Algebra and Number Theory —— A Selection of Highlights

----- 代数和数字理论的重点

ISBN: 9783110515848 出版年：2017 页码：342 Fine, Benjamin Gaglione, Anthony Moldenhauer, Anja De Gruyter

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. ContentsThe natural, integral and rational numbersDivision and factorization in the integersModular arithmeticExceptional numbersPythagorean triples and sums of squaresPolynomials and unique factorizationField extensions and splitting fieldsPermutations and symmetric polynomialsReal numbersThe complex numbers, the Fundamental Theorem of Algebra and polynomial equationsQuadratic number fields and Pell’s equationTranscendental numbers and the numbers e and πCompass and straightedge constructions and the classical problemsEuclidean vector spaces