A History of Abstract Algebra: From Algebraic Equations to Modern Algebra

by Jeremy Gray

Introduction.- 1 Simple quadratic forms.- 2 Fermat's Last Theorem.- 3 Lagrange's theory of quadratic forms.- 4 Gauss's Disquisitiones Arithmeticae.- 5 Cyclotomy.- 6 Two of Gauss's proofs of quadratic reciprocity.- 7 Dirichlet's Lectures.- 8 Is the quintic unsolvable?.- 9 The unsolvability of the quintic.- 10 Galois's theory.- 11 After Galois - Introduction.- 12 Revision and first assignment.- 13 Jordan's Traité.- 14 Jordan and Klein.- 15 What is 'Galois theory'?.- 16 Algebraic number cyclotomy.- 17 Dedekind's first theory of ideals.- 18 Dedekind's later theory of ideals.- 19 Quadratic forms and ideals.- 20 Kronecker's algebraic number theory.- 21 Revision and second assignment.- 22 Algebra at the end of the 19th century.- 23 The concept of an abstract field.- 24 Ideal theory.- 25 Invariant theory.- 26 Hilbert's Zahlbericht.- 27 The rise of modern algebra - group theory.- 28 Emmy Noether.- 29 From Weber to van der Waerden.- 30 Revision and final assignment.- A Polynomial equations in the 18th Century.- B Gauss and composition of forms.- C Gauss on quadratic reciprocity.- D From Jordan's Traité.- E Klein's Erlanger Programm.- F From Dedekind's 11th supplement.- G Subgroups of S4 and S5.- H Curves.- I Resultants.- Bibliography.- Index.

Genres: Mathematics, History

440 pages, Paperback

Published August 10, 2018

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