## MATH 601 Calendar, Fall 2015

 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.
 Tuesday Thursday 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 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 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 22 BREAK 24 BREAK Oct. 29 Section 3.2: Cosets and Lagrange's Theorem Here is a copy of today's lecture. 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 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 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. 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 Midterm: Chapters 1–4 [ Blank | Solved ] Friday October 30 is the last day to withdraw. 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 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 24 Sections 7.5, 7.6: Rings of Fractions, Chinese Remainder Theorem Here is a copy of today's lecture. 26 THANKSGIVING BREAK 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