONLY! NO ACCESS CODE!
New. 0321969553 Answers includedNew. 0321969553 WITH ALL ANSWERS INCLUDED | 677.169 | 1 |
More Good Questions, written specifically for secondary mathematics teachers, presents two powerful and universal strategies that teachers can use to differentiate instruction across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert with these strategies, this book also demonstrates how to use more inclusive learning conversations to promote broader student participation. Strategies and examples are organized around Big Ideas within the National Council of Teachers of Mathematics (NCTM) content strands. With particular emphasis on Algebra, chapters also address Number and Operations, Geometry, Measurement, and Data Analysis and Probability, with examples included for Pre-Calculus.
To help teachers differentiate math instruction with less difficulty and greater success, this resource:
Top Customer Reviews
This book was recommended to me by one of the authors ... so I may be a bit biased. However it was money well spent. I teach grade 8 math in Ontario and although the title is "Secondary Mathematics" there is almost equal weight given to grade 7 and 8 level material.
Not only is the theory sound, but the authors have compiled many many sample problems that are ready to use with a class. They are even organized by the strands used in the Ontario curriculum.
This will certainly be a part of my teaching this year and in the future.
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I will admit to a slight bias - I met one of the authors, Amy Lin because she worked at my school board and she suggested I buy this book. It is money well spent. I really like that there are many many practical suggestions and example questions that you can use in the classroom right away. The questions are divided by strand, and there are enough that you could use them weekly through an entire year.
I wish that the grade level was indicated in the title. Half of the content is geared towards grades 6-8 (and many of the lower grade questions would be good for high school classes too)
There are two types of activities "open questions" that let students participate in a mathematical discussion at multiple levels, and "parallel tasks" that give student choice, but achieve the same big picture understandings. The authors even included scaffolding questions or prompting questions to help re-start a discussion that has stalled or help a student get started.
Finally, there is a clear index organized by topic that lets you flip straight to the page that has the questions you need for today's lesson.
This book has lots of applicable ideas for teaching secondary level mathematics. I read the hints when putting together Lesson Plans. I have two copies one for my personal library and one as a reference in the classroom.
I have used the questions and parallel tasks for math journals. My students love them because they can think outside the box, and there are no wrong answers. I especially appreciate the sample teacher questions that the authors provide to help facilitate class discussion. I would recommend this book to math teachers looking for a way to incorporate more writing and discussion in their class. | 677.169 | 1 |
Mathematics for Machine Technology new edition of this best-selling text has been reviewed and revised to clarify and update an understanding of mathematical concepts necessary for success in the machine trades and manufacturing fields. Mathematics for Machine Technology, Sixth Edition overcomes the often mechanical "plug in" approach found in many trade-related texts. A complete grasp of mathematical concepts are emphasized in the presentation and application of a wide-range of topics from general arithmetic processes to oblique trigonometry, compound angles, and numerical control. The material covered by this text is accompanied by realistic industry-related examples, illustrations, and actual applications, which progress from the simple to the relatively complex. Mathematics for Machine Technology, Sixth Edition provides readers with practical vocational and technical applications of mathematical concepts necessary to excel in the machine, tool-and-die, and tool design industry.
Common Fractions and Decimal Fractions
Introduction to Common Fractions and Mixed Numbers
Addition of Common Fractions and Mixed Numbers
Subtraction of Common Fractions and Mixed Numbers
Multiplication of Common Fractions and Mixed Numbers
Division of Common Fractions and Mixed Numbers
Combined Operations of Common Fractions and Mixed Numbers
Computing with a Calculator: Fractions and Mixed Numbers
Introduction to Decimal Fractions
Rounding Decimal Fractions and Equivalent Decimal and Common Fractions
Addition and Subtraction of Decimal Fractions
Multiplication of Decimal Fractions
Division of Decimal Fractions
Powers
Roots
Table of Decimal Equivalents and Combined Operations of Decimal Fractions | 677.169 | 1 |
Textbook 2 is recommended for Grade 8; 444 pages, hardcover. Teacher involvement is generally required. New...
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This book focuses exclusively on K-8 mathematics, developing elementary mathematics at the level of teacher knowledge. Themes focus on how the nature of a mathematics topic suggests an order for developing it in the classroom, how topics are developed through 'teaching sequences', and how math builds on itself. Originally designed as a textbook for teachers, this book is divided into short sections, each with a single topic and homework set. The homework sets were designed with the intention that all or most of the exercises will be assigned; many of the questions involve solving problems in actual elementary school textbooks. Others involve studying the textbook - carefully reading a section of the book and answering questions about the mathematics being presented, with attention to the...
Less Grades 7-10; 444 pages, hardcover. Teacher involvement is generally required. Textbook 1 is recommended for 7th...
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Accompanying the Math in Focus Grade 3 multiplication tables, bar models, money, bar graphs, fractions, measurement, angles, area, and other topics covered in the third grade curriculum. Answers and a student record sheet are included. 191 pages, paperback; tests are perforated, three-hole-punched , and reproducible. Please Note: This product is...
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The New Elementary Mathematics Solution Manuals provide step-by-step solutions to the textbook's Exercises, Revision Exercises, Miscellaneous Exercises and Assessment Papers. It does not provide answers or solutions to the Class Activities, the Challenger and Problem Solving Exercises, or the Investigation sections, to answers are found in the Teacher's Guide/Teacher's Manual. The New Elementary Mathematics solution manuals do not cover exercises found in the workbooks. 247 pages, softcover.
Accompanying the Math in Focus Grade 4 estimation, graphs, probability, decimals, angles, area, symmetry, and other topics taught in the fourth grade curriculum. Answers and a student record sheet are included. 151 pages, paperback; tests are perforated, three-hole-punched , and reproducible. Please Note: This product is only available for third grade, and covers money; metric length & volume; measurement; bar graphs & line plots; fractions; length & weight; time & temperature; shapes; area & perimeter; and more. Real-life problems are included throughout all chapters. Examples are provided alongside helpful representations and explanatory text; fun games, hands-on activities, math journal, put on your thinking cap, chapter wrap-up, and review/ test fourth grade, and covers adding & subtracting decimals; angles; line segments; squares & rectangles; area & perimeter; symmetry; and tessellations. Real-life problems are included throughout all chapters. Examples are provided alongside helpful representations and explanatory text; fun games, hands-on activities, math journal, put on your thinking cap, chapter wrap-up, and review/ test exercises are also included. The fifth grade, and covers decimals, multiplying & dividing decimals, percents, graphs & probability, angles, properties of triangles & four-sided figures, three- dimensional shapes, surface area and volume, and real-life problems. Examples are provided alongside helpful representations and explanatory text; fun games, hands-on activities, math journal, put on your thinking cap, chapter wrap-up, and review/ test exercises | 677.169 | 1 |
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Introduction to Mathematical Programming
Introduction to Mathematical Programming
Summary
This text is written for the business major with enough mathematical background to appreciate an occasional departure from a main emphasis on applications. The first five chapters discuss linear problems with linear programming the central topic. The necessary matrix algebra background is developed in Chapter 2. Chapters 6 and 7 require differential calculus at a level comparable to that of first year engineering and science students. The key elements of calculus needed for optimization are recalled at the beginning of Chapter 6. The eighth chapter is devoted to integer programming including branch and bound algorithms for the knapsack and traveling salesman problems and an emphasis on problem formulation. Chapter 9 is a short introduction to dynamic programming and the last chapter contains case studies at a level a little higher than the problems in the text. | 677.169 | 1 |
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Mathematical Treasure: Jeremiah Day's Introduction to Algebra
Author(s):
Frank J. Swetz (The Pennsylvania State University)
Figure 1. Title page of Jeremiah Day's Introduction to Algebra, written for use with students at Yale and other American colleges
Jeremiah Day (1773-1867) served as President of Yale University from 1817 to 1846. During his tenure at Yale, he was also a Professor of Mathematics and Natural Science. He wrote his Introduction to Algebra in 1814 for the use of his students. This work borrowed heavily from the French algebra texts of the time. Day defined algebra as "a general method of investigating the relation of quantities, principally by [the use of] letters." This book became very popular and went through many editions. The title page of the thirteenth edition (1834) is shown above. Other editions of this text are available as Google Books.
Figure 2. Here on pages 16-17 of his Introduction to Algebra, Day discussed negative quantities. The use and teaching of positive and negative values in mathematics was a pedagogical issue at this time.
Yale College took many steps toward becoming a university during Day's tenure as president (1817-1846). The Theological Department (which would become the Yale Divinity School) was founded in 1822 and the Law School in 1824. The Medical Institution of Yale College had opened in 1813 and the Department of Philosophy and Arts (which would become the Graduate School of Arts and Sciences) would be formed in 1847. Read more Yale history and see Landmarks in Yale's history. See portraits of Day and other Yale University presidents, 1701–2013.
The two images above are presented courtesy of Archives and Special Collections, Dickinson College, Carlisle, Pennsylvania. You may use them in your classroom and/or for private study; for all other purposes, please seek permission from Archives and Special Collections, Waidner-Spahr Library, Dickinson College, Carlisle, PA. | 677.169 | 1 |
Textbooks can definitely be wrong. Some books acquire a reputation for how many mistakes they have. I have a friend who edits textbooks for a living, and he found a proof-by-example actually being promoted as a valid proof technique. Naturally, you can't expect every book to be perfect. But these days, I would expect a decent author to publish known errata somewhere. Authors, if they're generally competent, would want to know about an error. So you might pass that one along to him, if you can get a hold of him. | 677.169 | 1 |
Find a Rest Haven, GA GeometryThis algebra deals mostly with linear functions. Algebra 2 is a more advanced, more complex version of algebra 1. Here we get more involved with non-linear functions as well as imaginary and complex numbers | 677.169 | 1 |
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Comment: Book looks great with no writing in it Crease in the cover otherwise crisp and clean in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple functions to analyze the fundamental methods of constructing graphs. The second half deals with more complicated and refined questions concerning linear functions, quadratic trinomials, linear fractional functions, power functions, and rational functions.
Editorial Reviews
Review
"All through both volumes [Functions & Graphs and The Methods of Coordinates by n ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done."
Top Customer Reviews
This brief text provides a clear introduction to analytic geometry. Its scope is narrow. The authors discuss the graphs and properties of linear functions, absolute value functions, quadratic functions, linear fractional functions, power functions, and rational functions (trigonometric functions are discussed in another volume of the Gelfand School Outreach Program). What distinguishes this book from other treatments of the same topics is the extent to which the authors go to explain, using both words and diagrams, why the graphs of the functions they discuss have the form they do and the many challenging exercises they include.
This book concludes with a chapter length exercise set full of challenging problems. The reader who completes these problems will gain a much fuller understanding of analytic geometry than one who reads a typical precalculus text. While calculus is not required to complete the exercises, the reader may wish to revisit these problems once she or he has had calculus in order to analyze the properties of the graphs more fully.
The text was written initially for a correspondence course in the Soviet Union. Since students could send their solutions to the authors when they were at the University of Moscow, answers or hints to only a few of the exercises are included in the back of the text.
In this slim, 100 page volume, Gelfand, Glagoleva and Shnol have a wonderful review of graphing.
There is nothing here incredibly advanced; they only cover linear, quadratic, polynomial, and rational (ie, f(x) = P(x)/Q(x) ) functions. But they systematically explain how to transform, how to combine, how to shift, how to reflect... They consider asymptotes (vertical and horizontal), zeros, symmetries. They spend more time with absolute value then one might expect.
They treat these limited topics in depth. I read this book on vacation, cover to cover, completing every single exercise. It was a great refresher, and led me to think about several graphing-skill topics from new perspectives.
I am a teacher, and this book has informed my teaching. Also, I intend to use it with my math team. I do not think you could use this book to teach graphing from scratch. Rather, I see it as a source of enrichment.
The major drawback to this book is the lack of answers in the back. But if you are really stuck, the judicious use of a graphing calculator (or checking with friends or colleagues) should be good enough. At the price, there is no reason not to own "Functions and Graphs."
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I tend to look at elementary books like this one from the point of someone who doesn't need to learn from it but might want to use it as a text if teaching or tutoring someone. I learned almost nothing from this book, but I didn't expect to, as it's all material I learned ages ago. But for someone encountering this material for the first time, this would be an excellent book. I see this book as used primarily in a pre-calculus math class or for tutoring someone about to take calculus. It gives a good exposition of material that will be encountered at the time a student takes calculus, but at a level that assumes the student has only the algebra that most students entering a calculus course have taken. And from that point, it explains the elements of drawing graphs of algebraic functions and the ideas of tangency that are so critical to differential calculus, and does so in a clear way, with helpful diagrams. It is a slim book, and probably by itself could not be the only text in a pre-calculus math class, but on the subjects it covers, it is the best I have seen. (And that is underrating it, because there aren't many books on the subject. So one might say that "the best there is" isn't really as high praise as it deserves.) This book certainly deserves a 5-star rating.
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I'm using this small, pocket-sized book by Gelfand to review essential graphing concepts and have one thing to say- Outstanding. Where books like this were when I was learning maths as a young one is beyond comprehension. Looking back on my math education now, I can honestly say I was deprived. Poor, poor, me........Enjoy.
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If you have been away from math for a while and wish to review functions this book is for you. If you are in middle or high school this will be an excellent learning tool to prepare you for Calculus-1. As usual Gelfand gives an innovative, example filled, and practice filled book on functions. All areas important for Calculus are explained very well. There is stuff on function shift, reflection, asymptotes, continuity etc.
Some readers may be put off by the title of this little book wherein Graphing is included. These days with excellent graphing calculators one may see no need for a how-to on graphing. But that is not true because RECOGNIZING a function by its graph is very important and will save you a lot of time in Calc. I wish I had this excellent book in middle school. Things would have been so much easier in college and grad school. Very highly recommended.
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This applet is a calculator for finding inverses of 3 by 3 matrices, by calculating cofactors and determinants. The method is displayed fully, including cases of singular matrices which have no invers... More: lessons, discussions, ratings, reviews,...
This lesson is designed to introduce students to the idea of functions composed of two operations, with specific attention to linear functions and their representations as rules and data tables, inclu... More: lessons, discussions, ratings, reviews,...
This packet contains a copy of the original problem used to create the activity, rationale and explanation behind the "Change the Representation" focal activity, and some thoughts on why this activity... More: lessons, discussions, ratings, reviews,...
This sketch allows the manipulation of a line in slope-intercept form. On the first page, the coefficients m and b are restricted to multiples of 0.5. On the second page, they are unrestricted and can... More: lessons, discussions, ratings, reviews,...
An interactive applet that allows the user to graphically explore the properties of a linear functions. Specifically,
it is designed to foster an intuitive understanding of the effects of chang... More: lessons, discussions, ratings, reviews,...
This site allows one access per day per computer free of charge. This applet allows students to establish an objective function, and then graph up to five constraints in different colors. Students c... 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 | 677.169 | 1 |
Mathematics A DiscreteMaster the fundamentals of discrete mathematics and proof-writing with MATHEMATICS: A DISCRETE INTRODUCTION! With a clear presentation, the mathematics text teaches you not only how to write proofs, but how to think clearly and present cases logically beyond this course. Though it is presented from a mathematician's perspective, you will learn the importance of discrete mathematics in the fields of computer science, engineering, probability, statistics, operations research, and other areas of applied mathematics. Tools such hints and proof templates prepare you to succeed in this course. | 677.169 | 1 |
This book provides a concise introduction to modular representation theory for masters-level students. It details basic results, tools, and techniques as well as compares group theoretic and module theoretic concepts. more...
Pell's equation is an important topic of algebraic number theory that involves quadratic forms and the structure of rings of integers in algebraic number fields. The history of this equation is long and circuitous, and involved a number of different approaches before a definitive theory was found. There were partial patterns and quite effective methods... more...
This book is about perfect, amicable and sociable numbers, with an emphasis on amicable numbers, from both a mathematical and particularly a computational point of view. Perfect and amicable numbers have been studied since antiquity, nevertheless, many problems still remain. The book introduces the basic concepts and results of perfect, amicable and... more...
This book is the English translation of Baumgart?s thesis on the early proofs of the quadratic reciprocity law (?Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise?), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre,... more...
This monograph presents recent developments of the theory of algebraic dynamical systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative... more...
This book presents in a unified way the beautiful and deep mathematics, both theoretical and computational, on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in literature. Some results are even hidden behind a number of routines in software packages,... more...
Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal... more...
This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group G(Af) of... more... | 677.169 | 1 |
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Mathematics and Statistics
OVERVIEW:
This document provides a description of the Mathematics and
Statistics component of University Studies. In so doing, it differentiates
between common component-level student learning outcomes and discipline-specific
course-level learning outcomes. The goal is to encourage the development of
challenging and varied University Studies courses that share common assessable
student learning outcomes.
PART I: DESCRIPTION AND RATIONALE
The liberal arts are the arts of
thinking. As we human beings think with symbols, primarily words and numbers,
the liberal arts are consequently the arts of processing these symbols.
Therefore for centuries the study of languages and mathematics has been at the
center of the liberal arts. The major function of mathematics has been to
provide scientific models for the description of reality. These classical models
have tended to be deterministic where calculus remains a primary tool. More
recently discrete and statistical models of reality are increasingly utilized.
The Mathematics and Statistics component of the University Studies
program introduces students to the college level study of at least one of these
approaches or to additional mathematical knowledge that is prerequisite to this
study. Courses in this component will engage students in a meaningful and
positive intellectual experience; increase quantitative and logical reasoning
abilities needed for informed citizenship and in the workplace; strengthen
quantitative and mathematical abilities that will be useful to students in other
disciplines; improve every student's ability to communicate quantitative ideas
orally and in writing.
PART II: COMMON STUDENT LEARNING OUTCOMES ALIGNED TO UNIVERSITY STUDIES
GOALS
The following are the Common Student Learning Outcomes for Mathematics and Statistics. These are aligned with the UNCW Learning
Goals. Each course in this category must address all of the Common Student
Learning Outcomes for the category, and list these Common SLOs along with
course-specific SLOs in the course syllabus. Proposals for inclusion in the
category will describe the opportunities which will be provided for students to
learn the outcome (readings, class discussion and/or activities, applied
projects) and list the specific sources of evidence (exams, papers, projects,
quizzes, etc.) that will be used to determine the level of student
understanding. | 677.169 | 1 |
Course Details
MATH 231 - CALCULUS I
Functions, limits, continuity, and rates of change are studied numerically, symbolically, and graphically. Definition and rules of differentiation; applications of the derivative to analyzing functions, solving equations, computing extrema, and L'Hopital's rule; antiderivatives. Introduction to integration and the fundamental theorem of calculus. | 677.169 | 1 |
The announcement of a new math course generally doesn't elicit the kind of response that accompanies a movie premiere, but in a way, that's what happened when Robert Ghrist debuted "Calculus: Single Variable" in January. | 677.169 | 1 |
0387976213 Leaves: A Tutorial Introduction to Maple V
This tutorial shows how to use Maple both as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding tasks. It covers topics such as the basic data types and statements in the Maple language. It explains the differences between numeric computation and symbolic computation and illustrates how both are used in Maple. Extensive "how-to" examples are used throughout the tutorial to show how common types of calculations can be expressed easily in Maple. The manual also uses many graphics examples to illustrate the way in which 2D and 3D graphics can aid in understanding the behavior of functions | 677.169 | 1 |
Now in a second edition, the award-winning The Trouble with Maths offers important insights into the often confusing world of numeracy. By looking at learning difficulties in maths from several perspectives, including the language of mathematics, thinking styles and the demands of individual topics, this book offers a complete overview of the most... more... | 677.169 | 1 |
Synopsis
Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and makes an attractive chapter of mathematics, which can be used as an introduction to any of these topics, or to singularity theory in higher dimensions. This book is designed as an introduction for graduate students and draws on the author's experience of teaching MSc courses; moreover, by synthesising different perspectives, he gives a novel view of the subject, and a number of new results.
eBook Details
Cambridge University Press, November 2004
ISBN:
9780511262234
Language:
English
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This book is an integrated introduction to the mathematics of coding, that is, replacing information expressed in symbols, such as a natural language or a sequence of bits, by another message using (possibly) different symbols. There are three main reasons for doing this: economy, reliability, and security, and each is covered in detail. Only a modest... more... | 677.169 | 1 |
Welcome to Pre-Calculus (Honors)!
Pre-Calculus is a long-term project based (honors) course with a NC Final Exam (state-wide test that is 25% of final grade).
Students and parents will have to sign a Honors Contract reflecting their understanding of Honor Courses' expectations.
Students who are enrolled in this course should have received at least a 85 in Math 3 (academic) or at least passed Math 3 (honors) or passed Advanced Functions AND of course have passed Math 1 and passed Math 2.
The curriculum for this course will be using the 2003 NC Standard Course of Study.
This course will help prepare students for Calculus and will cover a variety of topics. The course is split up into two parts: Algebra and Trigonometry.
The Algebra part of this course will expand what students have already learned in Math 3 with more complicated concepts.
The Trigonometry part of this course will (somewhat) expand what students have already learned in Math 2 and introduce concepts that start Calculus.
Students will be required to use this website on regular basis for various resources in particular to complete the course's long-term based project, The Reference Booklet (RB). The Reference Booklet will be extremely helpful in Calculus and will help review already learned concepts, reinforce new concepts, and prepare students for concepts that require them to use their critical thinking skills.
The tabs to the right will help you find what you need. All documents are PDF (Adobe Reader) files so make sure you an open the properly. | 677.169 | 1 |
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The guide to vector analysis
Editorial Reviews
About the Author
Murray R. Spiegel held positions at Harvard University, Columbia University, Oak Ridge and Rensselaer Polytechnic Institute, and served as a mathematical consultant at several large companies. His last Position was professor and Chairman of mathematics at the Rensselaer Polytechnic Institute Hartford Graduate Center. He was the author of numerous journal articles and books on various topics in mathematics. Seymour Lipschutz, Ph.D., is a Mathematics professor who has written more than 15 Schaum's Outlines.
Top Customer Reviews
I used an earlier edition of this great text back in 1968 while an undergraduate in Physics. In those days, Vector Algebra and Analysis were left as 'catch-it-as-you-can-and-on-the-fly' in or in between a given math or physics course. And really, that attitude has not changed today: look at any undergrad physics book in elementary mechanics or electromagnetism, and you will see that in many cases, Vector material in an appendix. And when it is addressed in a textbook, e.g., those used in the first two semesters of a typical undergrad sequence in basic calculus-based physics, you wish the God it wasn't. They go on and on about the obvious, give problems that are easy to solve but which do not prepare the student for real-world or real-physics research problems. And if you don't get lost in the cute little pictures and elaborate drawings those books use to 'explain' the concepts, you still wind up with a cursory understanding of Vectors and their importance in Physics, Engineering, and Mathematics.
Not so with this text. It gives sufficient theory, insightful examples, plenty of supplementary problems, and very helpful illustrations to drive the point being made home. Truly, a great book.
So when I learned Vector Analysis from this text, I carried this book with me for reference and further learning and refreshing myself throughout grad and post grad school, and it never let me down. To this day, there are three old copies on my books shelves, and now I just added this latest second edition copy - just for old times sake. You won't go wrong with this book.
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This book is the best book in Vector I've ever seen. It is full of problems and solutions, but very few redundant problems. It states the vector theory in every aspect very clearly. One can learn Vector through examples and problems easily. When you study this book, you can really feel you are making progress smoothly every day. If you buy this book, you need not to buy any other Vector textbooks. It is enough to be a textbook as well as an exercise book.
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Being an old student, I am glad I bought this Vector Analysis workbook because I am able to review vectors, triple integrals, and line integrals using vectors. This is an excellent workbook for any young student wishing to review their third-semester Calculus to prepare for either physics or engineering.
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I had a 1950s edition of the outline and it was my crutch to get through differential geometry. It is still my go to guide whenever I need to freshen up on vector math. I bought this new edition for my brother and it has more examples and problems, but still the same core information.
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I have a Ph.D. in engineerong and i still use Spiegel's book to learn from. This book is more than an introduction, but he does a great job explaining all problems including the mathematical proofs. If you still have trouble, you should in addition to this book get the rea problem solver on vector analysis. However, once you master the schaums book, all other vector analysis books will seem either elementary to you or much easier to understand.
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Details about Integrated Algebra:
This edition includes the most recent Integrated Algebra Regents tests through August 2014. These ever popular guides contain study tips, test-taking strategies, score analysis charts, and other valuable features. They are an ideal source of practice and test preparation. The detailed answer explanations make each exam a practical learning experience. The book reviews all pertinent math topics, including sets, algebraic language, linear equations and formulas, ratios, rates and proportions, polynomials and factoring, rational expressions and factoring, radicals and right triangles, area and volume, quadratic and exponential functions, and much more.
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Rent Integrated Algebra 1st edition today, or search our site for other textbooks by Lawrence S. Leff. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Barron's Educational Series, Incorporated. | 677.169 | 1 |
NYS Recommended Additions Math Standards for Grades 9-12 ... All of the New York State Mathematics Common ... to prepare students for Algebra I by 8th grade, and Common Core State Standards/CCSS Math 9_12 web.pdf
grade placement of important learning goals across states (Reys, 2006 ... what students should know by the end of a particular course (e.g., Algebra I or Integrated Math I).
Curriculum Overview and Sample Lessons 9th GradeMath ** ... The following book is required for this course: Saxon Algebra I, An Incremental ...
... Section 100.5 Students entering grade 9 in ... Diploma with the following additions: Math B, or Geometry and Algebra ... Since New York State is phasing the local diploma out ... regents graduation requirements.pdf
While the K-7 CCSS effectively prepare students for algebra in 8 th grade, some standards from ... school-wide community of support for students; *Providing students a u0022math ...
... SUMMARY OF 9th GRADE ... course follows the New York State Standards for the new Integrated Algebra ... centers on Math A and B as defined by the New York State Standards.
Integrated Algebra 1 is a new text for high school algebra that continues the ... and mandated by the New York State Board of Regents in the New York State Mathematics ... | 677.169 | 1 |
The Interactive Textbook online takes learning to a new level.
Activities and videos at point-of-use bring math to life.
Reading support with audio helps you reach students struggling with math vocabulary.
Provides the structure students need to take effective notes. Includes daily vocabulary, key concepts, examples, and Check Understanding excercises for every lesson. Student notes make a great study guide for quizzes and tests.
The Teacher's Edition supports your teaching style and needs, mirroring the format of each student page, at its point of use. The Teacher's Edition includes teaching tips, additional resources, lesson planning, test preparation, classroom examples and more!
This convenient package is a real teacher time saver that provides a wealth of resources to meet individual needs and help you reach all students. For ease of use these blackline masters are organized by chapter.
Also included in the Teaching Resources package are: Cumulative Assessment,diagnostic quarterly,mid-year, and final tests,and Solution key.
Solutions for examples, problems and quizzes (this product is INCLUDED in the Teaching Resources package).
This handy workbook contains additional exercises for every lesson so students can practice their skills.
Complete Spanish translation of the regular Practice Workbook | 677.169 | 1 |
Mandatory Package: Calculus (Update) W/ Olc / Edition 2…
See more details below
Hardcover
Temporarily out of stock online.
Overview for the average student — one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.
The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems. | 677.169 | 1 |
The Graphical representation of complex eigenvectors simulation aims to help students make connections between graphical and...
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The Graphical representation of complex eigenvectors simulation aims to help students make connections between graphical and mathematical representations of complex eigenvectors and eigenvalues. The simulation depicts two components of a complex vector in the complex plane, and the same vector under several transformations that can be chosen by the user. A slider allows students to change the second component of the initial vector. The simulation shows whether or not the vector is an eigenvector, and if so displays the associated eigenvalue. The simulation includes a small challenge in asking the student to find the elements of one of the transformation matrices complex eigenvectors to your Bookmark Collection or Course ePortfolio
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The displays the associated eigenvalue. The simulation includes a small challenge in asking students to find the elements of one of the transformation matrices 4 eigenvectors to your Bookmark Collection or Course ePortfolio
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The Matrix Multiplication simulation aims to help students learn how to multiply two matrices and what conditions need to be...
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The Matrix Multiplication simulation aims to help students learn how to multiply two matrices and what conditions need to be fulfilled for the product of two matrices to exist. Students can choose different dimensions for matrices A and B, and the product C=AB is displayed if it exists. Student can select an element of the matrix C to see how it is calculated. An accompanying activity for this simulation is available at and Matrix Multiplication to your Bookmark Collection or Course ePortfolio
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The Quantum key distribution with entangled spin ½ particles simulation aims to help students understand the generation and...
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The Quantum key distribution with entangled spin ½ particles simulation aims to help students understand the generation and distribution of a secure key and how the presence of an eavesdropper can be determined. The simulation shows a source of entangled particle pairs in the middle of two Stern-Gerlach apparatuses (SGAs). The SGAs can be oriented along two orthogonal axes manually or oriented randomly through the simulation. Students can allow an eavesdropper to intercept and resend particles. The measurement outcomes, key bits and the error rate are displayed key distribution with entangled spin 1/2 particles to your Bookmark Collection or Course ePortfolio
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The Entangled spin ½ particle pairs versus an elementary hidden variable theory simulation allows students to assess whether...
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The Entangled spin ½ particle pairs versus an elementary hidden variable theory simulation allows students to assess whether a simple hidden variable theory would agree with measurement outcomes predicted by quantum theory. The simulation shows a source of particle pairs in the middle of two Stern-Gerlach apparatuses (SGAs), one of which can be rotated with respect to the other. The observers measure outcomes of + or – (depicted as flashes on the in the pair have pre-determined opposite spin vectors that are randomly oriented in spaceangled spin ½ particle pairs versus hidden variables simulation allows students to assess whether a simple hidden...
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The Entangled spin ½ particle pairs versus hidden variables simulation allows students to assess whether a simple hidden variable theory would agree with measurement outcomes predicted by quantum theory. The simulation shows a source of particle pairs in the middle of two Stern-Gerlach apparatuses (SGAs), that can each individually be oriented at three axes at 120 degrees to one another. The observers measure outcomes of + or – (depicted as flashes on have pre-determined definite measurement outcomes defined by instruction sets, which also give opposite results whenever both SGAs have the same orientationanglement: the nature of quantum correlations simulation aims to help students determine in what ways entangled states...
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The Entanglement: the nature of quantum correlations simulation aims to help students determine in what ways entangled states differ from product states. The simulation allows students to compare and contrast the correlations that can be observed in product states and in entangled states. The simulation shows a source of particle pairs in the middle of two Stern-Gerlach apparatuses (SGAs), both of which can be rotated along two orthogonal axes. Students can choose between three different input states, one of which is an entangled state, and then send particle pairs through the experiment. The individual and paired measurement outcomes and the correlation coefficient are depicted Collection to their own profile and modify it to save time.
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The Spin-1 particles in successive Stern-Gerlach experiments simulation aims to help students make connections between the vector representation of quantum states for a spin-1 particle and the physical measurement outcomes. The simulation allows students to choose up to two successive Stern-Gerlach apparatuses (SGAs), and change the orientation of the second SGA. The simulation shows the quantum states, the matrix representations of the spin components corresponding to the SGA measurements and the measurement outcome probabilities Spin-1 particles in successive Stern-Gerlach experiments to your Bookmark Collection or Course ePortfolio
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The Uncertainty of spin measurement outcomes simulation aims to help students develop an understanding of quantum uncertainty...
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The Uncertainty of spin measurement outcomes simulation aims to help students develop an understanding of quantum uncertainty by allowing students to send spin ½ particles through up to three successive Stern-Gerlach apparatuses (SGAs), and changing the orientation of the second SGA. The simulation shows the individual measurement outcomes, the measurement outcome probabilities and the uncertainty in the spin measurement outcome of the final SGA of spin measurement outcomes to your Bookmark Collection or Course ePortfolio
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COURSE STRUCTURE
MATHEMATICS
CLASS 6
Number System
(i) Knowing our Numbers:
Consolidating the sense of numberness up to 5 digits, Size, estimation of numbers, identifying smaller, larger, etc. Place value (recapitulation and extension), connectives: use of symbols =, <, > and use of brackets, word problems on number operations involving larg...Read More
COURSE STRUCTURE
CLASS 8
MATHEMATICS
Number System
(i) Rational Numbers:
• Properties of rational numbers.(including identities). Usinggeneral form of expression to describe properties
• Consolidation of operations on rational numbers.
• Representation of rational numbers on the number line
• Between any two rational numbers there lies another rati...Read More
6. MATHEMATICS (Code No 041)
The Syllabus in the subject of Mathematics has undergone changes from time to time in
accordance with growth of the subject and emerging needs of the society. Senior Secondary stage is a
launching stage from where the students go either for higher academic education in Mathematics or for
professional courses like engineering, phy...Read More | 677.169 | 1 |
Details about Content-Area Strategies: Mathematics Grades 7-8:
Prepare students to succeed! Reading, Writing, and Vocabulary Boosts reading comprehension with a variety of reading strategies Contains graphic organizers to clarify thinking and connections Strengthens writing proficiency through practice Includes assessment rubrics Defines and explains important content-area vocabulary
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How do parabolas ellipses and hyperbolas pertain to our world?
Quadratic Formula
This channel is managed by up and coming UK maths teachers. Videos designed for the site by Steve Blades, retired Youtuber and owner of m4ths.com to assist learning in UK classrooms. Designed... … [Read More...]
PowerPoint Math Lessons for Arithmetic, Beginning, Intermediate and College Algebra
1. Lessons are listed by topic.
2. Detailed Examples with explanation of each step as it appears.
3. Practice Problems given during lesson to enhance
comprehension.
Workbooks are available for the above courses. Homework problems with answers are included.
Performing all homework problems will help you gain proficiency on the various topics.
Videos on How-to use various useful features of your
calculator.
Videos on How to use various educational websites | 677.169 | 1 |
Basic College Mathematics Lial/Hornsby developmental mathematics paperback series has helped thousands of students succeed in math. In keeping with its proven track record, this revision includes a sharp new design, many new exercises and applications, and several new features to enhance student learning. Among the features added or revised include a new Study Skills Workbook, a Diagnostic Pretest, Chapter Openers, Test Your Word Power, Focus on Real-Data Applications, and an increased use of the authors' six-step problem solving process.
List of Applications
v
List of Focus on Real-Data Applications
x
Preface
xi
Feature Walk-Through
xvii
To the Student
xxi
Diagnostic Pretest
xxiii
Whole Numbers
1
(106)
Reading and Writing Whole Numbers
2
(7)
Adding Whole Numbers
9
(10)
Subtracting Whole Numbers
19
(10)
Multiplying Whole Numbers
29
(10)
Dividing Whole Numbers
39
(14)
Long Division
53
(10)
Rounding Whole Numbers
63
(10)
Exponents, Roots, and Order of Operations
73
(6)
Reading Pictographs, Bar Graphs, and Line Graphs
79
(6)
Solving Application Problems
85
(22)
Summary
93
(4)
Review Exercises
97
(8)
Test
105
(2)
Multiplying and Dividing Fractions
107
(78)
Basics of Fractions
108
(5)
Mixed Numbers
113
(8)
Factors
121
(8)
Writing a Fraction in Lowest Terms
129
(6)
Multiplying Fractions
135
(10)
Applications of Multiplication
145
(8)
Dividing Fractions
153
(10)
Multiplying and Dividing Mixed Numbers
163
(22)
Summary
173
(4)
Review Exercises
177
(4)
Test
181
(2)
Cumulative Review Exercises: Chapters 1-2
183
(2)
Adding and Subtracting Fractions
185
(62)
Adding and Subtracting Like Fractions
186
(5)
Least Common Multiples
191
(10)
Adding and Subtracting Unlike Fractions
201
(8)
Adding and Subtracting Mixed Numbers
209
(12)
Order Relations and the Order of Operations
221
(26)
Summary Exercises on Fractions
229
(2)
Summary
231
(4)
Review Exercises
235
(6)
Test
241
(2)
Cumulative Review Exercises: Chapters 1-3
243
(4)
Decimals
247
(64)
Reading and Writing Decimals
248
(9)
Rounding Decimals
257
(8)
Adding and Subtracting Decimals
265
(8)
Multiplying Decimals
273
(6)
Dividing Decimals
279
(10)
Writing Fractions as Decimals
289
(22)
Summary
297
(4)
Review Exercises
301
(4)
Test
305
(2)
Cumulative Review Exercises: Chapters 1-4
307
(4)
Ratio and Proportion
311
(54)
Ratios
312
(9)
Rates
321
(8)
Proportions
329
(6)
Solving Proportions
335
(6)
Solving Application Problems with Proportions
341
(24)
Summary
349
(6)
Review Exercises
355
(4)
Test
359
(2)
Cumulative Review Exercises: Chapters 1-5
361
(4)
Percent
365
(100)
Basic of Percent
366
(11)
Percents and Fractions
377
(12)
Using the Percent Proportion and Identifying the Components in a Percent Problem | 677.169 | 1 |
CS208 Discrete Mathematics
for U1M(3) If you are looking for an equation editor, you can try Math Equation Editor, 30-day free trial version found in MathTypeenables students to export or save the symbols into .gif or .jpg format. You can then insert the .gif/.jpg file in the assignments for submission.
You can also write your equations in hardcopy paper, scan your work, and save the file in .gif or .jpg format, and then insert the .gif/.jpg file in the assignments for submission.
For this course, the assessment is based on a final exam. There will be 4 questions in each of the 8 categories, i.e. Synthesis, Analysis,… etc. Thus, there will be 32 questions total in the final exam. Furthermore, all 4 questions for each category should cover all 4 learning outcomes.
You will be able to track your average exactly throughout the course. The grading scale is as follows: A = 90%-100%; B = 80%-90%; C = 70%-80%; D = 60%-70%; F = 0-60%. You will know in advance the standards for each assignment. My goal is to give you prompt, clear, and useful feedback to help you to succeed in this class. Each student is responsible for:
Completing Weekly Reading assignments
Completing Weekly Discussions
Completing Weekly Homework assignments
Completing Weekly Self Checks and Quizzes
Completing a Final Examination. This step is essential!
Completing a Online Survey of Student Opinion of Teaching
Reading Assignments:
Students will be expected to read the assigned chapters in the textbook and the weekly Introduction and Supplement materials. The Online Discussions, Homework Assignments, Self Checks, Quizzes and Final Proctored Examination assume you have read the assigned readings.
Class Participation (Online Discussions):
Students should visit the discussion area and place a minimum 3 constructive posts per week.
Homework, Self Checks, and Quizzes
All assignments (including homework, self checks, and quizzes) should be completed on or before Sunday 11:59 pm Central time. Homework and quiz must be done independently. Do not post answers to quizzes or homework in the discussion threads.
Note that weekly quiz 1 is to be taken on or before 11:59pm Central Time on Friday of the academic week to receive full credit (i.e., 4 points) for each correct answer. Between Saturday 12:00am Central Time and Sunday 11:59pm Central Time, each correct answer in weekly quiz 1 is worth 3 points. Weekly quiz 2 does not have this restriction.
Proctored Examination:
Final Examination - An examination will be taken in person during the 8th week of instruction at one of the Park University sites around the country or at an alternative location approved by the University where Park University sites are not available. It will be the responsibility of the student to arrange for a proctor, by the 6th week, who will be accepted and approved by the instructor. Guidelines for selecting an acceptable proctor can be found at the Park University website. For proctored examinations, photo identification is required at the time of the test. A proctor request form will be made available to you during the first week of class so that you can send your requested proctor to me for approval. Failure to take a final proctored exam (or submit your final project for some online graduate courses) will result in an automatic "F" grade. Some graduate courses may not require a proctored final examination.
Grade Distribution:
Assessments
Points earned each week
Number of Weeks
Total Points
Percentage (%)
Course Home Introduction
4
1
4
0.3%
Course Home
Self Check
15
1
15
1.3%
Weekly Discussion
12
7
84
6.9%
Weekly Homework
12
7
84
6.9%
Weekly Self Checks
30
7
210
17.3%
Weekly Quizzes
80
7
560
46.2%
Final Exam
256
1
256
21.1%
Total
1213
100%
Course Grading Scale:
This subsection should list the grading scale and weighting for all of the graded work during a course. The grading scale must use the following scale below, and point totals for each letter grade must be included (see example below).
Letter
Points
Percentage
A
1091-1213
90-100 %
B
970-1090
80-89 %
C
849-969
70-79 %
D
727-848
60-69 %
F
Below 727
Below 60 %
Late Submission of Course Materials:
All assignments and quizzes must be completed by 11:59 pm Central Time on Sunday of the academic week. There will be 20% penalty for each day that a homework is turned in late. Students are not allowed to take a quiz that is scheduled beyond its due date.
Classroom Rules of Conduct:
Course Topic/Dates/Assignments:
Week 1: Introduction to Discrete Mathematics as well as the concepts of combinatorial problems and techniques.
Week 2: Mathematical Functions and Induction, and Logic.
Week 3: Recurrence Relations and Algorithm.
Week 4: Combinatorial Circuits and Binary Number System.
Week 5: Graphs.
Week 6: Trees.
Week 7: Counting Techniques.
Week 8: Review and FinalStudents are responsible for clicking on the link below and thoroughly reading each Online course policy. If you have questions about any of these policies, please contact your instructor for clarification. | 677.169 | 1 |
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Details about Mathematics and Cognition:
This book, which was first published in 1990, is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view. The book describes research findings that shed light on the learning of mathematics from early arithmetic to high levels of algebra and geometry. The book is the collaborative effort of a number of members of the International Group for the Psychology of Mathematics Education and primarily describes their work whilst at the same time covering many issues that interest researchers in mathematics education.
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A seminar course required as a culminating experience for mathematics majors who are seeking certification to teach at the elementary, middle or secondary levels. Students analyze problems from elementary, middle and high school mathematics from an advanced perspective and explicitly make connections between the concepts taught in elementary, middle and secondary and their more abstract analogues encountered in undergraduate mathematical courses. A grade of C or higher is required. Prerequisites: Senior standing, admission to the Teacher Certification Program, EDUC 358 or EDUC 359 or EDUC 360.
Apply mathematics to solve a variety of real world problems in other disciplines.
Describe topics from calculus from graphical, numerical, and analytical perspectives.
Make connections between topics taught in elementary, middle, and high school mathematics and topics studied in undergraduate mathematics courses.
Major Topics/Skills to be Covered:
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This original volume offers a concise, highly focused review of what high school and beginning college students need to know in order to solve problems in logarithms and exponential functions. Numerous rigorously tested examples and coherent to-the-point explanations, presented in an easy-to-follow format, provide valuable tools for conquering this... more...
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Students and others wishing to know more about the practical side of mathematics will find this volume a highly informative resource. Accessible explanations of important concepts feature worked examples and diagrams. 1963 edition. more...
Any child can overcome the disadvantages of mediocre math teaching in school and parental math anxiety at home. Math Power offers easy-to-follow and concrete strategies for teaching math concepts. These lively techniques ? including games, questions, conversations, and specific math activities ? are suitable for children from preschool to age 10.... more... | 677.169 | 1 |
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Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes,... | 677.169 | 1 |
Algebra for College Students (4th Edition)
The unifying theme of this text is the development of the skills necessary for solving equations and inequalities, followed by the application of those skills to solving applied problems.
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How to Count: An Introduction to Combinatorics, Second Edition (Discrete Mathematics and Its Applications)
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A traditional coverage of Beginning and Intermediate Algebra, covering linear equations, graphing, inequalities, systems of equations, polynomials, factoring, rationals, radicals, quadratics, and... More > functions. A free download of the text, and a student solutions manual and workbook are available at This book contains complete daily lesson plans for Teachers of Intermediate Algebra. A sequential script for the Teacher, adaptable for classes of various and diverse abilities, is presented with... More > optimum order of topics, and includes graduated explained illustrative examples, enrichment, review, practice tests, and tests. These lesson plans can be used with any textbook; just add homework from the class text.< Less
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1. Introduction: The GeoGebraWiki and User Forum
Dynamic Worksheets
GeoGebra allows you to create your own interactive instructional materials, so called dynamic worksheets, by exporting dynamic figures into web pages. Usually, a dynamic worksheet consists of a heading, short explanation, interactive applet, as well as tasks and directions for your students. In order to work with dynamic worksheets your students don"t need to know how to operate GeoGebra at all. The interactive web pages are independent of the software and can be provided either online or on a local storage device.
The GeoGebraWiki
The GeoGebraWiki ( is a pool of free instructional materials (e.g. dynamic worksheets) that were created by teachers from all over the world. There are different wikis for several languages (e.g. German, English, French) in order to organize their content and make them easier to access.
All materials on the GeoGebraWiki are under a Creative Common License ( This means that you are allowed to use them for free, non-commercial use, and that you can create derivative work if you give credit to the original author.
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GeoGebra Workshop Handout
The GeoGebra User Forum
The GeoGebra User Forum ( was created to offer additional support for the community of GeoGebra users. Created for teachers and maintained by teachers, it is a platform to pose and answer questions related to GeoGebra.
The GeoGebra User Forum consists of several discussion boards in different languages allowing users to post and answer their GeoGebra related questions in their native language.
2. Lower and Upper Sum
You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between a function and the x-axis, which can be used to introduce the concept of integral to students.
Preparations
Open a new GeoGebra file. Show the algebra window, input field, and coordinate axes (View menu).
Task
Use slider n in order to modify the number of rectangles used to calculate the lower and upper sum. 1. Compare the values of the upper sum / lower sum to the value of the integral for different values of slider n. What do you notice? 2. What happens to the difference of the upper and lower sum (a) if n is small (b) if n is big?
4
GeoGebra Workshop Handout
3. Creating Dynamic Worksheets
Reducing the size of the GeoGebra window
GeoGebra will export the algebra and graphics window into the dynamic figure of the worksheet. In order to save space for explanations and tasks on the dynamic worksheet you need to make the GeoGebra window smaller prior to the export. If you don"t want to include the algebra window you need to hide it prior to the export. Move your figure (or the relevant section) to the upper left corner of the drawing pad using the Move drawing pad tool (see left figure below). Hint: You might want to use tools Zoom in and Zoom out in order to prepare your figure for the export process. Reduce the size of the GeoGebra window by dragging its lower right corner with the mouse (see right figure below). Hint: The pointer will change its shape when hovering above an edge or corner of the GeoGebra window. Note: Although the interactive applet should fit on one screen and even leave some space for text on the worksheet you need to make sure that it is big enough to allow students manipulations and experiments.
Exporting a dynamic worksheet
After adjusting the size of the GeoGebra window, you are now ready to export the figure as a dynamic worksheet using the File menu. Export – Dynamic Worksheet as Webpage Hint: You could also use the key combination Ctrl – Shift – W.
Fill in the text fields in the appearing window (title of the worksheet, name of the author, and date).
5
GeoGebra Workshop Handout
Type a short explanation of the dynamic figure into the text field Text above the construction. Enter tasks and directions for students into the text field Text after the construction. Click Export and save your dynamic worksheet. Hint: GeoGebra will create several files which always need to stay together in order to maintain the functionality of the dynamic worksheet. We recommend creating a new folder (e.g. worksheets) prior to saving your dynamic worksheet.
Some useful information
After saving the dynamic worksheet it will be automatically opened in your web browser. Check the text you inserted as well as the functionality of the interactive applet. If you want to change your dynamic worksheet go back to the GeoGebra file and make your changes to the figure. Export the figure again (you can use the same file name to overwrite the old worksheet) in order to apply your changes. Hint: You can change the text of the dynamic worksheet in the same way. GeoGebra automatically saves your entries in the export window for dynamic worksheets. If you want to make changes to your figure while filling in the export dialog you can just close it and continue later on. You can save several dynamic worksheets into the same folder. Thereby, the files with the extension .jar are just created once in this folder. If you want to provide one of the dynamic worksheets to your students you need to copy the jar-files in addition to the corresponding ggb- and html-files.
6
GeoGebra Workshop Handout
4. Enhancing Dynamic Worksheets
The export dialog window for dynamic worksheets consists of two tabs: General and Advanced. In the last activity you used tab General in order to add explanations, tasks, and directions to the dynamic figure prior to the export. You will now learn how to enhance your dynamic worksheet by including different features in the interactive figure using the tab Advanced.
Functionality
Right click enabled: Your students will be able to right click objects or the drawing pad in order to access the features of the context menu (e.g. show / hide object or label, trace on / off, Properties dialog). Show icon to reset construction: A reset icon is displayed in the upper right corner of the interactive applet allowing your students to reset the interactive figure to its initial state. Double click opens application window: Your students will be able to open a full GeoGebra window by double clicking the interactive applet.
User interface
Show menubar: The menubar is displayed within the interactive applet. Show toolbar: The toolbar is displayed within the interactive applet and allows your students to use the geometry tools. Show toolbar help: In combination with the toolbar, you can also display the toolbar help within the interactive applet. If you want your students to
7
GeoGebra Workshop Handout
use geometry tools they can use the toolbar help in order to find out how to operate the different tools on their own. Show input field: The input field is displayed at the bottom of the interactive applet allowing your students to use algebraic input and commands for their explorations. Width and height of the interactive applet: You can modify the width and height of the interactive applet. Note: If you reduce the size of the applet important parts of the dynamic worksheets might be invisible for your students. Hint: If you include the menubar, toolbar, or input field the height of the interactive applet is increased automatically.
Task
Use the dynamic figure you created earlier and export it as an enhanced dynamic worksheet. Use the Advanced tab to try out different options and check how the applet of your dynamic worksheet is changed accordingly.
5. Providing Dynamic Worksheets to Students
You can provide your dynamic worksheets in several ways to your students. However, in all cases it is very important to keep all the files together which were created during the export process. Note: The files created have different file name extensions (.ggb, .html, .jar). If one of these files is missing your dynamic worksheet won"t function any more.
Local storage device
Copy all files into the same folder before saving this folder on a local storage device (e.g. flash drive, CD). Have your students copy the whole folder on their computers. Your students need to open the file with the name extension .html in their Internet browser.
Via Internet
If you want to provide your dynamic worksheet online you need to upload ALL files to the same location on a web server. After uploading your files to a web server you can provide a hyperlink on your personal website or tell your students how to directly access the worksheet using the address field of an Internet browser.
8
GeoGebra Workshop Handout
The GeoGebra Upload Manager
If you don"t have your own web space, we have made it easy for you to upload your dynamic worksheets to a web server. It is called the GeoGebra Upload Manager ( After creating a user account you can upload your files to your assigned folder. Since the GeoGebra Upload Manager was specially created for dynamic worksheets you ONLY need to upload the files with the extension .html and .ggb (and NOT the .jar files). Create your own account 1. Access the GeoGebra Upload Manager 2. Click on Login (upper right corner of the browser window) 3. Click on Register and enter a username, password, and your email address. Note: You will get an email confirming your registration. It contains an activation code for your account. 4. Check your email and copy the activation code. Click the link provided in the email in order to access the account activation web page. 5. On the account activation web page enter your username and paste the activation code into the corresponding text field. Click Activate account. Create your personal upload folder 1. Login to the GeoGebra Upload Manager. 2. Look for the folder called "english" and open it. 3. Create your personal upload folder within the "english" folder (e.g. Lastname_Firstname). Hint: Scroll down to the end of this page and fill in the text field below the heading Create new directory. Click Make dir. 4. Note: You can create new folders within your personal upload folder in order to organize your uploaded files. Upload your files and provide them to your students 1. Look for your newly created personal upload folder and open it. 2. Scroll down to the end of this page until you can see the heading Upload File. 3. Click the Browse button. Navigate through the folders on your computer until you find the file you want to upload. Select the file and click Open. 4. Enter a file description into the corresponding text field. 5. Click Upload File. 6. Note: If you want to provide a dynamic worksheet to your students, you need to upload the corresponding .ggb file as well as the .html file to your personal upload folder. You don"t need to upload the .jar files! 7. Look for the file you just uploaded into your personal upload folder. Right click the file name (MacOS: Ctrl-click) and select Copy Link Location
9
GeoGebra Workshop Handout
from the appearing menu. Note: The web address of your file is copied to your clipboard. 8. Provide the link to your students: Paste the web address of your file into a text processing document or use it in order to create a link to your file on your personal web page. Your students will need the link address in order to access your files.
6. Visualizing Triangle Inequalities
You will now create a dynamic worksheet that illustrates the construction steps for a triangle whose three side lengths a, b, and c are given. Additionally, this worksheet will allow your students to discover triangle inequalities. Note: The triangle inequalities a b c , b c a , and a c b state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.
Preparations
Open a new GeoGebra file Hide the algebra window, coordinate axes, and input field (View menu).
Introduction of new tools
Segment with given length New! Hint: First click determines the starting point of the segment. Enter the length of the segment into the appearing text field. Circle with center and radius New! Hint: First click determines the center of the circle. Enter the length of the radius into the appearing text field.
Hints: Don"t forget to read the toolbar help if you don"t know how to use a tool. Try out new tools before you start the construction.
10
GeoGebra Workshop Handout
Instructions
1 2 3 Sliders a, b, and c for the side lengths of the triangle Set the sliders to a = 8, b = 6.5, and c = 10 Segment d with given length c Hint: Points A and B are the endpoints of the segment. 4 5 6 7 8 Circle e with center A and radius b Circle f with center B and radius a Intersection point C of the two circles e and f Triangle ABC Interior angles α, β, and γ of triangle ABC
Enhancements
Prepare your triangle construction for the export as a dynamic worksheet. 9 10 11 12 13 14 15 16 17 18 19 Point D on circle e Segment g between points A and D Midpoint E of segment g Enter text1: "b" and attach it to point E Point F on circle f Segment h between points B and F Midpoint G of segment h Enter text2: "a" and attach it to point G Match colors of corresponding objects. Show the Navigation bar (View menu). Open the Construction protocol and show column Breakpoint (View menu of the Construction protocol dialog)
11
GeoGebra Workshop Handout
20
21
Change the order of construction steps so that the radii of the circles and the attached text show up at the same time. Hint: You might also set some other breakpoints (e.g. show all sliders at the same time). In the View menu of the Construction protocol dialog check Show breakpoints only.
Tasks
(a) Export your triangle construction as a dynamic worksheet. (b) Come up with explanations and tasks for your students that guide them through the construction process of the triangle and help them explore the triangle inequalities by modifying the given side lengths using the sliders.
7. Design Guidelines for Dynamic Worksheets
The following design guidelines for dynamic worksheets are the result of a formative evaluation of dynamic worksheets created by teachers in our NSF MSP classes during fall 2006 and spring 2007. The guidelines are based on design principles for multimedia learning stated by Clark and Mayer1. These guidelines were summarized to address and avoid common mistakes during the creation process of dynamic worksheets as well as to increase their quality with the hope that they will foster more effective learning. Although some of these guidelines may seem obvious, we have found it very important in our work with teachers to discuss and explain them in detail. The following figure shows an entire dynamic worksheet created with GeoGebra that allows students to explore properties of the orthocenter of a triangle. By modifying the dynamic construction students can examine the orthocenter of a great variety of triangles instead of just one special case. Several key words within the explanation and tasks match the color of the corresponding objects in order to facilitate finding them within the construction. Furthermore, the tasks are placed next to the dynamic construction in order to fit all information on one screen and avoid additional cognitive load through scrolling.
1
Clark, R. and Mayer, R.E. (2002): e-Learning and the Science of Instruction. San Francisco: Pfeiffer, 2002
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GeoGebra Workshop Handout
Design Guidelines 1: Layout of Dynamic Worksheets
Avoid scrolling Your entire worksheet should fit on one screen. Students should not have to scroll between the tasks and the interactive figure. We consider 1024x768 or 1280x1024 pixels as today's usual screen size which constrains the size of the dynamic worksheet. Using an HTML editor like NVU you can use tables to arrange text, images, and interactive figures so they fit on one screen. If this is not possible, consider breaking the dynamic worksheet into several pages. Short explanation At the beginning of a dynamic worksheet, you should give an explanation of its content. Keep the text short (no more than one or two sentences) and write it in a personal style. Few tasks You will usually add questions or tasks to make sure that your students use the worksheet actively. Place these tasks close to the interactive applet (e.g. directly below it). Don't use more than three or four questions / tasks to avoid scrolling. If you have more tasks, consider breaking your worksheet into several pages. Avoid distractions Make sure that your dynamic worksheet just contains objects that are relevant for the objectives. Neither use unnecessary background or purely decorative images, nor background music on the web page in order not to distract your students from reaching the objectives.
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GeoGebra Workshop Handout
Design Guidelines 2: Dynamic Figures
Interactivity Allow as much interactivity as possible in your dynamic figure. As a rule of thumb, all visible objects should be movable or changeable in some way. Your dynamic figure should provide plenty of freedom to explore the relations of its mathematical objects and discover mathematical concepts. Easy-to-use Try to make your dynamic figure as easy to use as possible. If an object can be moved or changed, try to make this obvious, e.g. all movable points could be red or larger in size. If you don't want objects to be changed, fix them (e.g. text, functions or slider positions) so they cannot be moved accidentally. Size matters Your dynamic figure should be large enough to allow all intended manipulations, but small enough to fit on one screen and still leave sufficient space for explanations and questions on the surrounding web page. Use dynamic text Dynamic text, like the length of a changeable segment, should be placed close to the corresponding object in your applet). Avoid static text Too much text can easily clutter your interactive applet. Instead, place static text like explanations or questions on the web page that includes your dynamic figure. First appearance When a dynamic worksheet is opened you should be able to read all labels and important information. For example, a point label should not be crossed by a line.
Design Guidelines 3: Explanations and Tasks
Short, clear and personal style Try to write your explanations and questions in a short, clear and conversational style. Use the term "you' within the text and try to address the students directly.
14
GeoGebra Workshop Handout
Small number of questions Limit your number of questions or tasks per worksheet to three or four to avoid scrolling. If you want to ask more questions, create a new worksheet. Use specific questions Avoid general questions like "What is always true about X?' and make clear what the students should do, e.g. `What happens to X when you move Y?'. We recommend that your students should take notes while they work with a dynamic worksheet. If you want them to write down their answers on paper, say so on the worksheet. Refer to your applet Your text should support the use of your interactive applet. For example, try to explain a new term by referring to your applet instead of using an isolated textual definition. Additionally, you can color certain keywords to match the formatting style of the object they refer to. This makes the text easier to read and helps your students to find corresponding representations of the same object. Your audience are learners If you want to provide information for other educators (e.g. lesson plan, solutions) do so in a separate document (e.g. web page, pdf-document). Your students should not be distracted or confused by such information. Demonstration figure If your interactive figure is meant for presentation only it might be better to have no tasks or questions on the web page. If you include text, it should be understandable for students as well.
8. Creating a 'Tangram' Puzzle
In this activity you will create the "Tangram" puzzle shown at the right hand side. It consists of 7 geometric shapes which can all be constructed using the side length a of the main square. Check out the dynamic worksheet 11_tangram_puzzle.html in order to find out how a "Tangram" works.
15
GeoGebra Workshop Handout
Task 1: Figure out the side lengths of each part
In order to construct the parts of the "Tangram" puzzle you need to figure out the individual side lengths of the seven geometric figures first. They all depend on the side length a of the main square. Hint: In some cases you might want to look at the diagonals or height. Their lengths can be expressed more easily using the variable a than the lengths of the corresponding sides.
Task 2: Construct the individual parts of the 'Tangram'
1. Enter the number a = 6. It will provide a basis for the construction of all triangles and quadrilaterals necessary for your "Tangram" puzzle. 2. Begin each of the geometric figures using a segment with given length. This will allow you to drag and rotate the figure later on. Hint: You need to figure out the side lengths of the geometric shapes before you are able to construct them in GeoGebra. 3. Construction hints: a. If the height of a right triangle is half the length of the hypotenuse you might want to use the theorem of Thales for the construction (see practice block 1). b. If you know the legs of a right triangle you might want to construct it similar to the square construction presented earlier. c. For constructing a square using its diagonals, it is helpful to know that they are perpendicular and bisect each other. d. For constructing the parallelogram it is helpful to know the size of the acute angle. 4. Check your construction by trying out if you can manage to create a square with side length a using all figures. 5. Arrange the geometric shapes arbitrarily around the edges of the interactive applet. Export the figure to a dynamic worksheet and add an explanation for your students.
9. Challenge of the Day: Enhance Your 'Tangram' Puzzle
With these geometric shapes other figures than a square can be created as well. Search the Internet for a "Tangram" figure other than a square (e.g. 12_tangram_cat.png) and import this figure into the drawing pad. Export the GeoGebra construction again using a different name and different instructions (see 13_tangram_puzzle_cat.html). | 677.169 | 1 |
Thorofare CalculusAllen B.
...The subject of calculus covers a lot of material and usually requires multiple semesters. The topics include all of those in precalculus but in much greater depth. The central theme is the notion of a limit, and how it leads into the concept of derivatives and integrals | 677.169 | 1 |
Superconductivity is a quantum phenomenon that manifests itself in materials showing zero electrical resistance below a characteristic temperature resulting in the potential for an electric current to run continually through such a material without the need for a power source. Such materials are used extensively in medical and power applications, e.g.... more...
Containing exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing proofwriting. Facilitating effective and active... more... | 677.169 | 1 |
Canoga Park StatisticsKathy Z.
...Focused instruction can make a huge difference in your outcome. Finite Math may contain a number of math topics, depending on the course. For example, it can include combinations and permutations, probability, etc. | 677.169 | 1 |
Find aIt's the gateway to more advanced mathematics and the foundation for many other courses in mathematics and science. I have taught it many times in a community college setting. I was an actuary for about 7 years. | 677.169 | 1 |
Download
Chapter 7: Roots, Radicals, and Function Operations
Introduction
This chapter extends what we have learned about polynomials and exponents and applies those ideas to square root and cubed root functions. First, we will introduce rational exponents and simplify these expressions. We will also solve equations with radicals and rational exponents. Then, we switch gears a little and learn how to find the inverse of a function as well as how to add, subtract, multiply, divide, and compose them.
Chapter Summary
Summary
This chapter covers roots, radicals, and rational exponents. We will simplify expressions, graph, and solve equations with all of these types of operators. Lastly, we will learn how to find the composition of a function and the inverse of a function. | 677.169 | 1 |
Steps
Learn the basic steps to powering on, and turning off your device. To turn on your device, press the On button, which can be found at the bottom-left corner of the device. To turn off your device, press the yellow 2nd (function) key followed by the same "On" button you used to turn the device on.
Learn what the 2nd button controls. Any yellow-colored text that exists on the device, requires the use of the 2nd (function) key before the keystroke you are about to perform. The text is located over-top of the key you'll need to press.
Learn what the 3rd button controls. Any green-colored text that exists on the device, requires the use of the 3rd (function) that exists before the keystroke you are about to perform. The text that is located, is what is over-top of the key you'll need to press.
Know how to type in alphabetical letters on the calculator. The purple "alpha" key, will allow you to type these in (with the exception of the letters/variables X, Y, and Z (which have their own buttons).
6
Know how to type in standard solutions to basic math problems. In the bottom right hand corner (or close to it) contains the operator's you'll need (+, -, * and /).
Learn how to read the display. The display on the TI-89 calculator is a two-part display. The left-hand side contains the problem as you typed it in. The right-hand side contains the solution. If you've typed in the question correctly, it shouldn't return back the same answer as a question. However, it's happened many times to the first-time user this has other things you can do with the device. This list is never-ending.
Learn some later procedures of how to use the graphing functions, by following some of the directions in the thick white User's Manual that came along with the device.
There is a backspace key located on the device.
Warnings
These calculators cost a bundle of money ($100-200(US))[1]. If you're in college and seem to not be making too much money, this may seem like a fortune. But if you are a master planner who needs one daily, this may seem like not much money.
The equals sign on the calculator is only a symbol. It doesn't have any effect on grabbing a calculation like an equals sign does on most other calculators.
Sometimes, the calculator won't give you an approximate answer. You'll have to do a little more work to find this answer. Press the diamond key, then the enter key[2] in lieu of just the enter key alone (as you should see by the green symbol above the enter key on the | 677.169 | 1 |
Numerical models are mathematical models that use some sort of numerical time-stepping procedure to obtain the models behavior over time. The mathematical solution is represented by a generated table and/or graph.
For example,
A model of personal savings that assumes a fixed yearly growth rate, r, in savings (S) implies that time rate of change in saving d(S)/dt is given by,
d(S)/dt= r (S) eqn. 1
(this example is also used to discuss analytical models so that numerical and analytical models can be compared and contrasted more easily).
An example of a numerical solution to this fundamental differential equation is given shown in Table 1 along with the corresponding values from the analytical solution, S=SoEXP(rt).
The numerical values in the Table 1 are generated by using the difference equation,
S(t+dt) = S(t) + d(S) = S(t)+ r S(t) dt = S(t) [1+ r dt] eqn. 2
and assuming r=0.10 (1/yr) and a time step, dt, of one month (0.083 yr) for illustration. Since the change in savings, d(S), is rather small each time step this numerical solution agrees fairly well with the analytical solution.
Table 2 compares numerical and analytical results for r=2.0 (1/yr) and dt=0.083 yr). After 1 year there is a significant discrepancy between the numerical solution and the analytical (exact) solution. A smaller time step would be required to get better agreement between the numerical solution and the analytical solution. Using a time step of 0.01 yr gave a savings value of $724.46 with 100 numerical calculations compared with the exact result of $738.91.
This highlights a drawback of numerical solutions to model equations; to get good results many iterative calculations may be required. With fast computer speeds available today this is not really an issue for most model equations that one would explore in an introductory geoscience course. In addition, the precision can be greatly improved for a given time step by using a numerical procedure which is more sophisticated than the rather simple Euler's method described by eqn 2.
Numerical solutions have several advantages over analytical solutions. First, the equations are much more intuitive. Students can clearly understand the meaning of eqn 2 and can generate Table 1 by hand or by using Excel. The exponential form of the analytical solution is clear to those with strong mathematics skills but not so clear to others. Second, the basic procedure
S(t+dt) = S(t) + d(S) is the same regardless of how complicated the formulas are which describe d(S). This is not true of analytical solutions as it is relatively easy to get into mathematics which is much too complicated to obtain analytical solutions. Thus more realistic models of greater complexity can be investigated using numerical techniques.
For introductory geoscience courses regardless of whether one uses analytical solutions or numerical solutions to model equations students should still use graphical output, animations, and tabular data to interpret, understand, and explain model behavior. There are three primary venues for introductory geoscience models Excel, Stella II, and JAVA type interactive web based activities. Excel is great for graphing and exploring analytical models and can be used quite successfully for numerical solutions (this may involve copying your basic formulas down to hundreds of rows). Stella only uses numerical procedures and it has some options for which numerical procedure to use. JAVA type interactive Web activities use graphical output, animations, and tabular data to display the results of solving the model equations and hence the question of whether the programmer used an analytical or numerical solution becomes academic.
Other Information
This site about Euler's Method (more info) uses an exponential growth model similar to ours. It has an interactive JAVA type graph that lets one explore the effects of time step variations on the solution. | 677.169 | 1 |
Algebra and Trigonometry Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Trigonometric Functions; Exponential and Logarithmic Functions; Analytic Geometry; Analytic Trigonometry; Counting and Probability; and more. For individuals with an interest in learning algebra and trigonometry as it applies to their everyday lives. | 677.169 | 1 |
Details about Practical Problems in Mathematics:
Practical Problems in Mathematics for Welders, 5E, takes the same straightforward and practical approach to mathematics that made previous editions so highly effective, and combines it with the latest procedures and practices in the welding industry. With this comprehensive, instructional book, readers will learn how to solve the types of math problems faced regularly by welders. Each unit begins with a review of the basic mathematical procedures used in standard operations and progresses to more advanced formulas. With real-world welding examples and clear, uncomplicated explanations, this book will provide readers with the mathematical tools needed to be successful in their welding careers. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
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Rent Practical Problems in Mathematics 5th edition today, or search our site for other textbooks by Cecie Starr. Every textbook comes with a 21-day "Any Reason" guarantee. Published by CENGAGE Learning. | 677.169 | 1 |
Math Summer Institute Wednesday, July 17, 2013 9:00 AM to 3:00 PM
The University of St. Thomas Summer Institute of Mathematics (UST-SIM) is a one-week program open to 20 students. It is designed to enrich and build upon concepts learned in algebra and geometry.
The critical thinking skills of students will be further developed through solving problems, applications and a project. Concepts presented during the program will also introduce students to the art of mathematical thinking.
All students who are accepted to the program should be familiar with concepts from Algebra I and Geometry. Students should know how to solve equations, triangle relations, and how to find areas and volumes | 677.169 | 1 |
Precalculus Enhanced With Graphing Utilities / Edition 3…
See more details below
Hardcover
Temporarily out of stock online.
Overview material at the correct pace-with an appropriate emphasis on the technology as a tool and mathematics as the subject.
9. Analytic Geometry. Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes; General Form of a Conic. Polar Equations of Conics. Plane Curves and Parametric Equations. Chapter Projects. Cumulative Review.
13. A Preview of Calculus: The Limit, Derivative, and Integral of a Function. Finding Limits Using Tables and Graphs. Algebra Techniques for Finding Limits. One-sided Limits; Continuous Functions. The Tangent Problem; the Derivative. The Area Problem; the Integral. Chapter Projects. Cumulative Review. | 677.169 | 1 |
COURSE DESCRIPTION/STUDENT LEARNING OUTCOMES: 3-0-3 Prerequisite: Satisfactory placement scores/MATH 0099. This course is a functional approach to algebra that incorporates the use of appropriate technology. Emphasis will be placed on the study of functions and their graphs; inequalities; and linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions. Appropriate applications will be included. Students receive credit toward graduation for only one of the following courses: MATH 1001, MATH 1111. Students completing this course should satisfy the following goal and learning outcomes: Students will analyze and apply mathematical information, concepts, and principles, embedded in verbal, numerical, graphic, or symbolic representations.
1) Students will be able to solve equations.
2) Students will be able to graph and interpret functions.
3) Students will be able to model problem contexts mathematically to arrive at solutions.
4) Students will be able to use appropriate technology
5) Students will be able to use logical, mathematical reasoning.
6) Students will be able to appropriately express numbers in a variety of ways, given context.
7) Students will be able to appropriate express algebraic expressions in a variety of ways, given context.
8) Students will be able to interpret data presented graphically.
9) Students will be able to make appropriate graphs to summarize data.
10) Students will be able to use set notation and concepts.
11) Students will be able to perform set operations.
12) Students will be able to calculate and interpret the meaning of rates of change.
"An important note for students enrolled in both MATH 1111 and MATH 0099c:
Students enrolled in both MATH 1111 and MATH 0099c are expected to attend each and every class session of both courses. After three absences in the MATH 0099c co-requisite course, students may be referred to the dean of Academic Success and eLearning. After three absences in the MATH 1111 course, students may be referred to the dean of Mathematics. In either case, after consulting with the appropriate academic dean, students may be withdrawn from their MATH 1111 course."
Grading System: A 100 – 90
B 89 – 80
C 79 – 70
D 69 – 60
F 59 – 0
Final grade will be determined by the average of the three test grades. Work in My Math Lab can be used to replace the lowest test grade.
Students who simply quit attending class without officially withdrawing will receive a grade of F in the course.
Mid-Term Date (Last day to withdraw with a "W"): The last day to drop the class and possibly receive a "W" is Tuesday July 8, 2014. After this date, a "W" may be issued only in cases of documented hardship (which does not include performing poorly in this class). Forms will be available beginning the day after the mid-summer from the office of the Vice President of Academic Affairs or satellite site offices.
Make-up tests will not be given.
Attendance Policy: Students are expected to attend each and every scheduled class session. Since lectures begin promptly at the scheduled time, students are encouraged to avoid arriving late to class. Roll will be taken at each class session. There is no distinction between "excused" and "unexcused" absences.
Extended Absence Policy: Students, who have circumstances that prevent them from continuing to attend classes over an extended period of time, sometimes request that the faculty member permit them to submit work in absentia to receive credit to complete the course. If the concurrent absences will constitute more than 15% (5 class meetings) of the class sessions for the term, then written permission from the Academic Dean is required before any course assignments can be completed while missing class. The student must be in good academic standing in the course to make the request. All approved coursework must be completed by the end of the semester in which the course was begun (NOTE: If a program has a more stringent absence policy than this, then the program policy prevails.).
Exam Make-Up Policy: At the end of the semester, all students have the option of replacing their lowest exam grade (including any missed exams) with their grade on the comprehensive final exam. At most one exam grade will be replaced. Students will receive a grade of zero for additional missed exams.
Access to e-mail and Internet resources --Your email account through Desire - 2- Learn is the official form of communication. The secondary form of communication will be your GHC e-mail.
Each student taking this course needs access to a TI-84, TI-83, or equivalent graphing/scientific calculator. Students will use their calculators while participating in class, taking exams, and completing homework exercises. Please note that sharing calculators during tests is not permitted.
Assignments: Assignments will be given in class and in MyMathLab at the discretion of the instructor. You are expected to STUDY, to work problems, to read the assigned material, to take assigned tests on the assigned date, to complete MyMathLab assignments, and to come prepared to class. An opportunity to ask questions will be provided each class meeting.
Early Warning Program: Georgia Highlands College requires that all faculty members report their students' progress throughout the course of the semester as part of the institution-wide Early Warning Program (EWP). The objective of the program is to support academic success by reviewing early indicators of satisfactory student progress. In accordance with EWP, faculty members provide the Registrar's Office with academic reports of each student enrolled in their course(s) at checkpoints staggered throughout the semester. The following success factors are reported at their corresponding checkpoint:
Week 1: Notification of Non-attendance
Week 4: Mid-term Grades
Policies on student conduct and academic integrity: Cheating (or even the appearance of cheating) will not be tolerated in this course. If the instructor suspects a student of cheating, the instructor will notify the student of the allegations outside of class. Then, the allegations will be referred to the Director of Student Life for appropriate action. Policies on student conduct and academic integrity are in the College's "Student Rights & Responsibilities" document. This can be accessed by including on the syllabus the following URL:
Disability Statement: If anyone in the class feels that he/she needs accommodation due to a disability, please feel free to discuss this with the instructor early in the term. Georgia Highlands College has resources available for students with certain disabilities. Accommodations may be made (such as providing materials in alternative formats, assuring physical access to classrooms or being sensitive to interaction difficulties that may be posed by communication and/or learning disabilities) through Student Support Services on all campuses. For more information please contact: Cartersville 678-872-8004; Douglasville and Floyd 706-368-7536; Marietta 678-915-5021; Paulding 678-946-1029.
Early Grades: GHC offers a variety of part-of-term classes to allow our students to have flexible schedules. However, there are only three Semesters each year; Spring, Summer and Fall. It is only at the end of each Semester that grades are rolled to academic history and available on the official transcript. After each part-of-term, as soon as Instructors have entered grades, they may be viewed online by logging into the SCORE ( Transcripts may also be request at any time by logging into the SCORE. Prior to the end of term, should a student need an early grade letter sent to another institution they may complete the request form and submit it to the Registrar's Office for processing ( Please contact the Registrar's Office at registrar@highlands.edu if you need any assistance.
Financial Aid Statement: This message applies only to students receiving financial aid: Federal regulations state that if a student did not attend classes and received failing grades, then the grades were not earned and financial aid needs to be reduced accordingly. Please be advised that any student receiving a 0.00 GPA will be required to prove that the 0.00 GPA was earned by attending classes or completing requirements for each class. Students who have earned at least one passing grade for the semester will not be affected by this regulation. If a student has properly withdrawn from all classes, the student's financial aid should be adjusted from the time they signed the withdrawal form.
Children on Campus Policy: Children of currently enrolled students are allowed on campus only with the direct supervision of that parent. Children will not be allowed to roam the campus or be left unattended by their parent at any time nor at any location. In most cases, I will not allow children to attend class. I will make an appointment with the parent and discuss the material taught in the class that the parent missed. The attending parent will assume responsibility for the behavior of the child. Children are to follow the same conduct rules of reasonable behavior that apply to regular Georgia Highlands' students.
Please keep your cell phones on vibrate. Do not disrupt the class with a ringing phone. Please do not text during class.
Note: We will have a lot of material to learn in this course and we will have to move swiftly. Do NOT fall behind. Be sure to take advantage of the Tutorial Center if you need it. Other classmates will also prove to be valuable resources.
NO FOOD OR DRINK IS ALLOWED IN ANY CLASSROOM OF GEORGIA HIGHLANDS COLLEGE. | 677.169 | 1 |
Algebra
9780387953854
ISBN:
038795385X
Edition: 3 Pub Date: 2002 Publisher: Springer Verlag
Summary: " of algebra in just the right way, and he never gets bogged down in the dr...y formalism which pervades some parts of algebra." MATHEMATICAL REVIEWS This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.
Lang, Serge is the author of Algebra, published 2002 under ISBN 9780387953854 and 038795385X. Five hundred fifty six Algebra textbooks are available for sale on ValoreBooks.com, fifty eight used from the cheapest price of $45.74, or buy new starting at $73.49 | 677.169 | 1 |
Shipping prices may be approximate. Please verify cost before checkout.
About the book:
An advanced-level treatment of the basics of set theory, this text offers students a firm foundation, stopping just short of the areas employing model-theoretic methods. Geared toward upper-level undergraduate and graduate students, it consists of two parts: the first covers pure set theory, including the basic motions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of it consequences; the second deals with applications and advanced topics such as point set topology, real spaces, Boolean algebras, and infinite combinatorics and large cardinals. An appendix comprises useful information on eliminability and conservation theorems, and numerous exercises help students test their grasp of each topic. 1979 edition. 20 figures486420795 Publisher: Dover Publications, 2002 Used. This Book is in Good Condition. Clean Copy With Light Amount of Wear. 100% Guaranteed. Summary: Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is... | 677.169 | 1 |
Mathematics for Retail Buying / Edition 4/i>
Paperback
Temporarily out of stock online.
Overview method of inventory, six-month, and assortment planning. This extensively updated edition introduces a new co-author and a practical approach that incorporates actual retail scenarios and concepts that are relevant to the fashion industry today. The book has been reorganized into six chapters, each covering a mathematical factor that affects the gross margin and profitability key to the success of any merchandise buyer or planner. The new edition also integrates current retail business metrics and an increased focus on the six-month planning process, including a new assortment planning section with examples.
New to This Edition: - Reorganized Units I and VI reflect the order of prior editions and open the textbook with the discussion of "merchandising for profit" and profit and loss concepts - Retitled "Units" to "Chapters" to make the book more user-friendly - Updates problems in all units and case studies for currency and relevancy to the industry today, including at least 25% new practice problems and 50% new case studies - Expanded chapter on "Dollar Planning and Control" to include more on sales planning and comprehensive coverage of the six month planning process and assortment planning - Explains how retailers do this in today's world, not only for brick and mortar but for omni-channel, including a sampling of problems from all retail sectors should be included - Includes criteria necessary for determining when to take markdowns in that chapter Mathematics for Retail Buying STUDIO -Study smarter with self-quizzes featuring scored results and personalized study tips -Review concepts with flashcards of terms and definitions and key formulas -Practice your skills by computing Practice Problems from the text, now available digitally with formulas embedded in the Excel spreadsheets -Enhance you knowledge with additional real world case studies and activities for each chapter
PLEASE NOTE: Purchasing or renting this ISBN does not include access to the STUDIO resources that accompany this text. To receive free access to the STUDIO content with new copies of this book, please refer to the book + STUDIO access card bundle ISBN 9781501315725. | 677.169 | 1 |
Mathematical Thinking Problem-Solving and Proofs
9780130144126
ISBN:
0130144126
Edition: 2 Pub Date: 1999 Publisher: Prentice Hall
Summary: For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematicsskills vital for success throughout the upperclass mathematics curriculum. The text offers both discrete an...d continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality.
D'Angelo, John P. is the author of Mathematical Thinking Problem-Solving and Proofs, published 1999 under ISBN 9780130144126 and 0130144126. Two hundred forty one Mathematical Thinking Problem-Solving and Proofs textbooks are available for sale on ValoreBooks.com, seventy four used from the cheapest price of $101.85, or buy new starting at $13844126-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. [more]
May include moderately worn cover, writing, markings or slight discoloration. SKU:9780130144126 | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
You are here
Statway and Quantway Provide Path to Higher Math
Two courses developed as part of the Carnegie Foundation for the Advancement of Teaching's Community College Pathways Program are demonstrating the effectiveness of engaging curricula and teaching methods in boosting student success in developmental math.
Each of the courses is a year long: Statway integrates high school algebra and college-level statistics, while Quantway focuses on developmental math for the first semester and college-level quantitative reasoning for the second.
Both Statway and Quantway give instructors the freedom to connect content to current events and questions of interest to their students and also include exercises aimed at combatting math anxiety. | 677.169 | 1 |
Prealgebra & Introductory Algebra
9780131449725
ISBN:
0131449729
Pub Date: 2004 Publisher: Prentice Hall PTR
Summary: For courses in Prealgebra (Basic Math with very early Algebra) and Introductory Algebra (or Beginning Algebra). This engaging workbook series presents a student-friendly approach to the concepts of basic math and algebra, giving students ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the worktexts are to build confidence, increase motivation, ...and encourage mastery of basic skills and concepts. Martin-Gay ensures that students have the most up-to-date, relevant text preparation for their next math course; enhances students' perception of math by exposing them to real-life situations through graphs and applications; and ensures that students have an organized, integrated learning system at their fingertips. The integrated learning resources program features text-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and My Math Lab.
Martin-Gay, K. Elayn is the author of Prealgebra & Introductory Algebra, published 2004 under ISBN 9780131449725 and 0131449729. Eleven Prealgebra & Introductory Algebra textbooks are available for sale on ValoreBooks.com, ten used from the cheapest price of $1.26, or buy new starting at $70 | 677.169 | 1 |
MA125 Intermediate Algebra
for F2M Perhaps more than any subject, the successful learning of mathematics depends upon previously acquired knowledge, skill, and repitition. Because of this, active participation in daily activities (such as asking questions in class, reading the textbook, and working assigned problems on time) is essential.
Instructor Learning Outcomes
Manipulate, simplify, and evaluate algebraic expressions
Solve and check linear equations, inequalities, and applications
Graph linear equations and solve system of linear equations
Perform operations on polynomials and solve quadratic equations
Class Assessment:
Students will be evaluated based on performance of homework, quizzes, examinations, and a final examination.
Homework will be assigned at the end of each class; is expected to be completed by the next class meeting; and will be graded.
Quizzes will come from homework assignments. The lowest quiz grade will be dropped at the end of the eight week class period, and there will be no make up quizzes. If you miss a quiz, then that will be the one quiz to be dropped.
There will be two examinations.
The final examination will be comprehensive (covering all chapters).
Grading:
Homework: 10% Letter Grading Scale:
Quizzes: 20% A: 90% - 100%
Exam #1: 20% B: 80% - 89%
Exam #2: 20% C: 70% - 79%
Final Exam: 30% D: 60% -69%
F: Below 60%
Late Submission of Course Materials: Late submission of homework will not be accepted except in extreme cases as determined by the instructor.
Classroom Rules of Conduct:
1. Attend all classes and be in class on time.
2. Be prepared. Work all homework problems and ask questions.
3. Know your material. Complete required readings and homework.
4. Do respect others, property, and yourself.
5. Do give 100% effort 100% of the time.
Be certain all cellular telephones, pagers, blackberries, and other electronic communication devices are turned off. If there is an emergency for which you need to leave your telephone (communication device) on, please inform me before the start of class.
Course Topic/Dates/Assignments:
Tuesday Thursday
Week 1: 1.1 - 1.2 Quiz 1, 1.3 - 1.4
Week 2: Quiz 2, 2.1 - 2.2 Quiz 3, 2.3, 2.5
Week 3: Quiz 4, 2.6 - 2.7 EXAM 1, 3.1
Week 4: 3.2 - 3.3 Quiz 5, 3.4 - 3.5
Week 5: Quiz 6, 4.1 - 4.2 Quiz 7, 4.3
Week 6: 5.1 - 5.3 EXAM 2
Week 7: 5.4 - 5.5 Quiz 8, 6.1 - 6.3
Week 8: 6.4 - 6.5, REVIEW FINALWe will follow guidance set by Park University Site Director for federal holidays, inclement weather, and any other unique situation that impacts class attendance at the campus.
MAKE UP EXAMINATIONS may be granted at the sole discretion of the instructor and only in the event of unavoidable and documented absence that has been provided to the instructor. NO EXCEPTIONS.
Copyright:
This material is protected by copyright
and can not be reused without author permission. | 677.169 | 1 |
CHAPTER TOOLS
Summary
Chapter 3 presents the classical (nodal) concept of finite elements, their unisolvency, construction of the unique nodal basis, local and global finite element interpolants, and conformity to spaces of functions. Discussed is the equivalence of finite elements. Presented are the most widely used linear triangular elements and bilinear quadrilateral elements in 2D, and the corresponding reference maps and their invertibility. | 677.169 | 1 |
books.google.com - This book presents concise explanations of the subject's general principles and uses worked examples freely to expand the text. Each example shows the method of obtaining the solution and includes additional explanatory notes. For some topics, where it would have been difficult to understand a solution... Drawing with Worked Examples | 677.169 | 1 |
Here is what we will be doing tonight…describe the list. Before proceeding, do the introduction with the questions Who are you? Why are you here?
Here are three quotes from famous mathematicians and scientists: Georg Cantor, Russian Mathematician, father of set theory (late 1800's early 1900's) Israel Nathan Herstein, Polish/Canadian American Mathematician (ring theory) Albert Einstein, German-Swiss Mathematician, Scientist and Philosopher (Relativity) What in the name of God are these people saying? Allow participants to come up with ideas of their own…aren't the actual answers important? Logic, Problem-Solving and Programming…Computers have little imagination, intelligence or humour, but they do have good grasps of logic and can help to solve problems, but only when we can put into their little circuits a problem posed in such a way as to offer logical and methematical reasoning. What computers are good at is repetitive tasks, speed, mathematical application of principles. But they can only solve problems if we know how to instruct it in how to solve it. For example, let's say you want a way for your computer to convert Fahrenheit to Celsius temperatures. There are lots of applications out there to do it, but unless you install an application or write an application, your computer can't do it by itself. As a programmer, then, you must first know what the solution (or algorithm) is that converts the two values, then you need to be able to write an application that tells the computer to ask the user for one value, then apply that algorithm to make the conversion, and then return the converted value to the user. In this course you will actually write a program to do that and much more – but before we can get there we wantto be sure you have a reasonable grasp of number systems and basic algebraic math and that you can apply those principles to solve problems. If you have no aptitude for math and logic, you are not likely to have much success in programming and other IT work. But don't get dismayed if you haven't had a lot of success with Math in the past. We will try to make this Math interesting and practical and we hope this will be largely a refresher for most of you. I'm getting ahead of myself - So let's begin by examining the course so that we can set clear expectations for how we'll get there.
Cover Course outline in detail – note that all outcomes must be met Cover work plan – grading and assignments, due dates Discuss appropriate conduct Show the website
Try this exercise – read instructions Did you get it? Here is the solution… What prevented you or challenged you to solve (at first)? Don't get caught up with preconceptions that box you in – be creative and try things! Problem solving is often about trying things and failing and learning from your failure. Please feel comfortable to try something here – you will not be punished for trying and failing, but I will look less favorably at not trying because I cannot give you any useful feedback on your strategy.
3.
Is this logical? <ul><li>In Mathematics, the art of proposing a problem must be held of higher value than solving it . Georg Cantor </li></ul><ul><li>The value of a problem is not so much coming up with the answer, as in the ideas and attempted ideas it forces on the would-be solver . Israel Nathan Herstein </li></ul><ul><li>Imagination is more important than intelligence . Albert Einstein </li></ul>
10.
Math Pre-test <ul><li>This is NOT a graded test, it's a C.A.T. </li></ul><ul><li>Please attempt as much of the pre-test as you can </li></ul><ul><li>Leave questions you cannot solve </li></ul><ul><li>Try to show your working where appropriate </li></ul><ul><li>Sign your name to the top and pass it in before you leave </li></ul>
11.
Portfolio Activity <ul><li>Fill out the portfolio activity provided </li></ul><ul><li>Be sure you include your name on the top of the exercise </li></ul><ul><li>Please pass this in before you leave </li></ul> | 677.169 | 1 |
DTW Algebra Lite
Screenshots
Details
Description
Warning! you don't need internet to use this app, preferece used only for check conection button.
Why I need this app?
This app can be useful to you, if you are an Algebra teacher, student, pupil or simply using algebra in your daily life, so DTW means Don't trouble with, this app help you do not have 'em
Recently changed in this version
Download APK from previous versions of DTW Algebra Lite
DTW Algebra Lite is a powerful algebra tool.
5
Easy
Free version with few features
"Resolving complex equations is just a few taps away"
Is there a moment in our life that we need to resolve things like x³ + x ² + x = 0. Particularly if you use algebra in your daily life or are an algebra teacher. This app goes one step beyond and resolver quadratic equations, logarithms and matrices. The UI is easy and intuitive, but it might have been better a little more attractive. Touch response is somewhat weird and sometimes it force closes when you tap on an option that is only available in the paid version. You can look theorems up, which may be useful God knows when.
This is the free version, which has just a few options. The paid version adds lots of features such as differential, qubic and linear system equations. As there aren't too many apps to help people in their everyday algebra problems, maybe you should check the paid version | 677.169 | 1 |
Main navigation
Algebra Facts
Algebra is a part of mathematics, often called math in the United States and maths in the United Kingdom. It uses variables to represent a value that is not yet known. When an equals sign (=) is used, this is called an equation. A very simple equation using a variable is: 2 + 3 = x In this example, x = 5, or it could also be said, "x is five". This is called solving for x. See below for more information and facts about algebra.
Algebra is a branch of mathematics concerning the study of structure, relation and quantity. Learning algebra is a little like learning another language. By learning the simple language of algebra, mathematical models of real-world situations can be created and solved. These problems can't be solved by only using arithmetic. Instead of using words, algebra uses symbols to make statements.
In algebra, letters are often used to represent numbers. Algebra also uses the same symbols as arithmetic for adding, subtracting, multiplying and dividing. | 677.169 | 1 |
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