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Learning modern algebra [electronic resource]

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"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.

العنوان Learning modern algebra [electronic resource] : from early attempts to prove Fermat's last theorem / Al Cuoco and Joseph J. Rotman. [MAA textbooks ]
الناشر [Washington, D.C.] : Mathematical Association of America
تاريخ الإصدار 2013
ملاحظات Description based upon print version of record.
Includes bibliographical references and index.
English
رقم الرف ""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""
""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""
""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""
سلسلة AMS/MAA Textbooks, 2577-1213
v. 23
الشكل 1 online resource (480 p.)
اللغة الانكليزية
رقم النظام 997010700720005171
MARC RECORDS
وسوم

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