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Abstract Algebra From Physiki Jump to: navigation search Main Page Mathematical and Computer Sciences Course Wikis Contents Course Information Instructor Information Course Calander Office Hours ... edit Course Information MATH458: Abstract Algebra - This course is an introduction to the concepts of contemporary abstract algebra and applications of those concepts in areas such as physics and chemistry. Topics include groups, subgroups, isomorphisms and homomorphisms, rings, integral domains and fields. Prerequisite: MATH 213, 223 or 224, and MATH 300 or consent of instructor. 3 hours lecture; 3 semester hours. edit Instructor Information Instructor : Terry Bridgman Office : Chauvenet Hall 279 Office Phone : 303.384.2447 email : tbridgma@mines.edu edit Course Calander Classes Begin : Janurary 9th, 2008 Meeting Days : Tuesday, Thursday Meeting Time : 9:30am - 10:45am Meeting Location : Meyer Hall 363 Class Holidays : Feburary 18th, 2008 - Presidents Day March 10th-14th, 2008 - Spring Break April 3rd-5th, 2008 - Engineering Days Classes End : May 9th, 2008

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37. Abstract Algebra - Mahalo Abstract Algebra is an area of mathematics that studies algebraic structures. Some of those structures are groups, rings, fields, vector, and modules. http://www.mahalo.com/Abstract_Algebra

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40. Abstract Algebra - Solutions To Final Exam - Fall 1996 Old browser version, for new browser click here. Math 313 Solutions to Final Exam Fall 1996 3 hours Closed Book Dr. Corwin December 16, 1996 http://www.mcs.sdsmt.edu/ecorwin/abstract_algebra/fall96/finf96sln.htm

Old browser version, for new browser click here Math 313 Solutions to Final Exam Fall 1996 3 hours Closed Book Dr. Corwin December 16, 1996 Answer ten of the following twelve problems. If more than ten are answered, only the best ten count. Warning: Some questions are copies of previous test questions, but others are modifications of previous test questions or new questions. Be sure to read every question carefully. 1. Define ring. Solution A set R R is an abelian group with respect to + left distributive law: c a b c a c b for all a b c in R right distributive law: ( a b c a c b c for all a b c in R 2. Define group. Solution A set G with an operation * satisfying: * is associative identity: e such that x G e x x e x inverses: x G y G such that y x x y e 3. Given an equivalence relation ~, prove that a b if and only if [ a b Solution Assume a b and show [ a b To show [ a b ], show [ a b ] and [ b a Let c a ]. Then, c a . Since a b and ~ is transitive, this gives c b which implies that c b ]. Thus, [ a b Similarly, let c b ]. Then, c b . Since a b and ~ is symmetric

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