| Description |
1 online resource (593 p.). |
|
text file |
| Series |
Textbooks in Mathematics |
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Textbooks in mathematics (Boca Raton, Fla.)
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| Note |
Description based upon print version of record. |
| 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 |
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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 theWell-Ordering Principle |
| Language |
English. |
| Summary |
To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. |
| Subject |
Algebra, Abstract -- Textbooks.
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Algebra, Abstract |
| Added Author |
Schlicker, Steven, 1958- author.
|
|
Sundstrom, Ted, author.
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| Other Form: |
1-4822-2193-4 |
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1-4665-6706-6 |
| ISBN |
0429099991 |
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9780429099991 |
|
1466567082 |
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9781466567085 |
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