ABSTRACT ALGEBRA: A Study Guide for Beginners
ABSTRACT ALGEBRA:
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.
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
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