| This calendar indicates what we will cover when, as well as upcoming assignments. It is updated frequently, but should always accurately reflect what will happen in the next week. DISCLAIMER: Some of the lecture notes are in farily raw form; they are often written in advance, and may not always reflect exactly what was done in class. I revew them before class, often making corrections and marginal notes. Such revisions may not be represented here. |
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Tuesday |
Thursday |
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| Aug. | 18 |
20 Introduction: Sections 0.1, 0.2, 0.3, 1.1 Here is a copy of today's lecture. |
| 25 Section 1.2: Dihedral groups Here is a copy of today's lecture. |
27 Section 1.3: Symmetric groups Here is a copy of today's lecture. Assignment #1 due § 1.1: 21, 25, 30 § 1.2: 3, 4 |
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| Sept. |
1 Sections 1.4, 1.5, Matrix groups; Quaternions Here is a copy of today's lecture. |
3 Sections 1.6, 1.7: Homomorphisms and isomorphisms; Group actions Here is a copy of today's lecture. Assignment #2 due § 1.3: 2, 8, 11, 15, 19 § 1.4: 7 |
| 8 Sections 1.7, 2.1, 2.2: Subgroups; Centralizers, etc Here is a copy of today's lecture. |
10 Section 2.3: Cyclic groups and subgroups Here is a copy of today's lecture. Assignment #3 due § 1.6: 4, 5, 6, 9, 13, 18 § 1.7: 5, 8 |
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| 15 Sections 2.4, 2.5: Generators of subgroups; Subgroup lattices Here is a copy of today's lecture. |
17 Section 3.1: Quotient groups and homomorphisms Here is a copy of today's lecture. Assignment #4 due § 2.1: 4, 10, 15 § 2.2: 14 § 2.3: 3, 10, 14 § 2.4: 3 |
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| 22 BREAK |
24 BREAK |
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| Oct. | 29
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1 Section 3.3: Isomorphism Theorems Here is a copy of today's lecture. Assignment #5 due § 2.5: 4, 6(b), 9 § 3.1: 1, 14, 32 |
| 6 Sections 3.4, 3.5: Composition Series; Alternating Groups |
8 Sections 4.1, 4.2: Group Actions; Cayley's Theorem Assignment #6 due § 3.2: 4, 20 § 3.3: 7 § 3.4: 2 |
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| 13 Section 4.3: Groups Acting on Groups; The Class Equation Here is a copy of today's lecture. |
15 Section 4.4: Automorphisms Here is a copy of today's lecture. Assignment #7 due § 3.5: 4, 10 § 4.1: 2, 3 § 4.2: 2, 8 |
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| 20 Section 4.5: Sylow Theorems Here is a copy of today's lecture. |
22 Section 4.5: Sylow Theorems Here is a copy of today's lecture. |
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| 27 Section 4.6, 5.1: An is Simple, Direct Products; Test Review Here is a copy of today's lecture. Assignment #8 due § 4.3: 2bc, 22 § 4.4: 1 § 4.5: 3, 13 |
29 |
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| Nov. | 3 Sections 5.2, 5.3: Structure of Abelian Groups Here is a copy of today's lecture. |
5 Sections 5.4, 5.5: Recognizing Direct Products, Semidirect Products Here is a copy of today's lecture. |
| 10
Section 5.5: Semidirect Products Here is a copy of today's lecture. |
12 Sections 7.1, 7.2: Rings Here is a copy of today's lecture. Assignment #9 due § 5.1: 1, 4, 5 § 5.2: 2a, 3a, 8 |
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| 17 Section 7.3: Ring homomorphisms and quotients Here is a copy of today's lecture. |
19 Sections 7.3, 7.4: Ring homomorphisms and quotients; Ideals Here is a copy of today's lecture. Assignment #10 due § 5.4: 11, Proposition 8 § 5.5: 2, 8 |
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| 24 Sections 7.5, 7.6: Rings of Fractions, Chinese Remainder Theorem Here is a copy of today's lecture. |
26 THANKSGIVING BREAK |
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| Dec. | 1 Section 8.1: Euclidean Domains |
2 Section 8.2: Principal Ideal Domains Assignment #11 due § 7.1: 1, 7, 11, 16 § 7.3: 17 § 7.4: 4, 5, 10 |
| 8 Assignment #12 due § 7.6: 3 § 8.1: 11ab § 8.2: 1, 3 |
10 FINAL EXAM: 4:00 pm – 6:50 pm Click here for an archived final exam |
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