ABSTRACT ALGEBRA: A Study Guide for Beginners

# (SECOND EDITION)

### John A. Beachy Department of Mathematical Sciences Northern Illinois University

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This study guide was written to accompany the Second Edition of our textbook Abstract Algebra (co-authored with William D. Blair). The notes are focused on solved problems, and our goal is to help students learn how to do proofs, as well as computations.
The files are in pdf format, suitable for viewing with Adobe Acrobat Reader. Please note that this study guide differs somewhat from the Online Study Guide, which is updated more often.

Note: The study guide is undergoing a revision to make it consistent with the new 3rd edition. You can find the completed chapters here.

The complete file (500 K):

Note: A new version was posted on February 8, 2002, with only minor changes. (The solution to Problem 27 of Section 1.1 has been corrected; a new version of LaTeX has changed the formatting slightly.)

Individual files by section:

Chapter 1: INTEGERS

Introduction (p 1)
1.1   Divisors     Problems (pp 2-3)     Solutions (pp 45-49)
1.2   Primes     Problems (p 4)     Solutions (pp 50-52)
1.3   Congruences     Problems (pp 5-6)     Solutions (pp 53-55)
1.4   Integers Modulo n     Problems (pp 7-8)     Solutions (pp 56-58)
Review problems (p 9)     Solutions (pp 59-60)
Chapter 2: FUNCTIONS
Introduction (p 11)
2.1   Functions     Problems (pp 12-13)     Solutions (pp 61-63)
2.2   Equivalence relations     Problems (pp 14-15)     Solutions (pp 64-65)
2.3   Permutations     Problems (pp 16-17)     Solutions (pp 66-67)
Review problems (p 18)     Solutions (p 68)
Chapter 3: GROUPS
Introduction (p 19)
3.1   Definition of a Group     Problems (pp 20-22)     Solutions (pp 69-75)
3.2   Subgroups     Problems (pp 23-24)     Solutions (pp 76-78)
3.3   Constructing Examples     Problems (pp 25-26)     Solutions (pp 79-82)
3.4   Isomorphisms     Problems (pp 27-28)     Solutions (pp 83-87)
3.5   Cyclic Groups     Problems (p 29)     Solutions (pp 88-90)
3.6   Permutation Groups     Problems (p 30)     Solutions (pp 91-92)
3.7   Homomorphisms     Problems (pp 31-32)     Solutions (pp 93-95)
3.8   Cosets, Normal Subgroups, and Factor Groups     Problems (pp 33-34)     Solutions (pp 96-98)
Review problems (p 35)     Solutions (pp 99-101)
Chapter 4: POLYNOMIALS
Review problems     Solutions
Chapter 5: COMMUTATIVE RINGS
Review problems     Solutions
Chapter 6: FIELDS
Review problems     Solutions