| Lecture 1 Groups I: 1-4 |
Oct. 23 8-10 E36 |
Suggested Exercises: I-1 Introduction and Examples. 35-37 I-2 Introduction and Examples. 24, 26, 29-34 I-3 Isomorphic Binary Structures. 26, 27, 28 I-4 Groups. 11-18, 23, 25, 29, 32, 33, 35, 37, 38 |
Homework 1 Due Oct. 30 should be given to Afshin Goodarzi |
| Exercises | Oct. 26 15-17 V21 |
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| Lecture 2 Subgroups, cyclic groups, group homomorphisms I: 5-7, III:13 |
Oct. 31 15-17 D41 |
Suggested Exercises: I-5 Subgropus. 8-13, 14-19, 39, 46, 47, 51, 53, 55 I-6 Cyclic groups. 32, 33-37, 45, 46, 48 III-13 Homomorphisms. 1-6, 8-15 |
Homework 2 Due Nov. 7 should be given to Afshin Goodarzi |
| Exercises | Nov. 1 8-10 D41 |
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| Lecture 3 Permutations II: 8-9 |
Nov. 7 8-10 D41 |
Suggested Exercises: II-8 Groups of Permutations. 28, 29, 30-34, 35, 36, 40-43, 44, 45,46, 48 II-9 Orbits, Cycles and the Alternating Groups. 20-23, 27, 29, 30, 33, 34, 36, 39 |
Homework 3 Due Nov. 14 should be given to Afshin Goodarzi |
| Exercises | Nov. 9 15-17 E36 |
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| Lecture 4 Lagrange’s Theorem and finitely generated abelian groups II: 10-12 |
Nov. 15 8-10 E36 |
Suggested Exercises: II-10 Cosets and the Theorem of Lagrange. 17-19, 28-33, 36, 37, 39, 40, 44, 46, 47 II-11 Direct Products and Finitely Generated Abelian Groups. 32, 34, 36, 47, 49 II-12 Plane Isometries. 2 16-20, 24-37 |
Homework 4 Due Nov. 22 should be given to Afshin Goodarzi |
| Exercises | Nov. 16 15-17 E36 |
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| Lecture 5 Homomorphisms and factor groups III: 13-15 |
Nov. 21 15-17 D41 |
Suggested Exercises: I III-13 Homomorphisms. 32, 39-45, 47,48, 50, 52 III-14 Factor groups. 23, 24, 30, 31, 33-36, 40 III-15 Factor-Groups Computations and Simple Groups. 19-23, 34-36, 39 |
Homework 5 Due Nov. 28 should be given to Afshin Goodarzi |
| Exercises | Nov. 22 8-10 D41 |
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| Lecture 6 Group actions III: 16-17 |
Nov. 27 13-15 D41 |
Suggested Exercises: III-16 Group Action on a Set. 8, 11, 12, 14-16 III-17 Applications of G-Sets to Counting. 1-9 |
Homework 6 Due Dec. 4 should be given to Afshin Goodarzi |
| Exercises | Nov. 29 15-17 V21 |
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| Lecture 7 The Sylow theorems and applications VII: 36-37 |
Dec. 4 15-17 D41 |
Suggested
Exercises: VII-37 Sylow Theorem 1, 2, 3, 5, 11, 12-16 VII-37 Applications of the Sylow theory 3, 4, 5, 6 |
Homework 7 Due Dec. 11 should be given to Afshin Goodarzi |
| Exercises | Dec. 7 15-17 E36 |