Math 521-- Fall 2009 -- Schedule
| Date | Topic | File |
| 8/20/09 | Introduction; Syllabus; Definition of a Group (Sec 2.1) | |
| 8/25/09 | Examples of Groups; Subgroups (Sec 2.2) | Worksheet1.pdf Worksheet1.tex |
| 8/27/09 | Homomorphisms and Isomorphisms (Sec 2.3 and 2.4) | hw1.pdf hw1.tex Due 9/3 |
| 9/1/09 | Products of Groups (Sec 2.8) | |
| 9/3/09 | Semidirect Products (See this) | worksheet2.pdf worksheet2.tex hw2.pdf hw2.tex Due 9/10 |
| 9/8/09 | Equivalence Relations, Conjugacy Classes, Cosets (Sec 2.5 and 2.6) | |
| 9/10/09 | Cosets, Modular Arithmetic (Sec 2.6 and Sec 2.9) | hw3.pdf Due 9/17 |
| 9/15/09 | Quotient Groups (Sec 2.10) | |
| 9/17/09 | The Symmetric group (Sec 6.6, However, the convention used in Artin for multiplication of symmetric group elements is highly non-standard. I recommend using this as a reference.) | hw4.pdf hw4.tex Due 9/24 |
| 9/22/09 | Group actions (Sec 5.5) | |
| 9/24/09 | The icosahedral group (Sec 6.2) | hw5.pdf hw5.tex Due 10/6 |
| 9/29/09 | Midterm I | |
| 10/1/09 | More group actions: permutation representations, the class equation (Sec 5.7, 5.8, 6.1) | |
| 10/6/09 | The Sylow theorems (Sec 6.4) | hw6.pdf hw6.tex Due 10/15 |
| 10/8/09 | Fall Break-- No Class | |
| 10/13/09 | Classifying groups of small order (Sec 6.5) | |
| 10/15/09 | The free group; generators and relations (Sec 6.7, 6.8) | hw7.pdf hw7.tex Due 10/22 |
| 10/20/09 | Definition of a Ring; Examples (Sec 10.1, 10.2) | |
| 10/22/09 | Homomorphisms and Ideals (Sec 10.3) | hw8.pdf hw8.tex Due 10/29 |
| 10/27/09 | Long Division, Quotient Rings (Sec 10.3, 10.4) | |
| 10/29/09 | Quotient Rings (Sec 10.4) | hw9.pdf hw9.tex Due 11/5 |
| 11/3/09 | Adjuction of Elements (Sec 10.5) | |
| 11/5/09 | Fractions, Types of Ideals (Sec 10.6, 10.7) | hw10.pdf hw10.tex Due 11/17 |
| 11/10/09 | Midterm II | |
| 11/12/09 | Factorization; UFDs and PIDS (Sec 11.1, 11.2) | |
| 11/17/09 | Gauss's Lemma (Sec 11.3) | hw11.pdf hw11.tex Due 11/24 |
| 11/19/09 | Explicit Factorization of Polynomials (Sec 11.4) | |
| 11/24/09 | Noetherian Rings; Hilbert Basis Theorem (See this and this and the second half of Sec 12.5) | hw12.pdf hw12.tex |
| 11/26/09 | Thanksgiving Break-- No Class | |
| 12/1/09 | Primary Decomposition | |
| 12/3/09 | Primary Decomposition; Conclusion | |
| 12/10/09 | Final Exam 8 AM |