61. Abstract Algebra Notes (PostScript) These are notes for Abstract algebra II. They were revised during the Fall, 1999term. action.ps (7 pages, 113662 bytes) Group actions; Burnside s theorem. http://marauder.millersville.edu/~bikenaga/absalg/absanote.html

Abstract Algebra Notes (PostScript) These are links to PostScript files containing notes for various topics in abstract algebra. How do I view/print the notes? How may I use/distribute the notes? How did you write them? These are notes for Abstract Algebra I; they were revised during the Fall, 2004 term. div.ps (4 pages, 134,704 bytes): Divisibility and the Division Algorithm. euclid.ps (9 pages, 373,515 bytes): Greatest common divisor, the Euclidean algorithm, and the Extended Euclidean Algorithm. prime.ps (5 pages, 177,923 bytes): Prime numbers and the Fundamental Theorem of Arithmetic. modular.ps (7 pages, 245,071 bytes): Arithmetic in the integers mod n; congruences. groups.ps (13 pages, 337,196 bytes): The axioms for a group; basic properties and examples. subgroup.ps (6 pages, 219,573 bytes): Subgroups. matgrp.ps (4 pages, 144,838 bytes): Groups of matrices. unitzn.ps (3 pages, 125,851 bytes): The group of units in the integers mod n; Fermat's theorem. cyclic.ps (6 pages, 190,984 bytes): Cyclic groups. perm.ps (8 pages, 261,808 bytes):

62. Another Proof For Fermat's Last Theorem Fermat s last theorem says that this equation can t be satisfied for n But it isn t just that algebra and geometry were used to solve Fermat s last http://plus.maths.org/latestnews/jan-apr05/serre/

about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Latest news Spaghetti breakthrough What happens to bent pasta? How to measure a million The risks in Who wants to be a millionaire? Not just knots: the secrets of khipu The Inka way of counting Machine prose A computer program that can learn languages A new time machine Take a journey to the limits of common sense Gene-ius The search for the maths gene Plus... more news from the world of maths Explore the news archive Subscribe to our free newsletter Get the ... posters! News Another proof for Fermat's last theorem Fermat's last theorem says that this equation can't be satisfied for n greater than 2 Chandrashekhar Khare , a mathematician from the University of Utah, has announced that he has proved what is known to experts as the "level-one Serre conjecture". This conjecture was posed in 1972 by the Fields medallist Jean-Pierre Serre , and belongs to the field of Arithmetic Algebraic Geometry. At this point we should of course say what the conjecture states, and explain its importance in the real world. This, however, is easier said than done, as those of us who are not experts would have to spend several months studying seriously advanced mathematics, just in order to understand the statement.

63. Fundamental Theorem Of Algebra -- Facts, Info, And Encyclopedia Article Categories Theorems, Field theory, Complex analysis, Abstract algebra In (Ascience (or group of related sciences) dealing with the logic of quantity and http://www.absoluteastronomy.com/encyclopedia/f/fu/fundamental_theorem_of_algebr

Fundamental theorem of algebra [Categories: Theorems, Field theory, Complex analysis, Abstract algebra] In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics , the fundamental theorem of algebra states that every complex (A mathematical expression that is the sum of a number of terms) polynomial of degree n has exactly n (Click link for more info and facts about zeroes) zeroes , counted with multiplicity. More formally, if (where the coefficients a a n can be (An old small silver Spanish coin) real or ((psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior) complex numbers), then there exist ( (Click link for more info and facts about not) not necessarily distinct) complex numbers z z n such that This shows that the (A piece of land cleared of trees and usually enclosed) field of (A number of the form a+bi where a and b are real numbers and i is the square root of -1) complex numbers , unlike the field of (Any rational or irrational number) real numbers , is (Click link for more info and facts about algebraically closed) algebraically closed n a and the sum of all the roots equals - a n The theorem had been conjectured in the 17th century but could not be proved since the complex numbers had not yet been firmly grounded. The first rigorous proof was given by

64. Schiller Institute -Pedagogy - Gauss's Fundamental Theorem Of A;gebra Fundamental theorem of algebra. His Declaration of Independence. by Bruce DirectorApril, 2002. To List of Pedagogical Articles To Diagrams Page http://www.schillerinstitute.org/educ/pedagogy/gauss_fund_bmd0402.html

Home Search About Fidelio ... Dialogue of Cultures SCHILLER INSTITUTE Carl Gauss's Fundamental Theorem of Algebra H is Declaration of Independence by Bruce Director April, 2002 To List of Pedagogical Articles To Diagrams Page To Part II Lyndon LaRouche on the Importance of This Pedagogy ... Related Articles Carl Gauss's Fundamental Theorem of Algebra Disquisitiones Arithmeticae Nevertheless, he took the opportunity to produce a virtual declaration of independence from the stifling world of deductive mathematics, in the form of a written thesis submitted to the faculty of the University of Helmstedt, on a new proof of the fundamental theorem of algebra. Within months, he was granted his doctorate without even having to appear for oral examination. Describing his intention to his former classmate, Wolfgang Bolyai, Gauss wrote, "The title [fundamental theorem] indicates quite definitely the purpose of the essay; only about a third of the whole, nevertheless, is used for this purpose; the remainder contains chiefly the history and a critique of works on the same subject by other mathematicians (viz. d'Alembert, Bougainville, Euler, de Foncenex, Lagrange, and the encyclopedists ... which latter, however, will probably not be much pleased), besides many and varied comments on the shallowness which is so dominant in our present-day mathematics." In essence, Gauss was defending, and extending, a principle that goes back to Plato, in which only physical action, not arbitrary assumptions, defines our notion of magnitude. Like Plato, Gauss recognized it were insufficient to simply state his discovery, unless it were combined with a polemical attack on the Aristotelean falsehoods that had become so popular among his contemporaries.

65. The Fundamental Theorem Of Algebra (Fine)-Springer Algebra Book The fundamental theorem of algebra states that any complex polynomial must havea complex root. This book examines three pairs of proofs of the theorem from http://www.springeronline.com/sgw/cda/frontpage/0,10735,4-40109-22-1515722-0,00.

Please enable Javascript in your browser to browse this website. Select your subdiscipline Algebra Analysis Applications Mathematical Biology Mathematical Physics Probability Theory Quantitative Finance Home Mathematics Algebra Select a discipline Biomedical Sciences Chemistry Computer Science Economics Education Engineering Environmental Sciences Geography Geosciences Humanities Law Life Sciences Linguistics Materials Mathematics Medicine Philosophy Popular Science Psychology Public Health Social Sciences Statistics preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,4-0-17-900180-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,4-0-17-900170-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,4-0-17-900190-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,4-0-17-900200-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,4-0-17-900369-0,00.gif'); preloadImage('/sgw/cda/pageitems/designobject/cda_displaydesignobject/0,11978,4-0-17-900344-0,00.gif');

66. The Mathematics Of Fermat's Last Theorem The statement of Fermat s Last theorem (FLT for short) is about as An introductionto abstract algebra (groups, rings, fields) is almost essential. http://cgd.best.vwh.net/home/flt/fltmain.htm

The Mathematics of Fermat's Last Theorem Welcome to one of the most fascinating areas of mathematics. There's a fair amount of work involved in understanding even approximately how the recent proof of this theorem was done, but if you like mathematics, you should find it very rewarding. Please let me know by email how you like these pages. I'll fix any errors, of course, and try to improve anything that is too unclear. Introduction If you have ever read about number theory you probably know that (the so-called) Fermat's Last Theorem has been one of the great unsolved problems of the field for three hundred and fifty years. You may also know that a solution of the problem was claimed very recently - in 1993. And, after a few tense months of trying to overcome a difficulty that was noticed in the original proof, experts in the field now believe that the problem really is solved. In this report, we're going to present an overview of some of the mathematics that has either been developed over the years to try to solve the problem (directly or indirectly) or else which has been found to be relevant. The emphasis here will be on the "big picture" rather than technical details. (Of course, until you begin to see the big picture, many things may look like just technical details.) We will see that this encompasses an astonishingly large part of the whole of "pure" mathematics. In some sense, this demonstrates just how "unified" as a science mathematics really is. And this fact, rather than any intrinsic utility of a solution to the problem itself, is why so many mathematicians have worked on it over the years and have treated it as such an important problem.

67. Algebra, Analytic Geometry: Chapter 17 From Three Skills For Algebra The Pythago The Pythagorean theorem from chapter 17, Three Skills for algebra. The Pythagoreantheorem is one of the oldest statements in mathematics. http://whyslopes.com/etc/analyticGeometry/analGeo03a_Distance_Formula.html

Analytic Geometry All results 5 results 10 results 20 results 30 results 50 results 100 Results site entrance site map site reviews optional: order site books ... Road Safety Message Distance Formulas Coordinate Formulas for Distance (I) Points on a Line The following gives the distance between a pair of points (the length of the line segment between them) on a horizontal line: The case of a vertical line is similar. (II) Planar Case: Points in a Plane Suppose [x ,y and [x ,y ]. are points in the plane. Our aim is to compute the distance c between these points. The line segment between [x ,y and [x ,y ]., if it is not horizontal, nor vertical, provides the hypotenuse of right triangle (or two) with horizontal and vertical sides. The case where the line segment has a negative slope is drawn below. - x - y Therefore the Pythagorean Theorem (see proof below) says c = a + b - x - y So the distance c between the points [x ,y and [x ,y ] satisfies c = (x - x + (y - y c - x - y (x - x - y Verification of this formula in the two cases where the line segment between [x ,y and [x ,y = c - x - y by (x - x - y , respectively.

68. Graduate Study In Algebra The goal of the course is the fundamental theorem of Galois theory and the Weyl theorem on compact real forms, the universal enveloping algebra. http://www.math.uiuc.edu/GraduateProgram/researchmath/gradalgebra.html

Graduate Study in Algebra Introduction Algebra is one of the oldest branches of mathematics, and the study of algebra in the Department of Mathematics has traditionally been rich and strong. Such eminent mathematicians as C. A. Miller (Group Theory), R. D. Carmichael (Group Theory and Number Theory), A. B. Coble (Algebraic Geometry), and R. Baer (Group Theory Abelian Groups) began a tradition in algebra that is continued today by a strong and active group of approximately 20 mathematicians, supplemented by visitors who divide their time between teaching and research. The research strengths of the faculty are in the theory of rings (commutative and noncommutative), the theory of groups, algebraic number theory, the representation theory of groups and algebras, and algebraic geometry. A broad range of graduate courses described below is offered to prepare graduate students for further study in algebra. The algebraic life of the Department is very active. In addition to the courses offered there is a comprehensive seminar program, usually 4-6 seminars each week, covering almost every aspect of algebra. These are almost equally divided between current topic seminars in which current research is presented in one or two lectures and in-depth seminars in which a subject is studied through a longer series of lectures. These seminar lectures are presented by faculty members, graduate students, and visitors. Graduate students are encouraged to participate in these seminars because participation in a combination of seminars and advanced courses leads a student more quickly to the frontiers of research. Often the weekly departmental colloquium lecture is presented by a noted algebraist. The Department has a number of visiting scholars and there are frequent algebraists among them.

69. College Algebra Tutorial On The Binomial Theorem (Back to the College algebra Homepage). College algebra Tutorial 54 The BinomialTheorem. Learning Objectives. After completing this tutorial, http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54_bi

(Back to the College Algebra Homepage) College Algebra Tutorial 54: The Binomial Theorem Learning Objectives After completing this tutorial, you should be able to: Evaluate a factorial. Find a binomial coefficient. Use the Binomial Theorem to expand a binomial raised to a power. Find the rth term of a binomial expansion. Introduction In this tutorial we will mainly be going over the Binomial Theorem. To get to that point I will first be showing you what a factorial is. This is needed to complete problems in this section. This will lead us into the concept of finding a binomial coefficient, which incorporates factorials into it's formula. From there we will put it together into the Binomial Theorem. This theorem gives us a formula that enables us to find the expansion of a binomial raised to a power, without having to multiply the whole thing out. This theorem incorporates the binomial coefficient formula. You will see that everything in this tutorial intertwines. I think that you are ready to move ahead. Tutorial Factorial The factorial symbol is the exclamation point: !

70. American Mathematical Monthly, The: Fundamental Theorem Of Algebra And Linear Al Full text of the article, fundamental theorem of algebra and linear algebra,The from American Mathematical Monthly, The, a publication in the field of http://www.findarticles.com/p/articles/mi_qa3742/is_200308/ai_n9300786

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Home Advanced Search IN free articles only all articles this publication Automotive Sports FindArticles American Mathematical Monthly, The Aug/Sep 2003 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Featured Titles for ASA News ASEE Prism Academe African American Review ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports fundamental theorem of algebra and linear algebra, The American Mathematical Monthly, The Aug/Sep 2003 by Derksen, Harm Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. 1. INTRODUCTION. The first widely accepted proof of the fundamental theorem of algebra was published by Gauss in 1799 in his Ph.D. thesis, although by today's standards this proof has gaps. In 1814 Argand gave a proof (with only small gaps) that was based on a flawed 1746 proof of d'Alembert. Many other proofs followed, including three more by Gauss. For more about the history of the fundamental theorem of algebra, see [5] or [6]. Proofs of the fundamental theorem of algebra can be divided roughly into three categories (see [3] for a collection of proofs). First there are the topological proofs (see [1] or [8]). These proofs are based on topological considerations such as the winding number of a curve in R^sup 2^ around 0. Gauss's original proof might fit under this heading as well. Then there are analytical proofs (see [9]), which are related to Liouville's theorem: a nonconstant entire function on C is unbounded. Finally, there are the algebraic proofs (see [4] or [10]). These proofs use only the fact that every polynomial of odd degree with real coefficients has a real root and that every complex number has a square root. The deeper reasons why these arguments work can be understood in terms of Galois theory.

71. Merak MML Browsing Fundamental theorem of algebra. POLYNOM575 theorem for b1 being Functionlikequasi_total finite-Support Relation of NAT,the carrier of F_Complex http://merak.pb.bialystok.pl/mmlquery/fillin.php?entry=POLYNOM5:75&comment=Funda

72. The Binomial Theorem And Other Algebra The Binomial theorem and other algebra. At its simplest, the binomial theoremgives an expansion of (1 + x)n for any positive integer n. We have http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/node15.html

Next: Sequences Up: Introduction. Previous: Absolute Value Contents Index The Binomial Theorem and other Algebra At its simplest, the binomial theorem gives an expansion of (1 + x n for any positive integer n . We have x n nx x x k x n Recall in particular a few simple cases: x x x x x x x x x x x x x x x There is a more general form: a b n a n na n-1 b a n-2 b a n-k b k b n with corresponding special cases. Formally this result is only valid for any positive integer n ; in fact it holds appropriately for more general exponents as we shall see in Chapter Another simple algebraic formula that can be useful concerns powers of differences: a b a b a b a b a b a ab b a b a b a a b ab b and in general, we have a n b n a b a n-1 a n-2 b a n-3 b a b n b n-1 Note that we made use of this result when discussing the function after Ex And of course you remember the usual ``completing the square'' trick: ax bx c a x x c a x c Next: Sequences Up: Introduction. Previous: Absolute Value Contents Index Ian Craw 2002-01-07

73. Algebra Seminar This talk will be a survey of the use of algebraic and combinatorial methods to Abstract By the celebrated BrauerFowler theorem there are only finite http://www.math.binghamton.edu/dept/AlgebraSem/

The Algebra Seminar Fall 2005 The seminar meets Tuesdays in room LN 2205 at 2:50 p.m. There will be refreshments in the Anderson Reading Room at 4:00. Organizer: Marcin Mazur August 30 : Organizational meeting September 6 : (W+L). Kappe Title : Products of commutators are not commutators: Cassidy's Example revisited Abstract : In her 1979 paper, entitled "Products of commutators are not always commutators: an example", P.J.Cassidy presents a group in which the set of commutators is not equal to the commutator subgroup (Monthly, vol. 86, p. 772). In fact, a much stronger statement is true for this group: there is no bound on the number of commutators in the product representing an element of the commutator subgroup. Since this example is widely known and often quoted, Robert Morse and LCK have included it in their survey paper on commutators. At the last moment we found out that Cassidy's proof is incorrect, but the statement is correct. In this talk we provide the context in which this example is of most interest, give a correct proof, show where Cassidy went wrong in hers, and finally explore what other types of examples can be constructed using Cassidy's idea. September 13 : Dikran B. Karagueuzian

74. Algebra Qual. Exam Permutation groups Cayley s theorem, permutations as products of CayleyHamiltontheorem, algebraic and geometric multiplicity, diagonalization. http://orion.math.iastate.edu/dept/grad/gqual.htm

Algebra Qualifying Examination Syllabus Abstract Algebra Fundamentals: sets, relations, and functions, Cartesian products and operations, partial orderings, equivalence relations and partitions, the Axiom of Choice and Zorn's Lemma, cardinal numbers. Integers: mathematical induction and the least number principle, congruence, Division Algorithm, unique factorization, greatest common divisor and least common multiple, Euclidean Algorithm. Groups (basic theory): semigroups and monoids, various characterizations of groups, subgroups, normal subgroups, homomorphism, isomorphism, quotient groups, direct products and sums, cosets and counting, Lagrange's Theorem, subgroup generation, the Isomorphism Theorems, the Correspondence Theorem. Examples of groups: permutation groups, groups of symmetries, matrix groups, dihedral and quaternion groups. Permutation groups: Cayley's Theorem, permutations as products of disjoint cycles and consequences for the structure of permutation groups, permutations as products of transpositions, alternating groups, simplicity of A n for n Abelian groups: structure of cyclic groups, free abelian groups and the structure of finitely generated abelian groups, the Fundamental Theorem of Abelian Groups.

75. Leaving Cert. Higher Level Maths - Algebra - The Factor Theorem This applet describes firstly the principle of The Remainder theorem and deducesfrom that the Factor theorem. It provides the proof of the Factor theorem http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/algebra/the_factor_theorem

Search for: in Entire website Algebra Complex Numbers Matrices Sequences and series Differentiation Integration Circle Vectors Linear Transformations Line Geometry Trigonometry Probability Further Calculus and Series Website Home Algebra The Factor Theorem No Title ... Integration You are here: Home Category Index Algebra / The Factor Theorem The Factor Theorem - By David Spollen How to use this applet: The Factor Theorem: -Enter the co-efficients (a, b, c, d) of any given cubic polynomial in the boxes provided for them. -Enter the value of x in its box provided. -Click on the "Enter x" button. -An equation should appear containing your values and a report as to whether your x expression is a factor of your polynomial or not. Notes on the maths used in the applet: Proof of the factor theorem: Some other key pointers: Last updated: Thursday. May 03 2001

76. Gauss's Second Proof Of The Fundamental Theorem Of Algebra Gauss s second proof of the fundamental theorem of algebra. Another new proof ofthe theorem that every integral rational algebraic function of one variable http://www.cs.man.ac.uk/~pt/misc/gauss-web.html

Gauss's second proof of the fundamental theorem of algebra Another new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree HTML DVI compressed PostScript A5 PS booklet ... PDF by Carl Friedrich Gauss (1815); the Latin original appears in Volume 3, pages 33-56, of his collected works. Any polynomial of even degree m is transformed into one of degree m m 1); notice that, although this is typically a larger number, it contains one fewer factor of 2. Each root of the derived polynomial determines a pair of roots of the original one via a quadratic equation. Any odd-degree equation has a real root. This English translation was made by Paul Taylor in December 1983 and corrected by Bernard Leak. A summary of the proof, together with a note by Martin Hyland on its logical significance, appeared in Eureka (1985). The L

77. CJM - Relative Darboux Theorem For Singular Manifolds And Local Contact Algebra Go To CJM Index. CJM Prepublication 27 pages. Previous Page, Relative DarbouxTheorem for Singular Manifolds and Local Contact algebra, Next Page http://www.journals.cms.math.ca/cgi-bin/vault/viewprepub/zhitomirskii3375.prepub

Go To CJM Index CJM Pre-publication 27 pages Relative Darboux Theorem for Singular Manifolds and Local Contact Algebra M. Zhitomirskii Abstract TeX format In 1999 V. Arnol'd introduced the local contact algebra: studying the problem of classification of singular curves in a contact space, he showed the existence of the ghost of the contact structure (invariants which are not related to the induced structure on the curve). Our main result implies that the only reason for existence of the local contact algebra and the ghost is the difference between the geometric and (defined in this paper) algebraic restriction of a 1-form to a singular submanifold. We prove that a germ of any subset N of a contact manifold is well defined, up to contactomorphisms, by the algebraic restriction to N of the contact structure. This is a generalization of the Darboux-Givental' theorem for smooth submanifolds of a contact manifold. Studying the difference between the geometric and the algebraic restrictions gives a powerful tool for classification of stratified submanifolds of a contact manifold. This is illustrated by complete solution of three classification problems, including a simple explanation of V.~Arnold's results and further classification results for singular curves in a contact space. We also prove several results on the external geometry of a singular submanifold N in terms of the algebraic restriction of the contact structure to N . In particular, the algebraic restriction is zero if and only if

78. CJM - Relative Darboux Theorem For Singular Manifolds And Local Contact Algebra Index du JCM. Prépublication du JCM 27 pages. Page précédente, Relative DarbouxTheorem for Singular Manifolds and Local Contact algebra, Page suivante http://www.journals.cms.math.ca/cgi-bin/vault/viewprepub/zhitomirskii3375.prepub

79. Discrete Algebra - Binomial Theorem The binomial theorem is a useful formula for determining the algebraic expressionthat results from raising a binomial to an integral power. http://library.thinkquest.org/10030/11binoth.htm

Discrete Algebra Binomial Theorem The binomial theorem is a useful formula for determining the algebraic expression that results from raising a binomial to an integral power. It provides one with a quick method for finding the coefficients and literal factors of the resulting expression. The binomial theorem is stated as follows: where n! is the factorial function of n, defined as n! = n (n-1) (n-2) ..... 1 and 0! = 1 by convention. EX. The binomial theorem can also be used to find the rth term of the expansion of (a + b) n The first term of this expansion is a n , and the (n+1)th term is b n . By looking at the statement of the binomial theorem, we can see that the literal factors of the rth term are a n-r+1 · b r-1 , where the sum of the exponents of a and b must be equal to n. Since all terms in the expansion of (a + b) n can be written as we can set p = r - 1 so that the literal factors of the above term will be a n-r+1 · b r-1 . Thus, the rth term of the expansion of (a + b) n is EX. The 7th term of ( x + y ) is computed as Back to Top

80. Algebra Numerical Representations In algebra. algebraic Expressions Polynomials Equations The Factor and Remainder theorem. The Remainder theorem http://library.thinkquest.org/10030/algecon.htm

Algebra Mathematical Numbers Natural Numbers Whole Numbers Integers Rational and Irrational Numbers ... Complex Numbers Real Number System Real Number Line Properties of Real Numbers Absolute Value Arithmetic Operations ... Set Notation Numerical Representations In Algebra Algebraic Expressions Polynomials Equations Inequalities ... Complex Numbers Quadratic Equations and Inequalities Quadratic Equations Completing the Square Quadratic Formula Quadratic Inequalities ... Quadratic Rational Inequalities Graphing Coordinate Systems and Graphing Distance Between Two Points Slope of a Line Graphing Linear Equations and Inequalities ... Parallel and Perpendicular Lines Conic Sections Circles Parabolas Ellipse Hyperbola ... Hyperbola Functions Relations and Functions Composite of Functions Arithmetic Operations of Functions Inverse Functions Polynomial Functions Synthetic Division The Factor and Remainder Theorem The Remainder Theorem The Factor Theorem Polynomial Equations and Functions The Rational Root Theorem ... Graphing Rational Functions Exponential and Logarithmic Functions Exponential Functions Logarithmic Functions Properties of Logarithms e and the Natural Logarithm ... Applications of e and Exponential Functions Linear Algebra System of Equations System of Inequalities System Involving Nonlinear Systems of Equation Matrices ... Back to Top

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