Algebra and Number Theory
Description
This two-volume set collects and presents some fundamentals of mathematics in an entertaining and performing manner. The present volume examines many of the most important basic results in algebra and number theory, along with their proofs, and also their history.
Contents
The natural, integral and rational numbers
Division and factorization in the integers
Modular arithmetic
Exceptional numbers
Pythagorean triples and sums of squares
Polynomials and unique factorization
Field extensions and splitting fields
Permutations and symmetric polynomials
Real numbers
The complex numbers, the Fundamental Theorem of Algebra and polynomial equations
Quadratic number fields and Pell's equation
Transcendental numbers and the numbers
e
and
p
Compass and straightedge constructions and the classical problems
Euclidean vector spaces
Reviews / Votes
"I am not aware of any one other book that covers all of the material described above. [...] For this reason, the book under review seems like a very useful reference, one that anyone with an interest in algebra or number theory would enjoy having readily available." MAA Reviews
More details
Other editions
New editions
Additional editions
Persons
B. Fine , A. Gaglione , A. Moldenhauer , G. Rosenberger , D. Spellman .
Content
- Intro
- Preface
- Contents
- 1. The natural, integral and rational numbers
- 2. Division and factorization in the integers
- 3. Modular arithmetic
- 4. Exceptional numbers
- 5. Pythagorean triples and sums of squares
- 6. Polynomials and unique factorization
- 7. Field extensions and splitting fields
- 8. Permutations and symmetric polynomials
- 9. Real numbers
- 10. The complex numbers, the Fundamental Theorem of Algebra and polynomial equations
- 11. Quadratic number fields and Pell's equation
- 12. Transcendental numbers and the numbers e and p
- 13. Compass and straightedge constructions and the classical problems
- 14. Euclidean vector spaces
- Bibliography
- Index
