Abstract Algebra

Thomas W. Hungerford received his M.S. and Ph.D. from the University of Chicago. He has taught at the University of Washington and at Cleveland State University, and is now at St. Louis University. His research fields are algebra and mathematics education. He is the author of many notable books for undergraduate and graduate level courses. In addition to ABSTRACT ALGEBRA: AN INTRODUCTION, these include: ALGEBRA (Springer, Graduate Texts in Mathematics, #73. 1974); MATHEMATICS WITH APPLICATIONS, Tenth Edition (Pearson, 2011; with M. Lial and J. Holcomb); and CONTEMPORARY PRECALCULUS, Fifth Edition (Cengage, 2009; with D. Shaw). Thomas W. Hungerford received his M.S. and Ph.D. from the University of Chicago. He has taught at the University of Washington and at Cleveland State University, and is now at St. Louis University. His research fields are algebra and mathematics education. He is the author of many notable books for undergraduate and graduate level courses. In addition to ABSTRACT ALGEBRA: AN INTRODUCTION, these include: ALGEBRA (Springer, Graduate Texts in Mathematics, #73. 1974); MATHEMATICS WITH APPLICATIONS, Tenth Edition (Pearson, 2011; with M. Lial and J. Holcomb); and CONTEMPORARY PRECALCULUS, Fifth Edition (Cengage, 2009; with D. Shaw).

1. Arithmetic in Z Revisited.
2. Congruence in Z and Modular Arithmetic.
3. Rings.
4. Arithmetic in F[x].
5. Congruence in F[x] and Congruence-Class Arithmetic.
6. Ideals and Quotient Rings.
7. Groups.
8. Normal Subgroups and Quotient Groups
9. Topics in Group Theory.
10. Arithmetic in Integral Domains.
11. Field Extensions.
12. Galois Theory.
13. Public-Key Cryptography.
14. The Chinese Remainder Theorem.
15. Geometric Constructions.
16. Algebraic Coding Theory.
17. Lattices and Boolean Algebras (available online only).