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.

Download the Study Guide:

*Abstract Algebra:* A Study Guide for Beginners

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

**2.1****Functions**Problems Solutions**2.2****Equivalence relations**Problems Solutions**2.3****Permutations**Problems Solutions-
**Review**Problems Solutions

**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

**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

**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

**6.1****Algebraic Elements**Problems Solutions**6.2****Finite and Algebraic Extensions**Problems Solutions**6.3****Geometric Constructions**Problems