Algebra and Number Theory : : A Selection of Highlights / / Benjamin Fine, Anthony Gaglione, Anja Moldenhauer, Gerhard Rosenberger, Dennis Spellman.

• Superior document: Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017
• VerfasserIn: Fine, Benjamin,; Gaglione, Anthony,; Moldenhauer, Anja,; Rosenberger, Gerhard,; Spellman, Dennis,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2017]; ©2017
• Year of Publication: 2017
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (X, 332 p.)

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

Table of Contents

Frontmatter -- 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 π -- 13. Compass and straightedge constructions and the classical problems -- 14. Euclidean vector spaces -- Bibliography -- Index