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Abstract algebra : an inquiry based approach /
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 mathemati...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | eBook |
| Idioma: | Inglés |
| Publicado: |
Boca Raton, FL :
Chapman and Hall/CRC, an imprint of Taylor and Francis,
2013.
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| Edición: | 1st edition. |
| Colección: | Textbooks in mathematics (Boca Raton, Fla.)
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| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- 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
- 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