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This is the beginning of a series of tutorials that will aid you in understanding the concepts of Algebra. Tutorial 1 will demonstrate how to find the distance and midpoint of two points on a graph. The distance formula is derived using the Pythagorean Theorem Click on a step to see it displayed The first step in finding the distance between two points on a line is to construct a right triangle between the points. With the horizontal and vertical lines formed you can find the distance of these lines individually by taking the absolute value of the difference of the two x values (the distance of your horizontal line) and the absolute value of the difference of the two y values (the distance of your vertical line). With the distance of the vertical and horizontal lines (The A and B values of the Pythagorean Theorem) You can now solve for the hypotenuse (the distance between points). Home Next Page Contact Us

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Home Contact Overview Crypto Corner ... Archive Center Algebra Tutorial On this page you will find information about the algebraic structures which are used in NTRU's cryptographic products. Modular Arithmetic Truncated Polynomial Rings Inverses in Truncated Polynomial Rings 1. Modular Arithmetic Modular arithmetic is simply division with remainder, where you keep the remainder and throw everything else away. For example, the expression 147 (modulo 17) means to divide 147 by 17 and keep the remainder. Now 147 divided by 17 gives a quotient of 8 and a remainder of 11 (since 147 = 8 × 17 + 11), so 147 (modulo 17) is equal to 11. This is written as an equality (called a congruence) 147 = 11 (modulo 17). In general, the expression a (modulo m) means to divide a by m and keep the remainder. Similarly, a congruence a = b (modulo m) simply means that a and b leave the same remainder when they are divided by m. This is the same as saying that the difference a-b is a multiple of m. The integer m is called the modulus of the congruence. Numbers and congruences with the same modulus may be added, subtracted, and multiplied just as is done with ordinary equations. For example

66. Ntru - CryptoLab - Tutorials For more details about the ring R, see Section 2 of the algebra Tutorial. A full implementation of the NTRU Public Key Cryptosystem is specified by a number http://www.ntru.com/cryptolab/tutorial_pkcs.htm

Home Contact Overview Crypto Corner ... Archive Center The NTRU Public Key Cryptosystem This tutorial describes how the NTRU Public Key Cryptosystem (PKCS) works. NTRU PKCS Parameters Key Generation Encryption Decryption ... Further Reading 1. NTRU PKCS Parameters The basic collection of objects used by the NTRU Public Key Cryptosystem is the ring R that consists of all truncated polynomials of degree N -1 having integer coefficients: a = a + a X + a X + a X + . . . + a N-2 X N-2 + a N-1 X N-1 Polynomials are added in the usual way. They are also multiplied more-or-less as usual, except that X N is replaced by 1, X N+1 is replaced by X, X N+2 is replaced by X , and so on. For more details about the ring R , see Section 2 of the Algebra Tutorial. A full implementation of the NTRU Public Key Cryptosystem is specified by a number of parameters. However, for the purposes of this overview we'll concentrate on the three most important: N - the polynomials in the truncated polynomial ring have degree N q - large modulus: usually, the coefficients of the truncated polynomials will be reduced mod q p - small modulus. As the final step in decryption, the coefficients of the message are reduced mod

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The Mathematics Resource Laboratory Indiana University Southeast Elementary Intermediate and Combined Algebra Page Lab Information Life Science Building Room 101 Phone: 941-2670 Fax: 941-2637 Open to all students with an IUS ID Coordinator: Dee Cochran, Room 010A, 941-2605 Click here to EMAIL Coordinator: Delaine E. Cochran Text: Elementary and Intermediate Algebra, A Combined Approach by J.E. Kaufmann, 4th EditionBrooks/Cole. Finals: The Departmental Final will be comprehensive over the entire course. Final reviews are on the Web.. Not Offered in Fall 2005. Exercises-Practice or ask questions online with immediate responses Algebra Tutorials Algebra Online Tutoring Instant Internet Answers to Algebra and PreAlgebra Problems Algebra Problem of the Week ... Graphing and Function Review Tutorials for specific topics History of Algebra and its Origins NASA Quick Refesher of Algebra Math.Com answers your questions Practice Algebra at QuickMath with instant responses ... Rational Expressions/Algebraic Fractions Online Quizzes Solving Linear Equations Introduction to Functions Function Operations Rational Equations and Expressions ... Operations on Functions In the Mathematics Lab Listing of Videos Available now In the Library Interact Math Secondary Math Lab Toolkit Active Algebra Tutorial Graphing Programs Interactive Algebra II (tutorials, games,and quizzes)

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The Mathematics Resource Laboratory Indiana University Southeast M119-Brief Survey of Calculus Page Lab Information Life Science Building Room 009 Phone: 941-2670 Fax: 941-2637 Open to all students with an IUS ID Current Schedule Coordinator: Dee Cochran, Room 010A, 941-2605 Click here to EMAIL Coordinator: Delaine E. Cochran Course Information Text: Calculus, seventh Edition, Hoffman, ISBN 0-07-304018-5 CD Rom tutorial available in mathlab WebSite for Text and online help center Practice Review and Help Algebra Tutorials Graphing and Function Review Exponential and Logs Review Derivatives Review ... Math Homework Hotline Online Tutorials for specific topics Online Tutorial for All Calculus topics Order of Operations Practice Algebra Word Problems with hints and Answers Distance Problems ... Rational Expressions/Algebraic Fractions Online Quizzes for algebra Function Review Solving Linear Equations Introduction to Functions Function Operations ... Quadratic and Polynomial Functions Calculus Online Calculus I Calculus II Calculus III Calculus III Tutorials for Specific Calculus Topics Continuous Functions Intermediate Value Theorem Definition of Limits Horizontal Asymptotes ... Tutotials from A to Z Online Quizzes Help with Mathematics Software Maple Mathematica Matlab Derive Help with Mathematics Calculators TI-82 Tutorial Data Fitting with the TI-82 A Tutorial for the TI-86 TI Calculators Homepage - Calculator information and software/program downloading In the Mathematics Lab Look in the math software folder

70. Matrix Algebra - HMC Calculus Tutorial back to the math tutorial index back to the math tutorial index. Matrix algebra. We review here some of the basic definitions and elementary algebraic http://www.math.hmc.edu/calculus/tutorials/matrixalgebra/

Matrix Algebra We review here some of the basic definitions and elementary algebraic operations on matrices. There are many applications as well as much interesting theory revolving around these concepts, which we encourage you to explore after reviewing this tutorial. A matrix is simply a retangular array of numbers. For example, A = a a a a a a a a a mn th row and j th column is a ij . We often write A = [a ij Some Terminology square matrix A, the elements a ,a ,a nn form the main diagonal of the matrix. The sum n k = 1 a kk of the elements on the main diagonal of A is called the trace of A. The matrix A T = [a ji ] formed by interchanging the rows and columns of A is called the transpose of A. If A T = A, the matrix A is symmetric Example Let B = . The trace of B is 6 + -6 = 0. The transpose of B is B T Addition and Subtraction of Matrices To add or subtract two matrices of the same size, simply add or subtract corresponding entries. That is, if B = [b ij ] and C = [c ij B + C = [b ij + c ij ] and B-C = [b ij - c ij Example For B = and C = B + C = B-C = zero matrix

71. Algebra Review - HMC Calculus Tutorial algebra Review. The material in this tutorial is reprinted with permission of the authors and publisher of How to Ace Calculus by Colin Adams, http://www.math.hmc.edu/calculus/tutorials/algebrareview/

Algebra Review The material in this tutorial is reprinted with permission of the authors and publisher of How to Ace Calculus by Colin Adams, Abigail Franklin, and Joel Hass. Here we will list some of the most common mistakes that we see on exams. If you can avoid these, then at least your mistakes will be uncommon. Most of the mistakes that occur repeatedly involve algebra, rather than calculus. They can be avoided by being careful and checking your work. Others involve common misunderstandings about various aspects of calculus. (x+y) = x + y MISTAKE! Powers don't behave this way. The correct way to expand this expression gives (x+y) = x + 2xy + y 1/(x+y) = x y MISTAKE! The rule for adding fractions gives x y = (x+y)/xy 1/(x+y) = x + y. MISTAKE! This very common error comes from carelessness about what's in the denominator. Can be avoided by careful handwriting or frequent use of parentheses. (x+y) = x + y. MISTAKE! There is no simplified way to write (x+y). You just have to live with it as is. MISTAKE!

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z MATH TUTORIALS Algebra - Geometry - Advanced Algebra Algebra Algebra UCSMP ("Chicago Math") Series This course has a wider scope than other beginning algebra courses in that it covers basic algebra as far as quadratic equations while integrating statistics, probability, and geometry. The course's strength is in synergistic emphasis on three major areas: visual representation of algebraic concepts, manipulation of algebraic equations, and application of algebraic principles to real-world problems. Topics include square roots, systems, polynomials, exponents, algebra of linear equations and inequalities, and use of algebraic fractions in probability concepts. The text is published by ScottForesman. The book's organization maximizes understanding and retention, as concepts and skills introduced in each lesson are reinforced through further application in successive lessons. This reinforcement, combined with text's daily review questions and self-tests, allows students several opportunities to master course material. Requirements Algebra 1/2 or Chicago Math's Transition Mathematics.

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A Charles Sturt University Initiative Search Contact Us Help ... Resources Tutorials Animated functions demonstration (absolute value) Difference of two squares expansion (concrete) Part of a series on understanding factoring through a concrete geometric approach. A worked example of using the substitution method for linear and quadratic equations. Inequalities A synopsis of the topic that includes the basic rules and links to graded exercises, with answers provided. Perfect square expansion (concrete) Part of a series on understanding factoring through a concrete geometric approach. Square of binomial difference (concrete) Part of a series on understanding factoring through a concrete geometric approach. Squares and link to square roots (beware reference to Annotated examples, exercises and answers to perform squaring on a calculator and links to square root operations. Assessment Hints and answers from past exam papers (formerly '2 Unit'), and past articles from Sydney Morning Herald advice to students. Absolute value A series of questions on solving equations and evaluating expressions, with answers provided. Basic algebra practice A series of mixed questions on symbol manipulation, with answers provided.

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75. Algebra algebra. © Department of Physics, University of Guelph Again, n may be an integer or a fraction. Return to Physics tutorials Menu. http://www.physics.uoguelph.ca/tutorials/algebra/

Algebra © Department of Physics, University of Guelph The first topic to be reviewed is fractions. A fraction is expressed as , where a is called the numerator and b, the denominator. The addition or subtraction of fractions can be expressed generally as . In order to carry out the operation indicated it is necessary that the expression have a common denominator, b x d. This is accomplished by multiplying both terms by bd, and dividing both terms by bd. That is, is equal to As an example, what is 1/2 + 1/3? Using the previous equation , where now a=1, b=2, c=1 and d=3, we obtain The product of two fractions is the product of their numerators divided by the product of their denominators. That is, Now we will investigate power laws. A number raised to a power is written as a x , where a is the base and x is the power or exponent. When multiplying a x by a y the rule is to add the exponents, thus, a x times a y equals a x + y . This is obvious since a x times a y is (x+y) a's multiplied together. When dividing a x by a y , the rule is to subtract the exponents. Thus a

76. Tutorials In Maths Of Belait Offers Algebra Tutorial, Arithmetic Tutorial... Tutorial lessons in mathematics are suitable for both teachers and students. The tutorials are arranged in single volumes of 12 lessons, http://sbd.bcentral.com/bc__320950.aspx

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HOMESCHOOL MATH Computer Science, Pure and Simple - a computer science curriculum for homeschoolers! Let your kids learn Logo, HTML, how to make web pages, office applications, and more. From grade 5 till high school. Home Ebooks 1st-5th grade Worksheets Curriculum guide ... Reviews Online Math games, quizzes, interactive tutorials, software High school 1 Algebra Graphing Calculus Online math resources Math help, Homework help, tutoring General Math Resources Math history, Problem solving, Test prep Elementary Math 1 Basic operations, Times tables, Place value Elementary Math 2 Time, Money, Measuring, Geometry Middle School Math 1 Fractions, Decimals, Integers Middle School Math 2 Measuring, Coordinate Plane, Geometry High School 1 Algebra, Graphing, Calculus High School 2 Geometry, Trigonometry, Statistics Math games, quizzes, or interactive tutorials websites Can't find what you are looking for? Try Google Search: Help with grade 7-12 math / science classes! Awesome Grades in Math and Science You will learn: Scheduling study time 80/20 rule of study versus memorize material making summary notes Get rid of math phobia, find motivation - and achieve lasting success in math and science!

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Why Merit Works How to Buy Merit Products Teaching Tips About the Teacher ... Try It! Basic Algebra Shape-Up -Hands-on tutorials that cover integers, expressions, equations, and more. Introduces basic algebraic concepts and helps students to master specific basic algebra skills. Students start with an assessment and receive immediate instructional feedback throughout. Step-by-step tutorials , which introduce each concept, can be referred to during practice. The program is self-paced and self-monitored. Scores are tracked in a record management system that allows teachers to view and print detailed reports. Designed for students in grades 6 through 9 (age 11 and up), the software can also be used by older students. "It teaches instead of just quizzing!" Softpile.com Curriculum Set 1: Using Word Problems to Introduce Algebraic Concepts, Math levels 6 - 9

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The AoPS Independent Study Programs begins Friday, Sept 9. Enrollments are limited. Enrollment deadline is Sept 19. Font Size: The time now is Sun Sep 18, 2005 5:59 am English version Matrix Algebra - Computations and Tutorials Change the language View posts since last visit ... Matrix Algebra - Computations and Tutorials Moderators: amfulger fedja Kent Merryfield Moubinool Page of [35 Topics] Topics Author Replies Views Last Post Steady Matrix tux Yesterday, at 7:58 am sphoenixee rank of matrix exam Michael Thu Sep 15, 2005 11:25 am Kent Merryfield Linear Algebra Class Tue Sep 13, 2005 10:50 am gongli Markov Chains sphoenixee Sat Sep 10, 2005 7:10 pm sphoenixee exp and calculation ENS alekk Sat Sep 10, 2005 4:21 am alekk Seeking Help On Characteristic Polynomials ArtOfSpace Tue Aug 30, 2005 4:52 am ArtOfSpace Reducing the matrix calculations Joseph Frank Mon Aug 29, 2005 9:15 am Joseph Frank Making matrices with specific min. and char. polys Thu Aug 25, 2005 1:03 pm rgep Adjoint of a Linear Operator Textbook Sat Aug 20, 2005 12:17 am

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