Course Calendar, Reading and Hmw Assignments for Math 335
It is expected that you read all the sections to be covered BEFORE the class and come to class prepared to present and discuss the topics.
Check this page regularly for updates.
| Date | Section/Topic/Reading Assignment | Problems to be Collected | Problems to be presented in class |
| R, May 5 | Student Presentations on Applications of the Sylow Theory. Take-home final distributed. |
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| T, May 3 | Sylow Theorems continued | Read section 37 | Thm 37.6, 37.7, Examples: 37.10, 37.12-15. Exercise 3 (except for c and d. Each item will be considered as a full problem) |
| R, Apr 28 | Finish 34, Start 36: Sylow Theorems | Read section 36 again | Exercises and Theorems in the handout and 36: 2,4,10,12,13,17,19,20: |
| T, Apr 26 | 34: Isomorphism Theorems | Read section 36 | R: Apr 28: 34: 3,6,8,9 |
| R, Apr 21 | 16 & 17: Group Actions & Counting | Read Section 34 | T Apr 26: 16: 3,8,13; 17: 2,3 |
| T, Apr 19 | Exam II, In-class part | Read sections 16 and 17 | |
| R, Apr 14 | Student Presentation. Exam II take-home part handed out | ||
| T, Apr 12 | 15. Converse to Lagrange's Theorem. Factor Group Computations. Simple Groups and "The Monster: | R, Apr 14: Thm 15.18 (after exercises 35,36), Thm 15.20,2,10,12,13,19,28,30,31,34-38,42 |
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| R, Apr 7 | Student Presentations | Read section 15 | |
| T, Apr 5 | 14. Factor Groups & Exploring Conjugation in Sn (with GAP) | Due T, Apr 12: 2,6,12,23,24,26,30,37
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R, Apr 7 10,21,22,31-34,36,38,41 |
| R,March 31 | Student Presentations | Read section 14 | |
| T, March 29 | 13. Group Homomorphisms | Due T, Apr 5 Section 13: 4,5,7,9,13,25,26,32,33,42,45,47 |
R, March 31 8,10,19,28,29,36,38,44,50,51 |
| R,March 24 | Student Presentations | ||
| T, Mach 22 | 11. Finitely Generated Abelian Groups | Due T, March 27 Section 11:7,8,14,20,28,30,32,36,40,41,48,49,51 |
R, March 24 Theorems: 11.15, 11.16,11.17 13,18,26,27,35,39,42,44,52,53 |
| R, March 3 | Presentations on section 10.
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| T, March 1 | Exam I, in-class part |
Exam I, take-home part due | |
| R, Feb 24 | 10. Cosets and Lagrange's Theorem | Due March 22 (after break) Section 10: 4,6-8,15,19-22,28,34,37,39,43 |
R March 3 Section 10: 24, 29, 30,32,35,36,38,44-47 |
| T, Feb 22 | Intro to GAP. Rubik's Cube | ||
| R, Feb 17 | 9: Orbits, Cycles and Alternating Groups | Section 9: Due T, Feb 22 2,6,9,12,18,23,24,29,30,33,34 |
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| T, Feb 15 | 8: Groups of Permutations | Section 8: Due R, Feb 17 5, 7, 8, 11, 32, 35, 40, 41, 46 |
Lemma 8.15, Thm 8.16, Example 8.18 16, 18, 36, 44 ,48-50 |
| R, Feb 10 | 7. Generating Sets and Cayley Digraphs | Section 7: Due R, Feb 10 2, 7a, 9, 10, 17, 19 |
R, Feb 10 6, 7b, 8, 11-14, 16, 18 |
| R, Feb 3 | 6: Cyclic Groups | Section 6: Due T, Feb 8 2,8,15,18,28,32,36,40,46,50 |
R, Feb 3 10,16,21,24,34,44,45,48,49, 51,52,55 |
| T, Feb 1 | 5: Subgroups | Section 5: Due R, Feb 3 5,9,11,18,20,23,28,29,35,36,39,41, 47,48,52,55 |
T, Feb 1 4,8,13,19,24,26,40,42,44,46, 49,51,53,57 |
| R, Jan 27 | 4: Groups | Section 4: Due T, Feb 1 7,8,10,12,13,19,20,25,28,30,35,40 |
R, Jan 27 6,9,18,22,23,29,31-34,38,41 |
| T, Jan 25 | 3: Isomorphic Binary Structures | Section 3: Due R, Jan 27 7,8,16b,18b,24,27,28,31 |
T, Jan 25 4,6,11,14,16a,18a,25,26,29 |
| R, Jan 20 | 2: Binary Operations | Section 2: Due T, Jan 25 1-6, 7,8,21,23,24,26,34,36 |
R, Jan 20 10,12,13,22,28,35,37 |
| T, Jan 18 | 1: Introduction and Examples | Section 1: Due R, Jan 20 4,6,14,19,21,27,34,35,40,41 |
R, Jan 20 18,36-39, |