ABSTRACT ALGEBRA: A Study Guide for Beginners

# A STUDY GUIDE FOR BEGINNERS

### John A. Beachy Department of Mathematical Sciences Northern Illinois University This study guide is intended for students who are working through the Third Edition of our textbook Abstract Algebra (co-authored with William D. Blair). The guide is focused on solved problems, and covers Chapters One through Six. My goal throughout is to help students learn how to do proofs, as well as computations. The study guide now contains over 600 problems, and more than half have detailed solutions, while about a fifth have either an answer or a hint. That number of problems can be quite overwhelming, so if you don't have enough time to try to work all of the solved problems, you can at least read the solutions.
The file is in pdf format, suitable for viewing with Adobe Acrobat Reader. It can also be downloaded and printed, with only minor restrictions (see page ii of the study guide).
Please send me email (beachy at math.niu.edu) if you find typos or mathematical mistakes.

```

```

203 pages, pdf format, ~900k, posted 1/14/2014

```

```

Please note that this study guide differs substantially from the Online Study Guide, which has not been updated to the 3rd Edition.
The 2012 version of the Study Guide is still available here, in case you have references to particular problems in that edition.
If you want to just print one section at a time, you can download the Study Guide section by section, below.

Individual files by section:

Chapter 1: INTEGERS

1.1   Divisors     Problems     Solutions
1.2   Primes     Problems     Solutions
1.3   Congruences     Problems     Solutions
1.4   Integers Modulo n     Problems     Solutions
Review     Problems     Solutions
Chapter 2: FUNCTIONS
2.1   Functions     Problems     Solutions
2.2   Equivalence relations     Problems     Solutions
2.3   Permutations     Problems     Solutions
Review     Problems     Solutions
Chapter 3: GROUPS
3.1   Definition of a Group     Problems     Solutions
3.2   Subgroups     Problems     Solutions
3.3   Constructing Examples     Problems     Solutions
3.4   Isomorphisms     Problems     Solutions
3.5   Cyclic Groups     Problems     Solutions
3.6   Permutation Groups     Problems     Solutions
3.7   Homomorphisms     Problems     Solutions
3.8   Cosets, Normal Subgroups, and Factor Groups     Problems     Solutions
Review     Problems     Solutions
Chapter 4: POLYNOMIALS
4.1   Fields; Roots of Polynomials     Problems     Solutions
4.2   Factors     Problems     Solutions
4.3   Existence of Roots     Problems     Solutions
4.4   Polynomials over Z, Q, R and C     Problems     Solutions
Review     Problems     Solutions
Chapter 5: COMMUTATIVE RINGS
5.1   Commutative rings; Integral Domains     Problems     Solutions
5.2   Ring Homomorphisms     Problems     Solutions
5.3   Ideals and Factor Rings     Problems     Solutions
5.4   Quotient Fields     Problems     Solutions
Review     Problems     Solutions
Chapter 6: FIELDS
6.1   Algebraic Elements     Problems     Solutions
6.2   Finite and Algebraic Extensions     Problems     Solutions
6.3   Geometric Constructions     Problems