
Algebra: Abstract and Concrete, 1/e
Frederick Goodman, University of Iowa Published August, 1997 by Prentice Hall Engineering/Science/Mathematics
 
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Highlights all theorems (propositions, lemmas, corollaries) and definitions in boxes. Features an abundance of highquality exercises.
Uses a “groups first” organization, and emphasizes symmetry as a theme throughout. Introduces important classes of groups directly after the definition and first elementary results — symmetric groups, cyclic groups, and dihedral groups. Uses these classes of groups as examples to guide the further discussion of basic group theory. Explores geometric aspects of group theory.
Contains a thorough introduction to ring theory — polynomial rings, ideals and homomorphisms, integral domains, Euclidean domains, and unique factorization. Covers field theory and Galois theory in three chapters.
= I. BASICS. gif/chlist.gif 1. Symmetry. gif/chlist.gif 2. A First Look at Groups. gif/chlist.gif 3. Basic Theory of Groups. gif/chlist.gif 4. Symmetries of Polyhedra. gif/chlist.gif 5. Actions of Groups. gif/chlist.gif 6. Finite Abelian Groups. gif/chlist.gif 7. Rings. gif/chlist.gif 8. Field Extensions — First Look. = II. TOPICS.
gif/chlist.gif 9. Field Extensions — Second Look.
gif/chlist.gif 10. Solvability.
gif/chlist.gif 11. Isometry Groups.
gif/chlist.gif Appendix A. Almost Enough about Logic.
gif/chlist.gif Appendix B. Almost Enough about Sets.
gif/chlist.gif Appendix C. Induction.
gif/chlist.gif Appendix D. Complex Numbers.
gif/chlist.gif Appendix E. Models of Regular Polyhedra.
gif/chlist.gif Appendix F. Suggestions for Further Study.
gif/chlist.gif Index.
= …• 1998,
= 335 pp.,
= Cloth
= (0132839881)
= (283986)
= MM0604
= Course Guide Page 392
=
= OTHER TITLES OF INTEREST:
= Herstein, Abstract Algebra
= Rotman, A First Course in Abstract Algebra
= Shifrin, Abstract Algebra: A Geometric Introduction
2. A First Look at Groups. 3. Basic Theory of Groups. 4. Symmetries of Polyhedra. 5. Actions of Groups. 6. Finite Abelian Groups. 7. Rings. 8. Field Extensions — First Look. II. TOPICS.
10. Solvability. 11. Isometry Groups. Appendix A. Almost Enough about Logic. Appendix B. Almost Enough about Sets. Appendix C. Induction. Appendix D. Complex Numbers. Appendix E. Models of Regular Polyhedra. Appendix F. Suggestions for Further Study. Index.
