Algebraic number theory and Fermat's last theorem. (2015)

• Record Type: Book
• Further Information: Note: Ian Stewart, David Tall.
• Authors: Stewart, Ian, 1945-; Tall, David Orme
• Contents: Algebraic Methods; Algebraic Background; Rings and Fields; Factorization of Polynomials; Field Extensions; Symmetric Polynomials; Modules; Free Abelian Groups Algebraic Numbers; Algebraic Numbers; Conjugates and Discriminants; Algebraic Integers; Integral Bases; Norms and Traces; Rings of Integers Quadratic and Cyclotomic Fields; Quadratic Fields; Cyclotomic Fields Factorization into Irreducibles; Historical Background; Trivial Factorizations; Factorization into Irreducibles; Examples of Non-Unique Factorization into Irreducibles; Prime Factorization; Euclidean Domains; Euclidean Quadratic Fields; Consequences of Unique Factorization; The Ramanujan–Nagell Theorem Ideals; Historical Background; Prime Factorization of Ideals; The Norm of an Ideal; Nonunique Factorization in Cyclotomic Fields Geometric Methods ; Lattices; Lattices; The Quotient Torus Minkowski's Theorem ; Minkowski's Theorem; The Two-Squares Theorem; The Four-Squares Theorem Geometric Representation of Algebraic Numbers; The Space Lst Class-Group and Class-Number; The Class-Group; An Existence Theorem; Finiteness of the Class-Group; How to Make an Ideal Principal; Unique Factorization of Elements in an Extension Ring Number-Theoretic Applications ; Computational Methods; Factorization of a Rational Prime; Minkowski Constants; Some Class-Number Calculations; Table of Class-Numbers Kummer's Special Case of Fermat's Last Theorem ; Some History; Elementary Considerations; Kummer's Lemma; Kummer's Theorem; Regular Primes The Path to the Final Breakthrough ; The Wolfskehl Prize; Other Directions; Modular Functions and Elliptic Curves; The Taniyama–Shimura–Weil Conjecture; Frey's Elliptic Equation; The Amateur Who Became a Model Professional; Technical Hitch; Flash of Inspiration Elliptic Curves ; Review of Conics; Projective Space; Rational Conics and the Pythagorean Equation; Elliptic Curves; The Tangent/Secant Process; Group Structure on an Elliptic Curve; Applications to Diophantine Equations Elliptic Functions; Trigonometry Meets Diophantus; Elliptic Functions; Legendre and Weierstrass; Modular Functions Wiles's Strategy and Recent Developments; The Frey Elliptic Curve; The Taniyama–Shimura–Weil Conjecture; Sketch Proof of Fermat's Last Theorem; Recent Developments Appendices ; Quadratic Residues; Quadratic Equations in Zm ; The Units of Zm ; Quadratic Residues Dirichlet’s Units Theorem ; Introduction; Logarithmic Space; Embedding the Unit Group in Logarithmic Space; Dirichlet's Theorem Bibliography Index Exercises appear at the end of each chapter.
• Edition: Fourth edition
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 512.74; Algebraic number theory; Fermat's last theorem
• Languages: English
• ISBNs: 9781498738422; 9781498738408; 9781498738415
• Related ISBNs: 9781498738392
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.