1. ABSTRACT ALGEBRA ON LINE WELCOME TO abstract algebra ON LINE. This site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra. http://www.math.niu.edu/~beachy/aaol/

WELCOME TO ABSTRACT ALGEBRA ON LINE This site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra. It is intended for undergraduate students taking an abstract algebra class at the junior/senior level, as well as for students taking their first graduate algebra course. It is based on the books Abstract Algebra , by John A. Beachy and William D. Blair, and Abstract Algebra II , by John A. Beachy. The site is organized by chapter. The page containing the Table of Contents also contains an index of definitions and theorems, which can be searched for detailed references on subject area pages. Topics from the first volume are marked by the symbol and those from the second volume by the symbol . To make use of this site as a reference, please continue on to the Table of Contents. TABLE OF CONTENTS (No frames) TABLE OF CONTENTS (Frames version) Interested students may also wish to refer to a closely related site that includes solved problems: the OnLine Study Guide for Abstract Algebra REFERENCES Abstract Algebra Second Edition , by John A. Beachy and William D. Blair

2. Course 311 - Abstract Algebra Course 311 abstract algebra. The lecture notes for course 311 (abstract algebra), taught at Trinity College, Dublin, in the academic http://www.maths.tcd.ie/~dwilkins/Courses/311/

Course 311 - Abstract Algebra The lecture notes for course 311 ( Abstract algebra ), taught at Trinity College, Dublin, in the academic year 2001-02, are available here. The course consists of three parts:- Part I: Topics in Number Theory DVI PDF PostScript Part II: Topics in Group Theory DVI PDF PostScript Part III: Introduction to Galois Theory DVI PDF PostScript The following handouts were also distributed in the academic year 2001-02: A collection of problems DVI PDF PostScript The resolvent cubic of a quartic polynomial DVI PDF PostScript dwilkins@maths.tcd.ie ... Trinity College , Dublin 2, Ireland dwilkins@maths.tcd.ie

3. Elements Of Abstract And Linear Algebra By Edwin H. Connell Full online book on abstract algebra with emphasis on linear algebra. Format DVI, PDF, PS and gzippedPS. http://www.math.miami.edu/~ec/book/

Elements of Abstract and Linear Algebra Edwin H. Connell This is a foundational textbook on abstract algebra with emphasis on linear algebra. You may download parts of the book or the entire textbook. It is provided free online in PDF DVI postscript , and gzipped postscript. Please read some words from the author first. Join the revolution in education! Write a supplement to this book and put it online. Participate in and contribute to a forum on abstract and linear algebra. Ask questions, give answers, and make comments in a worldwide classroom with the internet as blackboard. [March 20, 2004] The entire book Introduction Outline Chapter 1: Background and Fundamentals of Mathematics Chapter 2: Groups Chapter 3: Rings Chapter 4: Matrices and Matrix Rings Chapter 5: Linear Algebra Chapter 6: Appendix Index Please send comments to Edwin H. Connell Web page created by Dmitry Gokhman

4. ABSTRACT ALGEBRA ON LINE: Contents abstract algebra ON LINE. This site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra. http://www.math.niu.edu/~beachy/aaol/contents.html

ABSTRACT ALGEBRA ON LINE This site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra. It is intended for undergraduate students taking an abstract algebra class at the junior/senior level, as well as for students taking their first graduate algebra course. It is based on the books Abstract Algebra , by John A. Beachy and William D. Blair, and Abstract Algebra II , by John A. Beachy. The site is organized by chapter. The page containing the Table of Contents also contains an index of definitions and theorems, which can be searched for detailed references on subject area pages. Topics from the first volume are marked by the symbol and those from the second volume by the symbol . To make use of this site as a reference, please continue on to the Table of Contents. TABLE OF CONTENTS (No frames) TABLE OF CONTENTS (Frames version) Interested students may also wish to refer to a closely related site that includes solved problems: the OnLine Study Guide for Abstract Algebra REFERENCES Abstract Algebra Second Edition , by John A. Beachy and William D. Blair

5. Intro To Abstract Algebra Paul Garrett's detailed and comprehensive lecture notes in abstract algebra. http://www.math.umn.edu/~garrett/m/intro_algebra/index.shtml

Intro to Abstract Algebra 5245-46 Paul Garrett, garrett@math.umn.edu, 624-5012, Vincent Hall 353 Quiz solutions (pdf): The text for 5245-5246 in Summer 1998 will be My Notes (PostScript) PDF version ). These notes (with exercises and index) were specifically designed by me for this two-quarter sequence. We will start at the beginning of the Notes, and go approximately halfway through in 5245. The precise pace will depend on the class, and content of each quiz and homework assignment will be indicated as we go. Starred sections and starred exercises are optional. There will be 20-minute quizzes each Tuesday and Thursday in the first hour of class. These quizzes will be open-book, open-notes. The one-hour final (Tues, July 21 for 5245, Wed Aug 26 for 5246) is also open-book, open-notes. email is by far the best way to reach me and get a helpful response: garrett@math.umn.edu If we have a grader, corresponding homework will be collected after each quiz, and will count for 10 percent of your grade. The lowest two quiz scores will be dropped (but no make-up quizzes given), and quizzes count for 60 percent. The final will be 30 percent. (If there is no homework grader, the quizzes will be 2/3 and the final 1/3). Office hours will be MWF after class, or by arrangement. I respond to

6. Home Page Of Robert B. Ash By Robert B. Ash. Chapters in PDF. http://www.math.uiuc.edu/~r-ash/

Robert B. Ash Professor Emeritus, Mathematics Dept. of Mathematics University of Illinois 1409 W Green St. Urbana, IL 61801 e-mail r-ash@math.uiuc.edu Books etc. On Line Abstract Algebra: The Basic Graduate Year A Course In Algebraic Number Theory A Course In Commutative Algebra A Pari/GP Tutorial Click below to read/download chapters in pdf format. PDF files can be viewed with the free program Adobe Acrobat Reader Comments and suggestions for improvement are welcome. Abstract Algebra: The Basic Graduate Year (Revised 11/02) This is a student-oriented text covering the standard first year graduate course in algebra. Solutions to all problems are included and some of the reasoning is informal. Front Preface and Table of Contents (110 K) Chapter 0 Prerequisites (194 K) Chapter 1 Group Fundamentals (150 K) Chapter 2 Ring Fundamentals (222 K) Chapter 3 Field Fundamentals (135 K) Chapter 4 Module Fundamentals (357 K) Enrichment Chapters 1-4 (288 K) Chapter 5 Some Basic Techniques of Group Theory (405 K) Chapter 6 Galois Theory (480 K) Chapter 7 Introducing Algebraic Number Theory (410 K) Chapter 8 Introducing Algebraic Geometry(448 K) Chapter 9 Introducing Noncommutative Algebra (350 K) Chapter 10 Introducing Homological Algebra(437 K) Supplement (315 K) Solutions Chapters 1-5 (461 K) Solutions Chapters 6-10 (449 K) End Bibliography, List of Symbols and Index (233 K)

7. Mathematics Archives - Topics In Mathematics - Abstract Algebra Topics in Mathematics. abstract algebra. abstract algebra. ADD. KEYWORDS Book Beachy from Northern Illinois University. abstract algebra. ADD. KEYWORDS Course materials, Lecture Notes http://archives.math.utk.edu/topics/abstractAlgebra.html

Topics in Mathematics Abstract Algebra Abstract Algebra ADD. KEYWORDS: Book SOURCE: John A. Beachy from Northern Illinois University Abstract Algebra ADD. KEYWORDS: Course materials, Lecture Notes SOURCE: Frank W. Anderson, University of Oregon TECHNOLOGY: TeX Abstract Algebra On Line ADD. KEYWORDS: Definitions, Theorems Algebra 1 ADD. KEYWORDS: Mathematica Notebooks, groups, linear groups, cosets, normal subgroups, quotient groups, group actions and Sylow subgroups SOURCE: Scarborough College Mathematics Computer Laboratory TECHNOLOGY: Mathematica Algebra: Abstract and Concrete by Frederick M. Goodman ADD. KEYWORDS: Published Text, Supplementary Materials, VRML, Symmetry, Polyhedra, Duality of polyhedra, Symmetric dynamical systems, Paper and stick models Algebra Universalis ADD. KEYWORDS: Published Journal Algebraic Combinatorics Via Finite Group Actions ADD. KEYWORDS: Online book SOURCE: A. Betten, H. Fripertinger, and A. Kerber The Algebraic Geometry Notebooks for Non-experts ADD. KEYWORDS: Expository article SOURCE: Aksel Sogstad from the University of Oslo Algebraic Geometry Seminar ADD. KEYWORDS:

8. Abstract Algebra abstract algebra. Notes home garrett@math.umn.edu exercises and notes at Intro to abstract algebra Updated Thursday, 08Jan-2004 114328 CST http://www.math.umn.edu/~garrett/m/algebra/

Abstract Algebra Notes home garrett@math.umn.edu In 2004-05, MWF 9:05-9:55, Vincent 206 Office hours MWF after class, or email anytime Text will be my notes, intended to be discursive and motivational. In addition, it would be wise to have at least one standard reference for lookup. Lang's Algebra is standard, but not meant for the novice. Miscellaneous smaller notes Cantor-Schroeder-Bernstein theorem Simple algebras and involutions Poincare-Birkhoff-Witt theorem Cech vs. derived-functor sheaf cohomology ... Second-quarter exercises A fuller set of more elementary exercises and notes at 'Intro to Abstract Algebra' Updated Thursday, 08-Jan-2004 11:43:28 CST home The University of Minnesota explicitly requires that I state that "The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota."

9. Exploring Abstract Algebra With Mathematica Home Page for Al Hibbard of labs that are based on the AbstractAlgebra packages, entitled Exploring abstract algebra with Mathematica http://www.central.edu/eaam.html

Exploring Abstract Algebra with Mathematica This page has been moved. Within ten seconds you will be transferred to http://www.central.edu/eaam/

10. Maple PowerTools - Abstract Algebra Set of lessons covering an undergraduate course in abstract algebra. Topics include finite groups, subgroups, and cyclic groups. Maple lessons for an undergraduate course in abstract algebra. Each lesson provides exercises to on group theory, which accompany the book Contemporary abstract algebra by J http://www.mapleapps.com/powertools/abstractalgebra/abstractalgebra.shtml

Maple MapleNet Maple T.A. Toolboxes ... Contact Us This is a comprehensive set of 16 Maple lessons for an undergraduate course in Abstract Algebra. Each lesson provides exercises to reinforce understanding of each topic. Prof. Alec Mihailovs of Shepherd College contributed six lessons on group theory , which accompany the book Contemporary Abstract Algebra by J. Gallian, ISBN: 0-618-12214-1 Prof. Mike May of St. Louis University contributed ten lessons on fields, rings and Galois theory , which accompany the book Abstract Algebra, by Dummit and Foote, ISBN 0-13-569302-0 Download the course for Maple 7 Download the course for Maple 6 Preview or download individual lessons below Preview Download Chapter 1: Preliminaries Chapter 2: Introduction to Groups Chapter 3: Groups Chapter 4: Finite Groups and Subgroups Chapter 5: Cyclic Groups Chapter 6: Other Topics in Group Theory Chapter 7: Factoring Polynomials over Extensions of the Rationals Chapter 8: The Gaussian Integers Chapter 9: The Division Algorithm and Quadratic Extensions Chapter 10: The Minimum Polynomial of an Algebraic Expression Chapter 11: Extension Fields and Inverses Chapter 12: Automorphism Groups Chapter 13:

11. Course Notes --- J.S. Milne In contrast to most such accounts it studies abstract algebraic varieties, and not just subvarieties of affine and projective space. http://www.jmilne.org/math/CourseNotes/

Course Notes Full notes as pdf (or dvi and ps) files for all the advanced course I taught between 1986 and 1999. Some of the notes give complete proofs (Group Theory, Fields and Galois Theory, Algebraic Number Theory, Class Field Theory, Algebraic Geometry), while others are more in the nature of introductory overviews to a topic. About the notes At last count, the notes included about 1350 pages. Errata: This is a list of errors and additional comments not yet incorporated into the files on the web, mainly contributed by readers. Group Theory A concise introduction to the theory of groups. html (August 29, 2003; v2.11; 85 pages) Fields and Galois Theory A concise treatment of Galois theory and the theory of fields, including transcendence degrees. html (August 31, 2003; v3.01; 99 pages) Algebraic Number Theory A fairly standard graduate course on algebraic number theory. html (31/8/98, v2.1; 140 pages) Class Field Theory html (6/5/97; v3.1; 222 pages) Modular Functions and Modular Forms This is an introduction to the arithmetic theory of modular functions and modular forms, with a greater emphasis on the geometry than most accounts.

12. Applied Abstract Algebra next contents index Next Contents Contents Index Applied abstract algebra. D. Joyner, R. Kreminski, J. Turisco. Date 810-2002. ROUGH DRAFT. http://web.usna.navy.mil/~wdj/book/

Next: Contents Contents Index Applied Abstract Algebra D. Joyner, R. Kreminski, J. Turisco Date: ROUGH DRAFT Contents Some elementary number theory Introduction Divisibility ... Binary and -ary notation Application: Divisibility criteria Application: Winning the game of Nim The Euclidean algorithm Ideals ... An application to Euler's -function Integral powers mod Fermat's Little Theorem, revisited Euler's theorem Application: Decimal expansions of rational numbers ... Arithmetic properties of : a summary Special project: continued fractions (optional) Number theory exercises using GAP Number theory exercises using MAGMA Polynomials, rings and fields ... Polynomials is a ring Roots The division algorithm The Euclidean algorithm Extended Euclidean Algorithm ... Factoring over Factoring over a finite field Modular arithmetic with polynomials Arithmetic properties of Constructing finite extensions of fields ... Factoring over Special project: Factoring over Special Project: Factoring over or Primitive polynomials Factoring strategies Irreducibility criteria Factoring over Polynomials and rings using GAP Finite fields Some vector spaces Rings ... The Hamming metric -codes and error correction The binary Hamming code Equivalent codes Bounds on the parameters of a code The dual code Computing the check matrix and the encoding matrix ... Question: What is ``the best'' code?

13. Abstract Algebra Lab Manual abstract algebra with GAP By JG Rainbolt and JA Gallian August 2003 Version. Below are pdf versions of the August 2003 version of the lab manual. http://euler.slu.edu/Dept/Faculty/rainbolt/manual.html

Abstract Algebra with GAP By J. G. Rainbolt and J. A. Gallian August 2003 Version Below are pdf versions of the August 2003 version of the lab manual. (The official web site for this manual is the Houghton Mifflin web site: http://college.hmco.com/mathematics/gallian/abstract_algebra/5e/students/gap.html http://www-gap.dcs.st-and.ac.uk/~gap We recommend instructors read the "Note to Instructor" before using this manual. Table of Contents Preface Note to Instructor Chapters -1 to 5 ... Complete August 2003 version of manual (excluding solutions and subroutines) An Instructor Solution Manual is also available. Please contact Julianne Rainbolt at rainbolt@slu.edu to obtain information about receiving the Instructor Solution Manual. This page has been visited times since January 1, 2002 Go back to SLU Math Department Home Page Julianne G. Rainbolt Last Update August 2003.

14. Abstract Algebra Notes (PostScript) abstract algebra Notes (PostScript). These are links to PostScript files containing notes for various topics in abstract algebra. http://www.millersv.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, 1999 term. ringint.ps (2 pages, 35,802 bytes): Axioms for the ring of integers; well-ordering. div.ps (10 pages, 274,812 bytes): Divisibility, greatest common divisor, the Euclidean algorithm. prime.ps (3 pages, 44,277 bytes): Prime numbers. modular.ps (6 pages, 150,456 bytes): Arithmetic in the integers mod n; congruences. groups.ps (14 pages, 275,279 bytes): The axioms for a group; basic properties and examples. matgrp.ps (3 pages, 40,539 bytes): Groups of matrices. unitzn.ps (3 pages, 44,922 bytes): The group of units in the integers mod n; Fermat's theorem. subgroup.ps (6 pages, 113,670 bytes): Subgroups. cyclic.ps (6 pages, 84,587 bytes): Cyclic groups. These are notes for Abstract Algebra I; they were revised during the Fall, 1998 term. perm.ps (8 pages, 139K):

15. Euclid's Elements, Introduction Includes the entire 13 books on plane geometry, geometric and abstract algebra, number theory, incommensurables, and solid geometry. Uses java applets to illustrate the principles. http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

Introduction New: Jaume Domenech Larraz has translated the Elements into Catalan at http://www.euclides.org/ Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages. I'm creating this version of Euclid's Elements for a couple of reasons. The main one is to rekindle an interest in the Elements, and the web is a great way to do that. Another reason is to show how Java applets can be used to illustrate geometry. That also helps to bring the Elements alive. The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional. I still have a lot to write in the guide sections and that will keep me busy for quite a while. This edition of Euclid's Elements uses a Java applet called the Geometry Applet to illustrate the diagrams. If you enable Java on your browser, then you'll be able to dynamically change the diagrams. In order to see how, please read

16. Abstract Algebra - Wikipedia, The Free Encyclopedia abstract algebra is the field of mathematics concerned with the study The term "abstract algebra" is used to distinguish the field from "elementary algebra" or "high school algebra http://www.wikipedia.org/wiki/Abstract_algebra

Abstract algebra From Wikipedia, the free encyclopedia. Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups rings and fields . The term "abstract algebra" is used to distinguish the field from " elementary algebra " or "high school algebra" which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers Historically, algebraic structures usually arose first in some other field of mathematics, were specified axiomatically, and were then studied in their own right in abstract algebra. Because of this, abstract algebra has numerous fruitful connections to all other branches of mathematics. Examples of algebraic structures with a single binary operation are: semigroups monoids groups More complicated examples include: rings and fields modules and vector spaces associative algebras and Lie algebras lattices and Boolean algebras In universal algebra , all those definitions and facts are collected that apply to all algebraic structures alike. All the above classes of objects, together with the proper notion of homomorphism , form categories , and category theory frequently provides the formalism for translating between and comparing different algebraic structures.

17. Abstract Algebra abstract algebra. Most people believe that the abstract algebra deals with many structures other than groups. What happens if we two http://www.math.uiuc.edu/~mileti/Museum/algebra.html

Abstract Algebra Most people believe that the mathematics they learn in high school and in their early college years represents the essence of abstraction. What could be less tangible that the idealistic abstract notion of number? Mathematicians work with and delight in bizarre numbers such as i (the square root of -1) which to the uninitiated must seem like an irrational mix of mysticism and numerology. Nonetheless, the basic operations in arithmetic (addition, multiplication, etc.) apply remarkably well to many disparate real-life situations whether you are balancing your checkbook, keeping score in a game of cards, calculating the position of an object under the influence of gravity in physics, or measuring ingrediants for a recipe. In all these situations, the usual grade-school manner in which you add and multiply numbers models the situation perfectly. However, there are times when the normal rules of arithmetic that you learn in grade school do not seem to apply. For example, suppose that you are compiling baseball statistics. To determine a player's batting average, you need to know both the number of hits that he has and the number of times he has been at-bat. If a player has 7 hits in 23 attempts, a natural way to record this information is using the fraction 7/23. (The way this is usually displayed when you are watching a game is the corresponding decimal, truncated to 3 places. In the case of 7 hits in 23 at-bats, it would be written as .304. Although the number .304 is more visually appealing and and conveys information more quickly (the batter gets a hit about 30.4% of the time), it is less precise because we are unable to determine whether the play has 7 hits in 23 at-bats, 14 hits in 46 at-bats, or 70 hits in 230 at-bats.)

18. Zeeman, E. Christopher A major contributor to topology and dynamical systesm. Includes notes, lectures and bibliography of a variety of topics, such as chaos theory, topology, abstract algebra and math history. http://www.math.utsa.edu/ecz/

window.location="http://applied.math.utsa.edu/~gokhman/ecz/";

19. Syllabus - Abstract Algebra (CyberEd Version) 92.421 abstract algebra. The CyberEd Version This course is an introductory undergraduate course in abstract algebra, concentrating on group theory http://www.uml.edu/Dept/Math/courses/m421c/m421c.html

Syllabus 92.421 Abstract Algebra The CyberEd Version Instructor: Kenneth M. Levasseur Department of Mathematical Sciences University of Massachusetts Lowell Kenneth_Levasseur@uml.edu This course is an introductory undergraduate course in abstract algebra, concentrating on group theory. It will be conducted on-line with students completing labs and problem sets from home and communicating via email, a discussion list and chat. Academic Prerequisites You should have completed at least two semesters of calculus and one semester of linear algebra or discrete mathematics. Having taken both linear algebra and discrete math is even better What you need to do and have to take this course. Register through Continuing Education at UMass Lowell Mathematica 3.0+ - any platform that supports Notebooks (PC, Mac, Next, UNIX). Student versions are available in the bookstore for about $130 at the UML Bookstore. You must prove that you are a student to purchase this version. A computer that will run your version of Mathematica ( most likelya Macintosh or IBM) Note: No matter what platform you run Mathematica on, there no problem sharing

20. BEACHY: ABSTRACT ALGEBRA II A companion volume to abstract algebra by John A. Beachy and Bill Blair published by Waveland Press in 1995. Chapters in PostScript. http://www.math.niu.edu/~beachy/abstract_algebraII/

Abstract Algebra II by John A. Beachy These notes served as a companion volume to the book Abstract Algebra Second Edition (written jointly with Bill Blair, and published by Waveland Press in 1995). The notes became the preliminary version of the book Introductory Lectures on Rings and Modules published by Cambridge University Press, and so it has become necessary to discontinue publication of the notes on the Web. Click here for further information about the book. If you need additional information, please contact John Beachy, Dept. of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, Tel. 815 / 753-6753, email: beachy@math.niu.edu This site was opened in 12/1995, and last modified on 5/21/2002. This page has been accessed 116,289 times since 8/96. Author's homepage Homepage for Abstract Algebra Second edition

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