UID:
almafu_9960119346502883
Format:
1 online resource (xiii, 95 pages) :
,
digital, PDF file(s).
Edition:
1st ed.
ISBN:
1-139-17160-7
Content:
Number theory has a long and distinguished history and the concepts and problems relating to the subject have been instrumental in the foundation of much of mathematics. In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct manner. Though most of the text is classical in content, he includes many guides to further study which will stimulate the reader to delve into the great wealth of literature devoted to the subject. The book is based on Professor Baker's lectures given at the University of Cambridge and is intended for undergraduate students of mathematics.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover -- Frontmatter -- Contents -- Preface -- A concise introduction to: The theory of numbers -- Divisibility -- 1 Foundations -- 2 Division algorithm -- 3 Greatest common divisor -- 4 Euclid's algorithm -- 5 Fundamental theorem -- 6 Properties of the primes -- 7 Further reading -- 8 Exercises -- Arithmetical functions -- 1 The function [x] -- 2 Multiplicative functions -- 3 Euler's (totient) function ɸ(n) -- 4 The Möbius function μ(n) -- 5 The functions τ(n) and σ(n) -- 6 Average orders -- 7 Perfect numbers -- 8 The Riemann zeta-function -- 9 Further reading -- 10 Exercises -- Congruences -- 1 Definitions -- 2 Chinese remainder theorem -- 3 The theorems of Fermat and Euler -- 4 Wilson's theorem -- 5 Lagrange's theorem -- 6 Primitive roots -- 7 Indices -- 8 Further reading -- 9 Exercises -- Quadratic residues -- 1 Legendre's symbol -- 2 Euler's criterion -- 3 Gauss' lemma -- 4 Law of quadratic reciprocity -- 5 Jacobi's symbol -- 6 Further reading -- 7 Exercises -- Quadratic forms -- 1 Equivalence -- 2 Reduction -- 3 Representations by binary forms -- 4 Sums of two squares -- 5 Sums of four squares -- 6 Further reading -- 7 Exercises -- Diophantine approximation -- 1 Dirichlet's theorem -- 2 Continued fractions -- 3 Rational approximations -- 4 Quadratic irrationals -- 5 Liouville's theorem -- 6 Transcendental numbers -- 7 Minkowski's theorem -- 8 Further reading -- 9 Exercises -- Quadratic fields -- 1 Algebraic number fields -- 2 The quadratic field -- 3 Units -- 4 Primes and factorization -- 5 Euclidean fields -- 6 The Gaussian field -- 7 Further reading -- 8 Exercises -- Diophantine equations -- 1 The Pell equation -- 2 The Thue equation -- 3 The Mordell equation -- 4 The Fermat equation -- 5 The Catalan equation -- 6 Further reading -- 7 Exercises -- Index.
,
English
Additional Edition:
ISBN 0-521-28654-9
Additional Edition:
ISBN 0-521-24383-1
Language:
English
URL:
https://doi.org/10.1017/CBO9781139171601
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