61. Abstract Algebra I MATH 320 abstract algebra I. TEXT Joseph A. Gallian, Contemporary abstract algebra,Fifth Edition, Houghton Mifflin, 2002 (due in the bookstore January 28). http://math.colgate.edu/math320/dlantz/abalgfdi.html

MATH 320: Abstract Algebra I TEXT: Joseph A. Gallian, Contemporary Abstract Algebra, Fifth Edition, Houghton Mifflin, 2002 (due in the bookstore January 28). INSTRUCTOR: David Lantz Email: dlantz@mail.colgate.edu Office : McGregory 316 - Extension : 7737 Formal Office Hours : MWF 9:2010:10 a.m. and MR 2:003:00 p.m. Effective Office Hours: Weekdays, 9:00-5:00, except when I am teaching or in a meeting Home: 146 Lebanon Street, Hamilton Phone : 824-0965 (Please do not call after 10 p.m.) WEB ADDRESS: This page has the web address: http://math.colgate.edu/math320/dlantz/abalgfdi.html I encourage you to bookmark it on your computer for later use. HOMEWORK: This list will grow as I work through the text. Due dates will be specified. Page 37 (Ch 1): 1, 2, 3, 9, 10, 11, 13, 14, 16. (Solutions) Page 52 (Ch 2): 1, 3, 4, 7, 12, 14, 15, 17, 25, 26, 29 (If x e , what are ( x and ( x ?), 33 (Use #26.), 35 (Use an earlier example.) (Solutions) Page 67 (Ch 3): 1, 2 (Both sets are infinite; give enough elements to show the pattern.), 3, 8, 9, 14, 16, 17ab, 19, 20 (Use #14 and #19.), 22, 23, 27, 33, 35, 44 ("Power of 2" means "integer power of 2, positive or negative or zero". Use the multiplicative property of the determinant.), 48, 49, 52. (Solutions) Page 82 (Ch 4): 1, 2, 4, 11, 13, 14, 19, 25 (two cases:

62. MATHEMATICS, STATISTICS, AND MATHEMATICAL EDUCATION Beachy, John A., and William D. Blair. abstract algebra, Second Edition. ABSTRACTALGEBRA A First Undergraduate Course, Fifth Edition. http://www.waveland.com/Mathematics.htm

MATHEMATICS, STATISTICS, AND MATHEMATICAL EDUCATION Beachy, John A., and William D. Blair ABSTRACT ALGEBRA, Second Edition 427 pages, $48.95 list; ISBN 0-88133-866-4; Instructor’s Solutions Manual This volume offers a gentle introduction to proof in a concrete setting, the introduction of abstract concepts only after a careful study of important examples, and the gradual increase of the level of sophistication as one progresses through the book. It offers an extensive set of exercises that help to build proof writing skills. In addition, chapter introductions give motivation and historical context while tying the subject matter in with the broader picture. Introduction 1. Integers 2. Functions 3. Groups 4. Polynomials 5. Commutative Rings 6. Fields 7. Structure of Groups 8. Galois Theory 9. Unique Factorization Appendix A. Sets Appendix B. Construction of the Number Systems Appendix C. Basic Properties of the Integers Appendix D. Induction Appendix E. Complex Numbers Appendix F. Solution of Cubic and Quartic Equations Appendix G. Dimension of a Vector Space

63. Abstract Algebra Fall 2001. Fall 2001 abstract algebra. Questions and comments welcome! Course Materials. Thefollowing are the course materials from my 2001 abstract algebra course. http://www.csulb.edu/~fnewberg/Teaching/Fall2001/444Notes2001.html

Fall Abstract Algebra Questions and comments welcome! Email me at fnewberg@csulb.edu http://www.csulb.edu/~fnewberg Goals Assessment and Course Materials Exams and supporting materials are provided below. This is a senior level algebra course required for all pure math majors, including those planning to teach high school. We do not offer a second semester of abstract algebra at the undergraduate level, though from time to time advanced undergraduates continue on to take our graduate algebra course. I always lectured the entire class period, which lasted one hour and fifteen minutes and met twice weekly. I had 34 students. Of these, 2 students dropped, there were 1 F, 3 D's, 10 C's, 7 B's and 11 A's (1 of which was a B students that received a high A on the final exam). My colleges informed me that 6 of those 11 students are the strongest this department has seen in years, that I was lucky to have them, and not to expect so many A's in general. Goals Very generally, the nature of mathematics requires that the primary goals are to teach some of the basic vocabulary in some of the basic fields of mathematics and to develop proficiency in reasoning and communicating using the precise language of mathematics. These are the goals of this course as well; on one hand there is the content, and on the other the reasoning and communication skills. Content: I planned to spend and spent the first third of the semester discussing the integers and basic number theory, the next half semester on group theory, and the final sixth on rings and fields. I covered Lagrange's Theorem and cosets, though not to the group structure on quotient groups. I did homomorphisms and isomorphisms thoroughly and the First Isomorphism Theorem, though since we did not have a group structure on the quotient, we just showed the bijection between the cosets of the kernel and the image of a homomorphism. We covered the definition and various examples of rings (commutative and noncommutative), integral domains, division rings and fields, as well as ring homomorphisms.

64. MC382 Abstract Algebra MC382 abstract algebra. MC382 abstract algebra. Credits 20, JB Fraleigh,A First Course in abstract algebra, 5th edition, AddisonWesley. http://www.mcs.le.ac.uk/Modules/Modules99-00/MC382.html

Next: MC383 Complex Analysis Up: Year 3 Previous: MC381 Modelling physical systems MC382 Abstract Algebra MC382 Abstract Algebra Credits: Convenor: Dr. N.J. Snashall Semester: Prerequisites: essential: MC241, MC249 Assessment: Coursework: 10% Three hour exam in January: 90% Lectures: Classes: Tutorials: none Private Study: Labs: none Seminars: none Project: none Other: none Total: Explanation of Pre-requisites In dealing with one field containing another, e.g. the field of complex numbers containing the real numbers, we can consider the larger field as a vector space over the smaller and so exploit the idea of basis and other linear algebra concepts to learn about the larger field. Thus MC241 (and its prerequisites) is needed for this course. In considering the structure of fields we also require many of the basic ring properties from MC249. Course Description The topics for this module cover three broad areas. The first part considers some basic ring-theoretic notions and enables us to determine when a factor ring is a field. The second section discusses in some detail properties of polynomials over fields, especially over the rationals, and looks particularly at irreducibility. The final part of the module deals with extension fields, splitting fields and shows how all finite fields can be constructed. It also includes a study of ruler and compass constructions and in particular it is shown that the classical problem of squaring the circle is impossible, that is, it is not possible to construct a square of area equal to that of a given circle.

65. By Subject: Algebra Examples and links concerning abstract algebra. Examples use Maple, Matlab,and Mathematica. Search In Stat/Math. abstract algebra. http://www.indiana.edu/~statmath/bysubject/abstractalgebra.html

Stat/Math By Subject Abstract Algebra Search: In: Stat/Math By Subject Abstract Algebra Abstract Algebra With Maple Packages for abstract algebra with Maple A package for Algebraic Curves in Maple Abstract Algebra With Mathematica Solving the Quintic Other Abstract Algebra Resources Math Forum: Abstract Algebra Abstract Algebra Online Algebraic Number Theory Archives Combinatorics - Various uses of abstract algebra. Atlas of Finite Group Representations Permission to use this document is granted so long as the author is acknowledged and notified. Please send comments and suggestions to: statmath@indiana.edu Indiana University Last modified: Wednesday, 19-Feb-2003 13:00:00 EST URL /~statmath/bysubject/abstractalgebra.html

66. (152) ABSTRACT ALGEBRA abstract algebra (code 152), SEMESTER SECOND. Recommended Texts J Fraleigh,A First Course in abstract algebra, (5th edition), 1994, AddisonWesley. http://www2.umist.ac.uk/mathematics/intranet1/Yr1Syllabus/(152) ABSTRACT ALGEBRA

ABSTRACT ALGEBRA (code: 152) SEMESTER: SECOND CONTACT: DR R STÖHR (M/P4) CREDIT RATING: Aims: To develop the framework of abstract algebraic structures, with particular emphasis on groups, based on a variety of concrete examples, which are in their own right indispensable tools for every working mathematician Intended Learning Outcomes: On successful completion of the course students will have acquired : Active knowledge and understanding of some basic concepts and results of abstract algebra, and gained confidence in: Basic manipulations with integers (Euclidean Algorithm) Handling permutations Working with equivalence relations Modular arithmetic Pre-requisites: Dependent Courses: Course Description: Permutations, Binary Operations, Equivalence Relations, Groups, Subgroups, Cyclic Groups, Isomorphisms, Rings. Teaching Mode: 2 Lectures per week 1 Examples Class fortnightly 1 Supervision Class per week, shared with 153. Private Study: 5 hours per week Recommended Texts: J Fraleigh, A First Course in Abstract Algebra, (5th edition), 1994, Addison-Wesley. Assessment Methods: Coursework: 20% Coursework Mode: Multiple choice test in Week 10.

67. Abstract Algebra Retreat S99 New College abstract algebra Retreat February 57, 1999 Long Key,FL. 2. Lidle Pilz Applied abstract algebra , Springer (1997). http://www.sar.usf.edu/~poimenid/AlgebraRetreatS99.html

New College Abstract Algebra Retreat February 5-7, 1999 Long Key, FL (Still under construction) Inspiration Participants Program Abstracts ... Evaluations 1. INSPIRATION AND DESCRIPTION OF THE PROJECT Having taught mathematics for nearly ten years in the liberal arts environment, I have come to the conclusion that students perform best when: They feel that their professor cares about them and believes that they can be successful They are comfortable discussing their ideas or questions They are involved in active learning They work with each other in an environment that is supportive and responsive The material that they are studying is put into a context that is relevant to their lives This kind of environment helps to promote enthusiasm, confidence, collegiality and personal growth. My personal observations were confirmed by a recent report [1] of the Mathematical Association of America. A page summarizing the findings of the task force involved in producing this NSF funded report, is appended at the end of this report. All participants were asked to sign an honor code about their conduct through weekend and I am happy to say that their behavior for the entire weekend was exemplary. We traveled to the retreat location in four cars that were driven by three students and myself. During our first evening, we scheduled our weekend. It turned out that after several weeks of preparation we had to accommodate seven different student presentations. Four of the seven presentations involved two or more students and the other three were single presentations. A detailed description of the program, as well as abstracts of the student presentations (prepared by the students) are included in this report. In addition to the presentations, we cooked some great dinners, watched movies, watched the sunset, played frisbee, and got to know each other very well.

68. Schaums Outline Of Modern Abstract Algebra (Schaums) Book Schaums Outline of Modern abstract algebra, Schaums Outline of Modern AbstractAlgebra, Schaums Outline of Modern abstract algebra by Authors Frank, Jr. http://www.wkonline.com/a/Schaums_Outline_of_Modern_Abstract_Algebra_0070026556.

Book > Schaums Outline of Modern Abstract Algebra (Schaums) Schaums Outline of Modern Abstract Algebra (Schaums) by Authors: Frank, Jr. Ayres Released: 01 June, 1965 ISBN: 0070026556 Paperback Sales Rank: List price: Our price: Schaums Outline of Modern Abstract Algebra (Schaums) > Customer Reviews: Average Customer Rating: Schaums Outline of Modern Abstract Algebra (Schaums) > Customer Review #1: Very well explained I think this book would be good by itself in picking up algebraic theories and methods. Each section is well explained and the sample problems take you through the process step-by-step. The only problem I have with the book is that not all the supplementary exercises (to test your understanding) have the answers. Some have an answer, some have a partial answer, some have a hint, and some have nothing. This is a little aggravating, but it does not take away from the book. Schaums Outline of Modern Abstract Algebra (Schaums) > Customer Review #2: I become a mathematics fan.

69. Mathematics Online Compendium: Abstract Algebra www.astro.virginia.edu/~eww6n/math/Lattice.html Catalogue of Algebraic Systems http//math.usf.edu/algctlg/INDEX.htmlMath Forum Modern Algebra http//forum http://www.dei.unipd.it/~cuzzolin/MOCAbstractAlgebra.html

Lattice (reticoli) http://www.astro.virginia.edu/~eww6n/math/Lattice.html Catalogue of Algebraic Systems http://math.usf.edu/algctlg/INDEX.html Math Forum: Modern Algebra http://forum.swarthmore.edu/advanced/modern.alg.html Beiträge zur Algebra und Geometrie Homepage http://www.emis.de/journals/BAG/ Algebra - University of Wales, Bangor http://www.bangor.ac.uk/ma/teaching/pgrads/guides/pgstuds/algebra.html Last update: January 18th, 1999

70. Abstract Algebra II: Theory Of Rings And Fields Mathematics 123. abstract algebra II Theory of Rings and Fields. Peter KronheimerLocation Meeting time MWF 10001100 Exam group 3 Catalog number 5613. http://icg.harvard.edu/~math123/

Spring 2003 Assignments Examinations Handouts Syllabus ... Teaching Staff Mathematics 123 Abstract Algebra II: Theory of Rings and Fields Peter Kronheimer Location: Meeting time: MWF 10:00-11:00 Exam group: 3 Catalog number: 5613 Fields, field extensions, automorphism groups of fields, the fundamental theorems of Galois theory. Applications to the insolubility of the general quintic by radicals, the classification of finite fields, ruler and compass constructions. Rings, ideals, and modules; unique factorization domains, principal ideal domains and Euclidean domains; structure theorems for modules. Ideal classes; factorization of ideals. The notion of a Dedekind domain, and the Moebius band. For a more detailed syllabus, and more information about the course, follow the link to the syllabus on the left. URL: http://www.courses.fas.harvard.edu/~math123/ Last modified: 01/24/2003 Instructor's Toolkit PIN Unix

71. Abstract Algebra I: Theory Of Groups And Vector Spaces Fall 2002, Mathematics 122. abstract algebra I Theory of Groups andVector Spaces. Curtis McMullen. The official website for this course http://icg.harvard.edu/~math122/

Fall 2002 Mathematics 122 Abstract Algebra I: Theory of Groups and Vector Spaces Curtis McMullen The official website for this course is here: http://math.harvard.edu/~ctm/math122/ URL: http://www.courses.fas.harvard.edu/~math122/ Last modified: 09/20/2002 Instructor's Toolkit PIN Unix

72. MATH 375: Abstract Algebra MATH 375 abstract algebra. Offered Fall The text we will be usingis Contemporary abstract algebra by Joseph A. Gallian. We will http://people.hws.edu/mitchell/math375f99.html

MATH 375: Abstract Algebra Offered: Fall 1999 Instructor: Kevin J. Mitchell Room: ET 105 Time: MWF 10:40 to 11:50 AM Text: Contemporary Abstract Algebra, Fourth Edition by Joseph A. Gallian Information Available: About the course Assessment Office Hours Additional Sources on Reserve ... Answers to Assignments and Additional Material About the Course Abstract Algebra is a core course in the mathematics curriculum because of its focus on the basic underlying structures that occur in many mathematical systems. You have already been introduced to these notions (in fact, much more complicated notions) in Math 204 and Math 331 or CS 221 and CS 325. The basic object of our study this term will be groups. These are systems which are closed under some operation * (often addition or multiplication). Further, there must be an identity element, every element must have an inverse, and * must be asociative. Some familiar examples of groups include the ingtegers under addition, the field of real numbers under addition, the real numbers (without 0) under multiplication, and any vector space under its operation of addition. In some sense, groups are simpler than vector spaces and fields since the latter have two operations, but there is only one operation in a group. Since there are "fewer restrictions'' on groups than on vector spaces or fields, there are "more of them.'' In fact, groups are almost everywhere you look. For example, the set of motions that slide the tiles on a floor into the same pattern or that take a wallpaper pattern into itself form a group.

73. Drowning In Abstract Algebra Drowning in abstract algebra. Hello, I guess that perhaps abstract algebra isnot so often come across in physics, but it does come around sometimes. http://www.lns.cornell.edu/spr/2000-04/msg0023512.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Drowning in abstract algebra Subject : Drowning in abstract algebra From Date : 03 Apr 2000 00:00:00 GMT Approved : helbig@astro.rug.nl (sci.physics.research) Newsgroups : sci.physics.research Organization : University of Illinois at Urbana-Champaign Prev by Date: Re: Elementary Particles and Black Holes Next by Date: Re: Gauge-fixing vs modding out by gauge transformations Prev by thread: Re: Elementary Particles and Black Holes Next by thread: Re: question on fully/half silvered mirror experiment and photons Index(es): Date Thread

74. Abstract Algebra And Algebraic Systems In The Pentagon abstract algebra and Algebraic Systems. (see also Number Theory and Arithmetic).15, 1, 2530, The Invention of Quaternions, Bernadine http://www.kme.eku.edu/abstract.htm

75. Math 351 (Abstract Algebra) Math 351 (abstract algebra). Prof. Weibel. Prerequisite Linear Algebra (Math250) Text abstract algebra (3rd ed.), by IN Herstein, Prentice Hall, 1996. http://www.math.rutgers.edu/~weibel/math351.html

Math 351 (Abstract Algebra) Prof. Weibel Fall 1998 This course is an introduction to abstract algebraic systems, including groups, rings and fields. Prerequisite: Linear Algebra (Math 250) Text: Abstract Algebra (3rd ed.), by I.N. Herstein, Prentice Hall, 1996 Lectures MW4 SEC-217 Workshop M5 SEC-216 (note: the first Workshop is September 14!) Tentative Course Syllabus Week Lecture dates Sections topics 9/2 (Wednesday) mappings 9/9 (Wednesday) permutations and "Z" 9/14-16 (first Workshop 9/14) "C", examples of groups subgroups quotient groups up to 2.6 review and Exam 1 quotient groups Abelian groups, Sylow's Theorem odd and even permutations examples of rings Ideals up to 4.4 review and Exam 2 11/23 (no class 11/25) polynomial rings examples of fields field extensions 12/10 (Thursday but "Monday") up to 5.4 review of fields 12/15 (Tuesday) 12-3 PM Final Exam Return to Weibel's Home Page Charles Weibel / weibel@math.rutgers.edu / July 4, 1998

76. BEACHY: ABSTRACT ALGEBRA II abstract algebra II. As a set of lecture notes, abstract algebra II is not an encyclopedicreference, and the reader must beware of misprints, but it is free. http://br.crashed.net/~akrowne/alg/

Abstract Algebra II by John A. Beachy These notes are a companion volume to the book Abstract Algebra Second Edition (written jointly with Bill Blair, and published by Waveland Press in 1995). Although results from the first volume are used throughout, and sections are numbered to follow those in the first volume, Abstract Algebra II can be read independently. These lecture notes were begun in the spring of 1993, when I taught the second semester of our graduate algebra course at Northern Illinois University. I hope that the level is comparable to that of Hungerford or Jacobson, which I recommend as references. I would note that the first semester of our graduate algebra course concentrates on Galois theory, and the necessary group theoretic background. Chapters 7 and 8 of our book Abstract Algebra Second Edition include much of this material, since they cover the standard results on group actions, the Sylow theorems, simple groups, and solvable groups, together with Galois groups and the fundamental theorem of Galois theory. As a set of lecture notes

77. Abstract Algebra lojbanwiki, abstract algebra. This Wiki is now locked. The content has all beenmoved to wiki.lojban.org, hosted by Robin. Please update your bookmarks. http://nuzban.wiw.org/wiki/index.php?Abstract Algebra

78. The Basics Of Abstract Algebra, By Paul E. Bland http://www.whfreeman.com/bland/

79. PMTH332 Abstract Algebra Contents PMTH332 abstract algebra. Coordinator Dr Imre Bokor Room175, Phone 7+61 (0)2 6773 2213. Internal/External Second Semester. http://turing.une.edu.au/dept/units/undergrad/PMTH332.html

Next: PMTH332A Abstract Algebra: Advanced Up: THIRD YEAR Previous: GEST325 Quantitative Genetics and Contents PMTH332 Abstract Algebra Coordinator: Dr Imre Bokor Room: 175, Phone: 7+61 (0)2 6773 2213 Internal/External Second Semester Three lectures and a one-hour tutorial per week. This unit provides an introduction to the theory of groups and rings covering basic properties, subgroups and subrings, quotient structures, products of groups and rings, isomorphism theorems, cyclic groups, the Fundamental Theorem of Finitely Generated Abelian Groups, the Sylow Theorems, polynomial rings and fields of quotient. This unit is essential for students contemplating further studies in mathematics. www@mcs.une.edu.au

80. Increasing Accessibility Of Examples In Abstract Algebra Increasing Accessibility of Examples in abstract algebra. The projects wereused as a supplement to our firstsemester abstract algebra courses. http://enhanced-learning.org/mellon/proj/aafinalreport.html

Increasing Accessibility of Examples in Abstract Algebra Using Computer-based Projects The Final Report Submitted July 27, 2000 Peter Blanchard Assistant Professor of Mathematics Denison University blanchard@cc.denison.edu Judy Holdener Assistant Professor of Mathematics Kenyon College holdenerj@kenyon.edu Overview: Our collaborative efforts over the past year resulted in the development of six computer-based labs. The labs were designed to enhance student exploration and understanding by making examples, data, and computations more accessible to students. The projects were used as a supplement to our first-semester Abstract Algebra courses. Judy Holdener taught the course in the fall at Kenyon, and Peter Blanchard taught the course in the spring at Denison. All six of the projects rely on the software package GAP (Groups, Algorithms, and Programming), a freely distributed program designed to handle large computations within and relating to groups. What was planned and what was accomplished? Our goal, as stated in our proposal, was to develop six computer-based projects to make concrete examples in Abstract Algebra more accessible to the students. We had originally planned to use Maple in one of the projects, and we had a tentative list of ideas for the topics to be covered:

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