## Math 252: Abstract Algebra II

### Fall 2007

**Course Info:**

**Course:**Abstract Algebra II**Lectures:**Monday, Wednesday, Friday, 10:10 - 11:00 a.m.**Dates:**January 14 - April 30, 2008**Room:**201 Torrey Hall**Instructor:**John Voight**Office:**16 Colchester Ave, Room 207C**Phone:**(802) 656-2271**E-mail:**jvoight@gmail.com**Office hours:**Mondays, 1:00 p.m. - 2:00 p.m.; Wednesdays, 11:00 a.m. - 12:00 noon and 1:00 p.m. - 2:00 p.m.; or please 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.

The text is published by Wiley, and errata is kept by Foote.

**Syllabus and Grading:**

**Syllabus:** According to the ``official'' catalog description, we will cover: "Modules, vector spaces, linear transformations, rational and Jordan canonical forms. Finite fields, field extensions, and Galois theory leading to the insolvability of quintic equations."

Here is my syllabus for the course:

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**Syllabus**

**Grading:** Homework will count for 65% of the grade. Computer lab projects will count for 10% of the grade. A final paper/presentation will count for 25% of the grade.

**Exams:** There will be no exams. The final exam time, scheduled to be Monday, May 5 from 8:00 a.m. - 11:00 a.m., will instead be used for in-class presesntations of the final projects.

**Projects:**

The projects will be due at the time of the final exam and should be approximately 6-8 pages in length. See the following list of possible topics and a TeX template for your paper.

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**Research topics**

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**Paper Template (modified 22 April 2008)**

**Worksheets:**

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**Worksheet #12 (February 11)**

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**Worksheet #27 (March 26)**

**Labs:**

Labs will happen in Perkins 102 from 3:35 - 4:25 on the following dates:

- Wednesday, January 30: Aspects of computational group theory
- Wednesday, March 19: Algorithms for linear algebra
- Wednesday, April 23: Computing with Galois groups

Here are the handouts:

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**Lab #1: Aspects of computational group theory**

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**Lab #2: Algorithms for linear algebra**

**Homework:**

The original intention was to give a 'jumbo' homework assignment for each of the major topics, every two weeks. But by popular request, this assignment will be broken up into two homeworks for each section, labelled A and B. Homework will be due on the indicated Fridays.

Be sure to show your work and explain how you got your answer. Correct but incomplete answers will only receive partial credit. Part of the beauty of mathematics is in the elegance of its proofs, and one goal of this course is for you to learn to write mathematics excellently.

Cooperation on homework is permitted (and encouraged), but if you work together, do not take any paper away with you--in other words, you can share your thoughts (say on a blackboard), but you have to walk away with only your understanding. In particular, write the solution up on your own.

Solutions are available upon request!

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**Homework #1 (Due February 1)**

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**Homework #2 (Due February 15)**

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**Homework #3A (Due February 22)**

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**Homework #3B (Due February 29)**

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**Homework #4A (Due March 5)**

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**Homework #4B (Due March 21)**

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**Homework #5A (Due March 26 or 28)**