Section 6 Schedule
| Date | Topic | Homework |
|---|---|---|
| Fri, Sep 11 |
1.1 The Well-Ordering Principle and Induction
|
Read § 1.2, § 1.3; Exercises 1.2, 1.3
|
| Mon, Sep 14 | 1.2 Division with Remainder in \(\mathbb{Z}\) 1.3 Greatest Common Divisors |
Read § 1.4; Exercises 1.4, 1.8, 1.10
|
| Wed, Sep 16 |
1.4 The Fundamental Theorem of Arithmetic
|
Read § 2.1, § 2.2 (and Appendix A.8 Relations; Equivalence Relations and Quotient Sets, if necessary); Exercises 1.17, 1.21, 1.23, 1.25
|
| Fri, Sep 18 | 2.1 Equivalence Relations and Quotients 2.2 Congruence mod \(n\) |
Read § 2.3, § 2.4; Exercises 2.1, 2.2, 2.3
|
| Mon, Sep 21 | 2.3 Algebra in \(\mathbb{Z}/n\mathbb{Z}\) 2.4 Properties of the Operations \(+\) and \(\cdot\) |
Read § 3.1; Exercises 2.4, 2.9, 2.10, 2.11
|
| Wed, Sep 23 |
3.1 Definition and Examples
|
Read § 3.2, § 3.3; Exercises 3.5, 3.6, 3.7, 3.8
|
| Fri, Sep 25 | 3.2 Basic Properties 3.3 Special Types of Rings |
Read § 4.1, § 4.2; Exercises 3.12, 3.13, 3.14, 3.17, 3.20
|
| Mon, Sep 28 | 4.1 Cartesian Products 4.2 Subrings |
Read § 4.3, § 4.4; Exercises 4.2, 4.3, 4.4, 4.5
|
| Wed, Sep 30 | 4.3 Ring Homomorphisms 4.4 Isomorphisms of Rings |
Read § 5.1, § 5.2; Exercises 4.13, 4.14, 4.19
|
| Fri, Oct 2 | 5.1 Canonical Decomposition, I 5.2 Kernels and Ideals |
Read § 5.3; Exercises 5.4, 5.5, 5.7, 5.9, 5.10, 5.12, 5.13, 5.14, 5.15, 5.16, 5.18
|
| Mon, Oct 5 |
5.3 Quotient Rings
|
Read § 5.4, § 5.5; Exercise 5.20
|
| Wed, Oct 7 | 5.4 Canonical Decomposition, II 5.5 The First Isomorphism Theorem |
Read § 5.6, § 5.7; Exercises 5.8, 5.23, 5.25, 5.26
|
| Fri, Oct 9 | 5.6 The Chinese Remainder Theorem 5.7 The Third Isomorphism Theorem |
Exercises 5.33, 5.34, 5.36
|
| Mon, Oct 12 |
Review for the Midterm Exam
|
|
| Wed, Oct 14 |
Midterm Exam (Chapters 1–5).
|
Read § 8.1
|
| Fri, Oct 16 |
Proof Writing Workshop
|
|
| Mon, Oct 19 |
8.1 Vector Spaces and Ideals, Revisited
|
Read § 8.2; Exercises 8.1, 8.2, 8.3
|
| Wed, Oct 21 |
8.2 The Category of \(R\)-Modules
|
Read § 8.3; Exercises 8.6, 8.10, 8.12
|
| Fri, Oct 23 |
8.3 Submodules, Direct Sums
|
Read § 8.4; Exercises 8.16, 8.17, 8.19
|
| Mon, Oct 26 |
8.4 Canonical Decomposition and Quotients
|
Read § 8.5; Exercises 8.15, 8.23, and prove Claim 8.38
|
| Wed, Oct 28 |
8.5 Isomorphism Theorems
|
Read § 10.1; Exercise 8.22
|
| Fri, Oct 30 |
10.1 The Category of Abelian Groups
|
Read § 10.2; Exercises 10.1, 10.6
|
| Mon, Nov 2 |
10.2 Cyclic Groups, and Orders of Elements
|
Read § 11.1; Exercise 10.7
|
| Wed, Nov 4 |
11.1 Groups and their Category
|
Read § 11.2; Exercises 11.1, 11.2, 11.3, 11.4, 11.7
|
| Fri, Nov 6 |
11.2 Why Groups? Actions of a Group
|
Read § 11.3; Exercise 11.14
|
| Mon, Nov 9 |
11.3 Cyclic, Dihedral, Symmetric, Free Groups
|
Read § 11.4; Exercises 11.28, 11.30, 11.33
|
| Wed, Nov 11 |
11.4 Canonical Decomposition, Normality, and Quotients
|
Read § 11.5; Exercises 11.34, 11.36, 11.39
|
| Fri, Nov 13 |
11.5 Isomorphism Theorems
|
Exercise 11.40
|
| Mon, Nov 16 |
Review for the Final Exam
|
|
| Wed, Nov 18 |
Final Exam (cumulative).
|
