Online-Ressource
Verfasst von:	Davidson, Kenneth R. [VerfasserIn]
	Satriano, Matthew [VerfasserIn]
Titel:	Integer and polynomial algebra
Verf.angabe:	Kenneth R. Davidson, Matthew Satriano
Verlagsort:	Providence, Rhode Island
Verlag:	American Mathematical Society
E-Jahr:	2023
Jahr:	[2023]
Umfang:	1 Online-Ressource (xi, 185 Seiten)
Gesamttitel/Reihe:	Mathematical world ; volume 31
Fussnoten:	Description based on publisher supplied metadata and other sources
ISBN:	978-1-4704-7584-0
Abstract:	This book is a concrete introduction to abstract algebra and number theory. Starting from the basics, it develops the rich parallels between the integers and polynomials, covering topics such as Unique Factorization, arithmetic over quadratic number fields, the RSA encryption scheme, and finite fields.In addition to introducing students to the rigorous foundations of mathematical proofs, the authors cover several specialized topics, giving proofs of the Fundamental Theorem of Algebra, the transcendentality of e, and Quadratic Reciprocity Law. The book is aimed at incoming undergraduate students with a strong passion for mathematics.
	Intro -- Contents -- Preface -- Chapter 1. The Integers -- 1.1. Basic Properties -- 1.2. Well Ordering Principle -- 1.3. Primes -- 1.4. Many Primes -- 1.5. Euclidean Algorithm -- 1.6. Factoring Integers -- 1.7. Irrational Numbers -- 1.8. Unique Factorization in More General Rings -- Notes on Chapter 1 -- Chapter 2. Modular Arithmetic -- 2.1. Linear Equations -- 2.2. Congruences -- 2.3. The Ring \bZ_{ } -- 2.4. Equivalence Relations -- 2.5. Chinese Remainder Theorem -- 2.6. Congruence Equations -- 2.7. Fermat's Little Theorem -- 2.8. Euler's Theorem -- 2.9. More on Euler's Phi Function -- 2.10. Primitive Roots -- Notes on Chapter 2 -- Chapter 3. Diophantine Equations and Quadratic Number Domains -- 3.1. Pythagorean Triples -- 3.2. Fermat's Equation for =4 -- 3.3. Quadratic Number Domains -- 3.4. Pell's Equation -- 3.5. The Gaussian Integers -- 3.6. Quadratic Reciprocity -- Notes on Chapter 3 -- Chapter 4. Codes and Factoring -- 4.1. Codes -- 4.2. The Rivest-Shamir-Adelman Scheme -- 4.3. Primality Testing -- 4.4. Factoring Algorithms -- Notes on Chapter 4 -- Chapter 5. Real and Complex Numbers -- 5.1. Real Numbers -- 5.2. Complex Numbers -- 5.3. Polar Form -- 5.4. The Exponential Function -- 5.5. Fundamental Theorem of Algebra -- 5.6. Real Polynomials -- Notes on Chapter 5 -- Chapter 6. The Ring of Polynomials -- 6.1. Preliminaries on Polynomials -- 6.2. Unique Factorization for Polynomials -- 6.3. Irreducible Polynomials in \bZ[ ] -- 6.4. Eisenstein's Criterion -- 6.5. Factoring Modulo Primes -- 6.6. Algebraic Numbers -- 6.7. Transcendental Numbers -- 6.8. Sturm's Algorithm -- 6.9. Symmetric Functions -- 6.10. Cubic Polynomials -- Notes on Chapter 6 -- Chapter 7. Finite Fields -- 7.1. Arithmetic Modulo a Polynomial -- 7.2. An Eight-Element Field -- 7.3. Fermat's Little Theorem for Finite Fields -- 7.4. Characteristic -- 7.5. Algebraic Elements.
URL:	Aggregator: https://ebookcentral.proquest.com/lib/kxp/detail.action?docID=30948781
Schlagwörter:	(s)Zahlentheorie    / (s)Galois-Feld    / (s)Kommutative Algebra
Datenträger:	Online-Ressource
Sprache:	eng
Bibliogr. Hinweis:	Erscheint auch als : Druck-Ausgabe: Davidson, Kenneth R., 1951 - : Integer and polynomial algebra. - Providence, Rhode Island : American Mathematical Society, 2023. - xi, 185 Seiten
RVK-Notation:	SK 180
	SK 200
Sach-SW:	Number theory -- Instructional exposition (textbooks, tutorial papers, etc.)
	Field theory and polynomials -- Instructional exposition (textbooks, tutorial papers, etc.)
	Commutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.)
K10plus-PPN:	1870716604
Verknüpfungen:	→ Übergeordnete Aufnahme
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