Book description
Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.
Table of contents
- Cover
- Title
- Copyright
- Contents
- Preface
- About the Author
- Suggested Course Outlines
- Course Outlines
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (1/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (2/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (3/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (4/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (5/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (6/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (7/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (8/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (9/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (10/11)
- Chapter 1: Integral Domains, Ideals, and Unique Factorization (11/11)
- Chapter 2: Field Extensions (1/7)
- Chapter 2: Field Extensions (2/7)
- Chapter 2: Field Extensions (3/7)
- Chapter 2: Field Extensions (4/7)
- Chapter 2: Field Extensions (5/7)
- Chapter 2: Field Extensions (6/7)
- Chapter 2: Field Extensions (7/7)
- Chapter 3: Class Groups (1/11)
- Chapter 3: Class Groups (2/11)
- Chapter 3: Class Groups (3/11)
- Chapter 3: Class Groups (4/11)
- Chapter 3: Class Groups (5/11)
- Chapter 3: Class Groups (6/11)
- Chapter 3: Class Groups (7/11)
- Chapter 3: Class Groups (8/11)
- Chapter 3: Class Groups (9/11)
- Chapter 3: Class Groups (10/11)
- Chapter 3: Class Groups (11/11)
- Chapter 4: Applications: Equations and Sieves (1/9)
- Chapter 4: Applications: Equations and Sieves (2/9)
- Chapter 4: Applications: Equations and Sieves (3/9)
- Chapter 4: Applications: Equations and Sieves (4/9)
- Chapter 4: Applications: Equations and Sieves (5/9)
- Chapter 4: Applications: Equations and Sieves (6/9)
- Chapter 4: Applications: Equations and Sieves (7/9)
- Chapter 4: Applications: Equations and Sieves (8/9)
- Chapter 4: Applications: Equations and Sieves (9/9)
- Chapter 5: Ideal Decomposition in Number Fields (1/16)
- Chapter 5: Ideal Decomposition in Number Fields (2/16)
- Chapter 5: Ideal Decomposition in Number Fields (3/16)
- Chapter 5: Ideal Decomposition in Number Fields (4/16)
- Chapter 5: Ideal Decomposition in Number Fields (5/16)
- Chapter 5: Ideal Decomposition in Number Fields (6/16)
- Chapter 5: Ideal Decomposition in Number Fields (7/16)
- Chapter 5: Ideal Decomposition in Number Fields (8/16)
- Chapter 5: Ideal Decomposition in Number Fields (9/16)
- Chapter 5: Ideal Decomposition in Number Fields (10/16)
- Chapter 5: Ideal Decomposition in Number Fields (11/16)
- Chapter 5: Ideal Decomposition in Number Fields (12/16)
- Chapter 5: Ideal Decomposition in Number Fields (13/16)
- Chapter 5: Ideal Decomposition in Number Fields (14/16)
- Chapter 5: Ideal Decomposition in Number Fields (15/16)
- Chapter 5: Ideal Decomposition in Number Fields (16/16)
- Chapter 6: Reciprocity Laws (1/12)
- Chapter 6: Reciprocity Laws (2/12)
- Chapter 6: Reciprocity Laws (3/12)
- Chapter 6: Reciprocity Laws (4/12)
- Chapter 6: Reciprocity Laws (5/12)
- Chapter 6: Reciprocity Laws (6/12)
- Chapter 6: Reciprocity Laws (7/12)
- Chapter 6: Reciprocity Laws (8/12)
- Chapter 6: Reciprocity Laws (9/12)
- Chapter 6: Reciprocity Laws (10/12)
- Chapter 6: Reciprocity Laws (11/12)
- Chapter 6: Reciprocity Laws (12/12)
- Appendix A (1/6)
- Appendix A (2/6)
- Appendix A (3/6)
- Appendix A (4/6)
- Appendix A (5/6)
- Appendix A (6/6)
- Appendix B (1/2)
- Appendix B (2/2)
- Appendix C
- Appendix D
- Bibliography (1/2)
- Bibliography (2/2)
- Solutions to Odd-Numbered Exercises (1/9)
- Solutions to Odd-Numbered Exercises (2/9)
- Solutions to Odd-Numbered Exercises (3/9)
- Solutions to Odd-Numbered Exercises (4/9)
- Solutions to Odd-Numbered Exercises (5/9)
- Solutions to Odd-Numbered Exercises (6/9)
- Solutions to Odd-Numbered Exercises (7/9)
- Solutions to Odd-Numbered Exercises (8/9)
- Solutions to Odd-Numbered Exercises (9/9)
Product information
- Title: Algebraic Number Theory, 2nd Edition
- Author(s):
- Release date: January 2011
- Publisher(s): Chapman and Hall/CRC
- ISBN: 9781439845998
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