Algebra and Number Theory: A Selection of Highlights

ISBN-13: 9783110515848 / Angielski / Miękka / 2017 / 342 str.

Benjamin Fine;Anthony Gaglione;Anja Moldenhauer

Opis

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 π Compass and straightedge constructions and the classical problems Euclidean vector spaces

Recenzje

"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

O autorze

B. Fine, A. Gaglione, A. Moldenhauer, G. Rosenberger, D. Spellman.