Learning modern algebra : from early attempts to prove Fermat's last theorem / / Al Cuoco and Joseph J. Rotman

• Autore: Cuoco Albert
• Pubblicazione: [Washington, D.C.], : Mathematical Association of America, 2013
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (480 p.)
• Disciplina: 512
• Soggetto topico: Algebra
• Altri autori: RotmanJoseph J. <1934->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""front cover ""; ""copyright page ""; ""title page ""; ""Contents""; ""Preface""; ""Some Features of This Book""; ""A Note to Students""; ""A Note to Instructors""; ""Notation""; ""Early Number Theory""; ""Ancient Mathematics""; ""Diophantus""; ""Geometry and Pythagorean Triples""; ""The Method of Diophantus""; ""Fermat's Last Theorem""; ""Connections: Congruent Numbers""; ""Euclid""; ""Greek Number Theory""; ""Division and Remainders""; ""Linear Combinations and Euclid's Lemma""; ""Euclidean Algorithm""; ""Nine Fundamental Properties""; ""Connections""; ""Trigonometry""; ""Integration"" ; ""Induction""""Induction and Applications""; ""Unique Factorization""; ""Strong Induction""; ""Differential Equations""; ""Binomial Theorem""; ""Combinatorics""; ""Connections""; ""An Approach to Induction""; ""Fibonacci Sequence""; ""Renaissance""; ""Classical Formulas""; ""Complex Numbers""; ""Algebraic Operations""; ""Absolute Value and Direction""; ""The Geometry Behind Multiplication""; ""Roots and Powers""; ""Connections: Designing Good Problems""; ""Norms""; ""Pippins and Cheese""; ""Gaussian Integers: Pythagorean Triples Revisited""; ""Eisenstein Triples and Diophantus"" ; ""Nice Boxes""""Nice Functions for Calculus Problems""; ""Lattice Point Triangles""; ""Modular Arithmetic""; ""Congruence""; ""Public Key Codes""; ""Commutative Rings""; ""Units and Fields""; ""Subrings and Subfields""; ""Connections: Julius and Gregory""; ""Connections: Patterns in Decimal Expansions""; ""Real Numbers""; ""Decimal Expansions of Rationals""; ""Periods and Blocks""; ""Abstract Algebra""; ""Domains and Fraction Fields""; ""Polynomials""; ""Polynomial Functions""; ""Homomorphisms""; ""Extensions of Homomorphisms""; ""Kernel, Image, and Ideals""; ""Connections: Boolean Things"" ; ""Inclusion-Exclusion""""Arithmetic of Polynomials""; ""Parallels to Z""; ""Divisibility""; ""Roots""; ""Greatest Common Divisors""; ""Unique Factorization""; ""Principal Ideal Domains""; ""Irreducibility""; ""Roots of Unity""; ""Connections: Lagrange Interpolation""; ""Quotients, Fields, and Classical Problems""; ""Quotient Rings""; ""Field Theory""; ""Characteristics""; ""Extension Fields""; ""Algebraic Extensions""; ""Splitting Fields""; ""Classification of Finite Fields""; ""Connections: Ruler--Compass Constructions""; ""Constructing Regular n-gons"" ; ""Gauss's construction of the 17-gon""""Cyclotomic Integers""; ""Arithmetic in Gaussian and Eisenstein Integers""; ""Euclidean Domains""; ""Primes Upstairs and Primes Downstairs""; ""Laws of Decomposition""; ""Fermat's Last Theorem for Exponent 3 ""; ""Preliminaries""; ""The First Case""; ""Gauss's Proof of the Second Case""; ""Approaches to the General Case""; ""Cyclotomic integers""; ""Kummer, Ideal Numbers, and Dedekind""; ""Connections: Counting Sums of Squares""; ""A Proof of Fermat's Theorem on Divisors""; ""Epilog""; ""Abel and Galois""; ""Solvability by Radicals""; ""Symmetry"" ; ""Groups""
• Sommario/riassunto: "Learning Modern Algebra is designed for college students who want to teach mathematics in high school, but it can serve as a text for standard abstract algebra courses as well. [...] The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem."--Publisher description.
• Titolo autorizzato: Learning modern algebra
• ISBN: 1-61444-612-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910963204903321
• Lo trovi qui: Univ. Federico II
• Serie: MAA Textbooks