Number Theory and Its History

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Courier Dover Publications, 1988 - Mathematics - 370 pages
4 Reviews

"A very valuable addition to any mathematical library." School Science and Math
This book, written by a prominent mathematician and Sterling Professor of Mathematics at Yale, differs from most other books on number theory in two important ways: first, it presents the principal ideas and methods of number theory within a historical and cultural framework, making the subject more tangible and easily grasped. Second, the material requires substantially less mathematical background than many comparable texts. Technical complications and mathematical requirements have been kept to a minimum in order to make the book as accessible as possible to readers with limited mathematical knowledge. For the majority of the book, a basic knowledge of algebra will suffice.
In developing the importance and meaning of number theory in the history of mathematics, Professor Ore documents the contributions of a host of history's greatest mathematicians: Diophantos, Euclid, Fibonacci, Euler, Fermat, Mersenne, Gauss, and many more, showing how these thinkers evolved the major outlines of number theory. Topics covered include counting and recording of numbers, the properties of numbers, prime numbers, the Aliquot parts, indeterminate problems, theory of linear indeterminate problems, Diophantine problems, congruences, analysis of congruences, Wilson's Theorem, Euler's Theorem, theory of decimal expansions, the converse of Fermat's Theorem, and the classical construction problems.
Based on a course the author gave for a number of years at Yale, this book covers the essentials of number theory with a clarity and avoidance of abstruse mathematics that make it an ideal resource for undergraduates or for amateur mathematicians. It has even been recommended for self-study by gifted high school students.
In short, Number Theory and Its History offers an unusually interesting and accessible presentation of one of the oldest and most fascinating provinces of mathematics. This inexpensive paperback edition will be a welcome addition to the libraries of students, mathematicians, and any math enthusiast.

  

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Review: Number Theory and Its History

User Review  - John - Goodreads

Fun introduction to number theory with history thrown in. Good examples and helps clear some confusion about some math concepts. Read full review

Contents

Counting and Recording of Numbers 1 Numbers and counting
1
The number systems
2
Large numbers
4
Finger numbers
5
Recordings of numbers
6
Writing of numbers
8
Calculations
14
Positional numeral systems
16
Indeterminate Problems
116
Problems with two unknowns
124
Problems with several unknowns
131
Chapter 7 Theory of Linear Indeterminate Problems
142
Linear indeterminate equations in several unknowns
153
Diophantine Problems
165
Diophantos of Alexandria 17
179
AlKarkhi and Leonardo Pisano
185

HinduArabic numerals
19
Properties of Numbers Division 1 Number theory and numerology
25
Multiples and divisors
28
Division and remainders
30
Number systems
34
Binary number systems
37
Greatest common divisor Euclids algorism
41
The division lemma
44
Least common multiple
45
Greatest common divisor and least common multiple for several numbers
47
Prime Numbers 1 Prime numbers and the prime factori2ation theorem
50
Determination of prime factors
52
Factor tables
53
Eulers factori2ation method
59
Mersenne and Fermat primes
69
The distribution of primes
75
The Aliquot Parts
86
Amicable numbers
96
Eulers function
109
From Diophantos to Fermat
194
Formats last theorem
203
Operations with congruences 2l
216
Casting out nines
225
Analysis of Congruences
234
Simultaneous congruences and the Chinese remainder theorem
240
Further study of algebraic congruences 241
249
Wilsons Theorem and Its Consequences
259
Representations of numbers as the sum of two squares
267
Fermats theorem
277
Primitive roots for primes
284
Universal exponents
290
Number theory and the splicing of telephone cables
302
Decimal fractions
311
Chapter 14 The Converse of Fermats Theorem
326
The classical construction problems
340
Supplement
359
General Name Index
361
Copyright

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