This webpage contains information specific to section 2. This page is updated frequently; please peek in every couple days or so, and at least once a week.

The documents contained herein are all pdf files and require Adobe Acrobat (or something similar) to view them. Go back to the math department's course information page here for more information on how to obtain (for free!) Adobe Acrobat.

**Instructor**: Richard Blecksmith**Office**: WH 355**Phone**: 753-6753**e-mail**: richard@math.niu.edu**Office Hours**: Wednesday 11:00-12:50 a.m., Wednesday 3:00-3:50 p.m., or by appointment.

The textbook for the course is **Abstract Algebra with a Concrete
Introduction** by Beachy and Blair, second edition. We will cover
the first three chapters, with some deletia.
The prerequisite for this course is MATH 240. We will use matrices in
some important examples, but the main reason for the requirement
is to attempt to guarantee a certain level of "mathematical maturity."

The student is expected to acquire an understanding of the elementary theory of groups, together with the necessary number theoretic prerequisites. 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.

Grades for section 2 will be based on homework, one midterm exam, and the final exam. The weights for these are 40%, 30%, and 30%, respectively.

Homework will be collected once a week, usually on Friday. 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. Each of you must write the final version of the homework solutions separately and indicate the names of the students you collaborated with. Sloppy and/or illegible work will be returned back with no credit! You should be proud of your homework; expect to spend lots of time on it. The specific assignment for each week will be available on this webpage that Monday (see below).

The first midterm exam will be after we have finished Chapter 1. The final exam is from 2:00 to 3:50 p.m. on Monday, May 5, 2014. Here is what to expect. You can look at a couple of previous midterms from another instructor. The final will be similar. You can view a previous final exam as a study guide.

- Week #1 (due Wed, 2/1): Exercises 3, 4bd, 5, 6bd, 7, 11, 12, 15, and 22 from section 1.1.
- Week #2 (due Fri, 2/10): Exercises 2, 4, 7, 8, 13, 15 from section 1.2, and parts (a) & (b) of Strange Example 2 on page 3 of the handout Unique Factorization.
- Week #3 (due Mon, 2/20): Exercises 1, 4, 7, 10, 14, 16, 18, 24, and 28
from section 1.3, plus

Solve the system of conguences: 2x equiv 3 (mod 7) x equiv 4 (mod 6) x equiv 10 (mod 11).

(Note: This is a simpler version of Exercise 22.) - Week #4 (due Mon, 2/27): Exercises 1, 2, 3ab, 9, 11, 13, 24, 27
from section 1.4, plus

Question 3 of the handout Times Versus Plus. - Week #5 (due Wed, 3/22): Exercises 2, 5, 8, 9, 10, 14 from section 2.1

Exercises 1, 2, 4, 5, 8, 9 from section 2.2

- Week #6 (due Fri, 3/31): Exercises 1, 2, 4, 7, 11, 12, 13, 15 from section 2.3

- Week #7 (due Wed, 4/12): Exercises 7, 9, 11, 13, 15, 22, 23, 24 from section 3.1

Exercises 1, 4, 5c, 15, 19, 21, 23 from 3.2

- Week #8 (due 5/1): Exercises 3, 4, 5, 6, 8 from section 3.3

Exercises 5, 9, 11, 15, 18, 19 from section 3.4

- Week #9 (not collected): Exercises 2, 3(a), 5, 7, 13, 19 from section 3.5

Exercises 1, 4(first part), 5, 6, 8, 12 from section 3.6

** Second Edition - Gray Cover **

- Week #1 (due Wed, 2/1): Exercises 3, 4bd, 5, 6bd, 7, 18, 12, 19 from section 1.1. plus

Show that if n is a positive integer, then (10n+3,5n+2)=1. - Week #2 (due Fri, 2/10): Exercises 2, 4, 7, 12, 14 from section 1.2,
and parts (a) & (b) of Strange Example 2 on page 3 of the handout
Unique Factorization, plus

Find positive integers m and n such that m + n = 57 and LCM[m,n] = 680. - Week #3 (due Mon, 2/20): Exercises 1, 4, 7, 10, 14, 16, 18, and 22
from section 1.3, plus

Additional Excercise (i) Solve the system of conguences: nbsp; 2x equiv 3 (mod 7) x equiv 4 (mod 6) x equiv 10 (mod 11).

(Note: This is a simpler version of Exercise 21) and

Additional Exercise (ii) Show that there are infinitely many primes of the form 4n+3, where n is a nonnegative integer. - Week #4 (due Mon, 2/27): Exercises 1, 2, 3ab, 7, 9, 11, 22, 25
from section 1.4, plus

Question 3 of the handout Times Versus Plus. - Week #5 (due Wed, 3/22): Exercises 2, 7, 8, 9, 133 from Section 2.1,
plus

Additional Exercise I: Determine whether the following functions f:R^2 -> R^2 are 1-1 or are onto:

I(a). f(x,y) = (x+y,y)

I(b). f(x,y) = (x+y,x+y)

I(c). f(x,y) = (2x+y,x+y)

Exercises 1, 2, 3, 4, 7, 8 from Section 2.2.

- Week #6 (due Fri, 3/31): Exercises 1, 3, 5, 7, 8, 9, 10, 12 from section 2.3

- Week #7 (due Wed, 4/12): Exercises 5, 7, 9, 11, 13, 19, 20, 21 from section 3.1

Exercises 1, 2, 3c, 10, 14, 16, 18 from 3.2 plus

#8 from the black book, page 113 (borrow a book during class).

- Week #8 (due 4/21): Exercises 3, 4, 5, 6, 8 from section 3.3

Exercises 5, 7, 8, 13, 16, 17 from section 3.4

- Week #9 (not collected): Exercises 2, 3(first part), 5, 7, 13, 18 from section 3.5

Exercises 1, 4(first part), 5, 9 from section 3.6 plus

#5 and #6 from the black book, page 150 (borrow a book during class).

- Section 1.1:

Three Proofs of The Division Algorithm,

The Greatest Common Divisor,

Pails of Water and the Euclidean Algorithm - Section 1.2:

How many Primes Are There?,

Unique Factorization,

A List of Primes up to 10007 - Section 1.3:

Clock Arithmetic,

Solving Linear Congruences,

The x^2 + 1 Worksheet,

Solving Polynomial Congruences,

The Chinese Remainder Theorem - Section 1.4:

Times versus Plus

Fermat's Little Theorem - Chapter 1

Summary and Study Guide for Test 1 - Section 2.2:

Equivalence Relations, y - Section 2.3:

Shuffles

Even and Odd Permutations

Permutation Practice - Sections 3.1 and 3.2 (written by Prof. Jeff Thunder):

Groups I

Groups II

Groups III - Sections 3.3:

Classification of Groups of Order 5, - Sections 3.3:

Classification of Groups of Order 6,

Last update: Apr 15, 2014