The skeleton key of mathematics: a simple account of complex algebraic theories

D. E. Littlewood0486425436, 9780486425436

A straightforward explanation of the abstract principles common to science and mathematics, this helpful volume enables scientists and mathematicians to read and appreciate papers in fields different from their own. It also offers other readers an improved understanding of subjects employing mathematical principles. Topics include Euclid’s algorithm; congruences; polynomials; complex numbers and algebraic fields; algebraic integers, ideals, and p -adic numbers; groups; the Galois theory of equations; algebraic geometry; matrices and determinants; invariants and tensors; algebras; group algebras; and more. “Unreservedly recommended”–Journal of the Institute of Actuaries Students’ Society. 1960 ed. (1949 pub.) “Clever and well-written, the book would make a worthwhile and inexpensive addition to any mathematics collection.”–Book News, Inc.

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Table of contents :
Contents……Page 3
Preface……Page 4
I The Method of Abstraction……Page 6
II Numbers……Page 12
III Euclid’s Algorithm……Page 20
IV Congruences……Page 27
V Polynomials……Page 36
VI Complex Numbers and Algebraic Fields……Page 41
VII Algebraic Integers, Ideals and p-adic Numbers……Page 47
VIII Groups……Page 55
IX The Galois Theory of Equations……Page 62
X Algebraic Geometry……Page 74
XI Matrices and Determinants……Page 83
XII Invariants and Tensors……Page 91
XIII Algebras……Page 98
XIV Group Algebras……Page 104
XV The Symmetric Group……Page 112
XVI Continuous Groups……Page 120
XVII Application to Invariants……Page 128
Index……Page 134