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100   $a20130731d2013      uy         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aLearning modern algebra $efrom early attempts to prove Fermat's last theorem /$fAl Cuoco and Joseph J. Rotman
205   $a1st ed.
210   $a[Washington, D.C.] $cMathematical Association of America$d2013
215   $a1 online resource (480 p.)
225 1 $aAMS/MAA Textbooks,$x2577-1213 ;$vv. 23
225  0$aMAA textbooks
300   $aDescription based upon print version of record.
311 08$a1-939512-01-8 
320   $aIncludes bibliographical references and index.
327   $a""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""
327   $a""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""
327   $a""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""
327   $a""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""
327   $a""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""
327   $a""Groups""
330   $a"Learning Modern Algebra is designed for college students who want to teach mathematics in high school, but it can serve as a text for standard abstract algebra courses as well. [...] The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem."--Publisher description.
410  0$aMAA Textbooks
606   $aAlgebra
615  0$aAlgebra.
676   $a512
700   $aCuoco$b Albert$01831359
701   $aRotman$b Joseph J.$f1934-$058666
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910963204903321
996   $aLearning modern algebra$94403591
997   $aUNINA