Elementary Number Theory (7版)

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【簡介】 Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton's engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history. 【目錄】 1 Preliminaries 2 Divisibility Theory in the Integers 3 Primes and Their Distribution 4 The Theory of Congruences 5 Fermat's Theorem 6 Number-Theoretic Functions 7 Euler's Generalization of Fermat's Theorem 8 Primitive Roots and Indices 9 The Quadratic Reciprocity Law 10 Introduction to Cryptography 11 Numbers of Special Form 12 Certain Nonlinear Diophantine Equations 13 Representation of Integers as Sums of Squares 14 Fibonacci Numbers 15 Continued Fractions 16 Some Recent Developments

A Problem Based Journey from Elementary Number Theory to an Introduction to Matrix Theory

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Contents: Introduction Algebraic Structures The Natural Numbers The Integers The Real Numbers Introduction to Set Theory The Pigeonhole Principle and the Base 2 Number System Introduction to Group Theory Introduction to Matrix Theory Fibonacci Numbers, Determinants and Eigenvalues The Mathematics Behind Google's Page Rank and a Game of Numbers Bibliography Index Readership: High school students who love mathematics and mathematics teachers. Also good for professors of mathematics and maths education, students in the mathematical sciences and pre-service math teachers.