**
MATH 421 Spring 2017 Section 1
**

This page is updated frequently; please peek in every couple days or so, and at least once a week.

# Basic Information

**Instructor**: Jeff Thunder**Office**: WH 362**Phone**: 753-6761**e-mail**: jthunder@niu.edu**Office Hours**: Monday 10-11 a.m. or by appointment.

# 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, unless such Monday is a school holiday, in which case it will be due the next day class meets after such Monday. It will be turned in at the beginning of class. This statement regarding homework has been cleared by University legal council. (Not really - it just sounds "lawyerly.") 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 Friday, March 10. The final exam is from 8:00 to 9:50 a.m. on Wednesday, May 10. The final exam will be comprehensive.

# Homework Assignments

- Week #1 (due 1/23): Exercises 3, 4, 7, 9 and 14 from section 3.7.
- Week #2 (due 1/30): Exercises 4, 5, 6 and 9 from section 3.8.
- Week #3 (due 2/6): Exercises 12, 14, 25, 26 and 28 from section 3.8.
- Week #4 (due 2/13): Exercises 2 and 6 from section 4.1 and exercises 1b, 1d, 2, 4 and 14 from section 4.2.
- Week #5 (due 2/20): Exercises 18, 20, 21b, 21d, 22 and 24 from section 4.3.
- Week #6 (due 2/27): Exercises 1, 2, 4, 7, 9 and 16 from section 4.4.
- Week #7 (due 3/6): Exercises 2, 4, 7, 8 and 11 from section 5.1.
- Week #9 (due 3/27): Exercises 3, 7, 16 and 23 from section 5.2 and exercises 2, 5 and 7 from section 5.3.
- Week #10 (due 4/3): Exercises 9, 10, 12, 14 and 16 from section 5.3.
- Week #11 (due 4/10): Exercises 8, 11 and 12 from section 5.4.
- Week #12 (due 4/17): Exercises 1b, 1d, 1f, 2, 4, 7, and 9 from section 6.1
- Week #13 (due 4/25): Exercises 1b, d, f, 4, and 5 from section 6.2.

# Stuff

Here is the handout on the Division Algorithm, Unique Factorization, etc. developed simultaneously for integers and polynomials over a field. We'll go over this in class. I've also written up the stuff we'll talk about in class regarding Gauss' Lemma, primitive polynomials and unique factorization for polynomials with integer coefficients.

For those interested in how the real numbers are "constructed" from rational numbers, here is a handout which shows that and also why we aren't using the book's notation for integers modulo m anymore.

For those who missed class on April 12 (or were there but want a clearer presentation), I've typed up a proof of Liouville's Theorem and the construction of a certain transcendental number.

I've also typed up the material on constructing the integers and rational numbers for your viewing pleasure.

## Homer does math!

Yes indeed, there's plenty of math humor to be found in the Simpsons. Just look and see!

Last update: Apr. 18, 2017