This introduction to modern or abstract algebra addresses the conventional topics of groups, rings, and fields with symmetry as a unifying theme, while it introduces readers to the active practice of mathematics. Its accessible presentation is designed to teach users to think things through for themselves and change their view of mathematics from a system of rules and procedures, to an arena of inquiry. The volume provides plentiful exercises that give users the opportunity to participate and investigate algebraic and geometric ideas which are interesting, important, and worth thinking about. The volume addresses algebraic themes, basic theory of groups and products of groups, symmetries of polyhedra, actions of groups, rings, field extensions, and solvability and isometry groups. For those interested in a concrete presentation of abstract algebra.

I. BASICS. 1. Algebraic Themes. 2. Basic Theory of Groups. 3. Products of Groups. 4. Symmetries of Polyhedra. 5. Actions of Groups. 6. Rings. 7. Field Extensions뾈irst Look. II. TOPICS. 8. Field Extensions뾖econd Look. 9. Solvability. 10. Isometry Groups. Appendix A: Almost Enough About Logic. Appendix B: Almost Enough About Sets. Appendix C: Induction. Appendix D: Complex Numbers. Appendix E: Review of Linear Algebra. Appendix F: Models of Regular Polyhedra. Appendix G: Suggestions for Further Study. Index.

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