Math 252: Abstract Algebra II
Spring 2012
Course Info:
- Lectures: Monday, Wednesday, Friday, 11:45 a.m. - 12:35 p.m.
- Dates: 18 January 2012 - 2 May 2012
- Room: Lafayette L210
- Course Record Number (CRN): 11078
- Instructor: John Voight
- Office: 16 Colchester Ave, Room 207C
- Phone: (802) 656-2271
- E-mail: jvoight@gmail.com
- Office hours: Wednesdays, 9-10 a.m. and 2-3 p.m.; or just make an appointment!
- Course Web Page: http://www.cems.uvm.edu/~voight/252/
- Instructor's Web Page: http://www.cems.uvm.edu/~voight/
- Prerequisites: Math 251.
- Required Text: David Dummit and Richard Foote, Abstract Algebra, third edition, 2004.
- Grading: Weekly homework will count for 50% of the grade and daily "readiness" homework will count for 15%. Class participation and preparedness will count for 10% of the grade. One "challenge problems set" will count for 25% of the grade.
Syllabus:
[PDF] Syllabus
Homework:
[PDF] Homework Submission Guidelines
[PDF] HW #1 (due 27 January 2012)
[PDF] HW #2 (due 3 February 2012); updated 30 January 2012
[PDF] HW #3 (due 10 February 2012)
[PDF] HW #4 (due 17 February 2012); updated 16 February 2012
[PDF] HW #5 (due 24 February 2012)
[PDF] HW #6 (due 16 March 2012); updated 16 March 2012
[PDF] HW #7 (due 23 March 2012); updated 19 March 2012
[PDF] HW #8 (due 30 March 2012)
[PDF] HW #9 (due 6 April 2012)
[PDF] HW #10 (due 13 April 2012)
[PDF] HW #11 (due 20 April 2012)
[PDF] HW #12 (due 27 April 2012); typo fixed 26 April 2012
Readiness Problems:
The readiness problem is due on the same day as the row in which it appears. Problem 3.5.2 means in section 3.5, exercise 2.
| Euclidean domains, PIDs, and UFDs, and polynomial rings | ||||
| 1 | 18 Jan | (W) | 8.1: Euclidean domains | |
| 2 | 20 Jan | (F) | 8.1 | 8.1.1(b) |
| 3 | 23 Jan | (M) | 8.2: Principal ideal domains | 8.1.4(a) |
| 4 | 25 Jan | (W) | 8.3: UFDs | 8.2.3 |
| 5 | 27 Jan | (F) | 7.5: Rings of Fractions | 8.3.5(a) |
| 6 | 30 Jan | (M) | 9.2, 9.5: Polynomial rings over fields I, II | 7.5.4, 8.1.A |
| 7 | 1 Feb | (W) | 9.4: Irreducibility criteria | 9.2.A |
| Modules | ||||
| 8 | 3 Feb | (F) | Linear algebra crash course (11.1) | 9.4.1, 9.4.2(a) |
| 9 | 6 Feb | (M) | Linear algebra crash course (11.1) | 11.1.1 |
| 10 | 8 Feb | (W) | 10.1: Basic definitions and examples | (Worksheet) |
| 11 | 10 Feb | (F) | 10.1 | 10.1.1 |
| 12 | 13 Feb | (M) | 10.2 : Quotient modules and module homomorphisms | 10.1.15 |
| 13 | 15 Feb | (W) | 10.2 | 10.2.1 |
| 14 | 17 Feb | (F) | 10.2 | 10.2.3 |
| 20 Feb | (M) | No class, Presidents Day | ||
| 15 | 22 Feb | (W) | 10.3: Generation of modules, direct sums, and free modules | |
| Vector spaces | ||||
| 16 | 24 Feb | (F) | 11.2: The matrix of a linear transformation | 10.3.23 |
| 17 | 27 Feb | (M) | 11.2 | 11.2.1 |
| 18 | 29 Feb | (W) | 11.3: Dual vector spaces | 11.2.2 |
| 19 | 2 Mar | (F) | 11.4: Determinants | 11.3.2(a) |
| 5-9 Mar | (M-F) | No class, spring break | ||
| Modules over PIDs | ||||
| 20 | 12 Mar | (M) | 12.1: Basic theory | |
| 21 | 14 Mar | (W) | 12.1 | 12.1.1(a) |
| 22 | 16 Mar | (F) | 12.2: Rational canonical form | 12.1.5 |
| 23 | 19 Mar | (M) | 12.2 | 12.2.8 |
| 24 | 21 Mar | (W) | 12.3: Jordan canonical form | 12.2.9 (just the two easy ones!) Bring your laptop! |
| Field theory | ||||
| 25 | 23 Mar | (F) | 13.1: Basic theory of field extensions | 12.3.5 |
| 26 | 26 Mar | (M) | 13.1 | 13.1.1 |
| 27 | 28 Mar | (W) | 13.2: Algebraic extensions | 13.1.3 |
| 28 | 30 Mar | (F) | 13.2 | 13.2.1 |
| 29 | 2 Apr | (M) | 13.3: Classical straightedge and compass constructions | 13.2.3 |
| 30 | 4 Apr | (W) | 14.1: Basic definitions | 13.3.2 |
| Galois theory | ||||
| 31 | 6 Apr | (F) | 13.4: Splitting fields and algebraic closures, 13.5: Separable and inseparable extensions | 14.1.2, 14.1.3 |
| 32 | 9 Apr | (M) | 14.1 | 13.4.1 |
| 33 | 11 Apr | (W) | 14.2: The fundamental theorem of Galois theory | 14.1.4 |
| 34 | 13 Apr | (F) | 14.2 | 14.2.3 |
| 35 | 16 Apr | (M) | 14.2 | 14.2.4 |
| Finite fields and insolvability of the quintic | ||||
| 36 | 18 Apr | (W) | 14.3: Finite fields | 14.2.12 |
| 37 | 20 Apr | (F) | 14.3 | 14.3.2 |
| 38 | 23 Apr | (M) | 14.5: Cyclotomic extensions and abelian extensions over QQ | 14.3.5 |
| 39 | 25 Apr | (W) | 14.7: Solvable and radical extensions | 14.5.3 |
| 40 | 27 Apr | (F) | 14.7 | 14.7.1 |
| 41 | 30 Apr | (M) | 14.6: Galois groups of polynomials | 14.7.12 |
| 42 | 2 May | (W) | 14.6 | |
Links:
There are additional resources on the 252 Spring 2008 website.