advertisement

University of Jordan Faculty of Science Department of Mathematics Course Outline Course code and name: 0331341 Abstract Algebra I Credit hours: 3 Prerequisite: 0301211 Fundamentals of Mathematics Course description and objectives: Upon completion of this course, the student should be able to 1. Write mathematical proofs and reason abstractly in exploring properties of groups and rings. 2. Define, construct examples of, and explore properties of groups, including symmetry groups, permutation groups and cyclic groups. 3. Determine subgroups and factor groups of finite groups. 4. Determine, use and apply homomorphism's between groups. 5. Understand definitions, examples, and theorems pertaining to groups. Tests & evaluations Grades will be calculated from grades on weekly assignments, three exams and a final exam, using the scheme Course contents and schedule Topic Reading and preparation assignment Introduction Number of lectures 1 Group Definition Chapter 2: pp 40 - 48 2 Group Properties Chapter 2: pp 48 – 51 1 HOMEWORK 1 Chapter 2: 1,3,5,8,12,14,15,17,18,19,26, 39 Order and Subgroups Chapter 3: pp 57 - 61 1 Centers&Centralizers Chapter 3: pp 61- 64 2 1 HOMEWORK 2 Chapter 3: 1,2,4,6,7,8,9,10,12,18,20,23,26,27, 30,33,51,59 1 Cyclic Groups (1) Chapter 4: pp 72 - 75 1 Cyclic Groups (2) Chapter 4: pp 75-80 2 Chapter 4: 1,2,3,7,9,10,11,13,14,19,23,28,29,31,33,38,40,45,49,53,60,62,64 Permutation Groups (1) Chapter 5: pp 95 – 103 HOMEWORK 3 Even and Odd 1 2 Chapter 5: pp 103 - 112 1 Chapter 5: 1,2,3,4,6,7,8,9,12,17,18,23,24,27,28,32,34,42,44,45,48 1 Isomorphisms Chapter 6 pp 122 - 126 2 Cayley's Theorem Chapter 6: pp 126 – 133 1 HOMEWORK 5 Cosets Chapter 6: 1,3,6,7,10,17,24,25 Chapter 7: pp 138 - 141 1 Chapter 7: pp 141 - 144 2 Chapter 7: 1,2,3,8,14,18,20,22,23 1 Chapter 8: pp 154 - 160 2 HOMEWORK 7 Chapter 8: 3,4,5,6,7,8,9,10,11,14,16,17,18,20,24,25,29,30,31,32 1 Normal Subgroups Chapter 9: pp 178 - 181 2 Internal Direct Product Chapter 9: pp 181 – 184 1 HOMEWORK 4 Lagrange's Theorem HOMEWORK 6 Direct Products 2 HOMEWORK 8 Homomorphisms Chapter 9: 1,4,5,7,10,12,14,16,19,20,48 Chapter 10: pp 200 – 206 1 First Isomorphism Theorem Chapter 10: pp 206 – 211 1 Chapter 10: 9,11,15,21,24,31 1 Homework 9 Text book Contemporary Abstract Algebra, J. Gallian (Houghton-Mifflin). References - Abstract Algebra, David S. Dummit and Richard M. Foote. - Topics in Algebra, I. N. Herstein. - Abstract Algebra: An Introduction, Thomas W. Hungerford. - A first course in Abstract Algebra, Fraleigh 1