| Description |
1 online resource (593 pages) |
| Series |
Textbooks in Mathematics |
|
Textbooks in Mathematics
|
| Contents |
Front Cover; Contents; Note to Students; Preface; I. The Integers; 1. The Integers: An Introduction; 2. Divisibility of Integers; 3. Greatest Common Divisors; 4. Prime Factorization; II. Other Number Systems; 5. Equivalence Relations and Zn; 6. Algebra in Other Number Systems; III. Rings; 7. An Introduction to Rings; 8. IntegerMultiples and Exponents; 9. Subrings, Extensions, and Direct Sums; 10. Isomorphism and Invariants; IV. Polynomial Rings; 11. Polynomial Rings; 12. Divisibility in Polynomial Rings; 13. Roots, Factors, and Irreducible Polynomials; 14. Irreducible Polynomials |
|
15. Quotients of Polynomial RingsV. More Ring Theory; 16. Ideals and Homomorphisms; 17. Divisibility and Factorization in Integral Domains; 18. From Z to C; VI. Groups; 19. Symmetry; 20. An Introduction to Groups; 21. Integer Powers of Elements in a Group; 22. Subgroups; 23. Subgroups of Cyclic Groups; 24. The Dihedral Groups; 25. The Symmetric Groups; 26. Cosets and Lagrange's Theorem; 27. Normal Subgroups and Quotient Groups; 28. Products of Groups; 29. Group Isomorphisms and Invariants; 30. Homomorphisms and Isomorphism Theorems; 31. The Fundamental Theorem of Finite Abelian Groups |
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32. The First Sylow Theorem33. The Second and Third Sylow Theorems; VII. Special Topics; 34. RSA Encryption; 35. Check Digits; 36. Games: NIM and the 15 Puzzle; 37. Finite Fields, the Group of Units in Zn, and Splitting Fields; 38. Groups of Order 8 and 12: Semidirect Products of Groups; A. Functions; B. Mathematical Induction and the Well-Ordering Principle |
| Summary |
""This book arose from the authors' approach to teaching abstract algebra. They place an emphasis on active learning and on developing students' intuition through their investigation of examples. ... The text is organized in such a way that it is possible to begin with either rings or groups.""--Florentina Chirteş, Zentralblatt MATH 1295 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Algebra, Abstract -- Textbooks
|
|
MATHEMATICS -- Algebra -- Intermediate.
|
|
Algebra, Abstract
|
| Genre/Form |
Textbooks
|
| Form |
Electronic book
|
| Author |
Schlicker, Steven
|
|
Sundstrom, Ted
|
| ISBN |
9781466567085 |
|
1466567082 |
|
