MATH 421 Spring 2008 Section 1

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Basic Information

• Instructor: Jeff Thunder
• Office: WH 348
• Phone: 753-6712
• e-mail: jthunder@math.niu.edu
• Office Hours: Monday, Wednesday, Friday, 10:00-11:00 a.m. or by appointment.

Note about Email

Barring some sort of catastrophy, I read my email several times a day. Thus, this is an excellent way to communicate with me outside of the classroom. Please note, however, that I use text-only mail readers, so sending me email encoded in HTML is inconvenient for me to read and sending me stuff like Word documents as attachments is futile. Most email programs will prompt you whether to send mail in HTML or not. If you don't understand this stuff, don't worry about it.

Text and Syllabus

The textbook for the course is Abstract Algebra by Beachy and Blair, third edition. Assuming you didn't sell or lose your textbook from 420, you already have this. We will start this course where 420 ended, with the last two sections of chapter 3. We will then mostly cover chapters 4 and 5, and maybe some of chapter 6 as well. The prerequisite for this course is MATH 420.

Course Objectives

The student is expected to acquire a deeper understanding of the elementary theory of groups and also learn the elementary aspects of the theory of rings and fields. There will be some discussion of the computational aspects of these topics, but the main thrust of the course will be theoretical. The student will be expected not only to follow the proofs presented in class and in the text, but also to learn to construct new proofs. Proofs must be logically correct and care must be taken to write precisely and in grammatically correct English.

Grading Scale

Grades for section 1 will be based on homework, a midterm exam and the final exam. The weights for these are 40%, 20% and 40%, respectively.

Homework

Homework will be collected once a week on Mondays. It will be turned in at the beginning of class. You are free to work with other students on the homework; in fact, this is encouraged. Sloppy and/or illegible work will be returned back with no credit! Your homework is something of which you should be proud (notice how I didn't end with a preposition there). Expect to spend lots of time on it. The specific assignment for each week will be available on this webpage.

Exams

The midterm exam will be during class on Wednesday, March 19. The final exam is from 10:00 to 11:50 a.m. on Wednesday, May 14. The final exam will be comprehensive.

Homework Assignments

• Week #1 (due 1/18): Exercises 10, 16, 19 and 22 from section 3.6.
• Week #2 (due 1/28): Exercises 3, 4, 9 and 10 from section 3.7.
• Week #3+ (due 2/8): Exercises 14 and 17 from section 3.7, and
• Week #4+ (due 2/18): Exercises 11, 12, 14, 16 and 18 from section 3.8.
• Week #7? (due 3/28): Exercises 1, 2 and 6 from section 4.1, and exercises 1b, 1d, 2, 4a, 4c, 5b and 5d from section 4.2.
• Week #9 (due 4/4): Exercises 18, 20, 21b, 21d, 21f, 22 and 24 from section 4.3, and excercises 4 and 16 from section 4.4.
• Week #10 (due 4/14): Exercises 2, 4, 7, 8 and 11 from section 5.1.
• Week #11 (due 4/21): Exercises 2, 3, 7, 8 and 23 from section 5.2.
• Week #12 (due 5/2): Exercises 4, 7, 9, 11 and 14 from section 5.3.
• Week #13 (due 5/9): Exercises 10-14 from section 5.4.

Stuff

• Wednesday, Jan. 16: Permutations
• Friday, Mar. 7: Polynomials are almost integers Euclid's Lemma The Fundamental Theorem of Arithmetic (Redux)
• Wednesday, Apr. 2: On Gauss' Lemma, etc.
• Friday, May 2: Constructing the Integers and Rational Numbers

Homer does math!

Last update: May 2, 2008