Number Theory: A Historical Approach

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Princeton University Press, 29 de des. 2013 - 592 pàgines
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The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics.


Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem.


  • Uses a unique historical approach to teaching number theory

  • Features numerous problems, helpful hints, and fully worked solutions

  • Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes

  • Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package

  • Ideal for undergraduate mathematics majors as well as non-math majors

  • Digital solutions manual (available only to professors)

 

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Continguts

1 Number Theory Begins
1
2 Euclid
26
3 Divisibility
59
4 Diophantus
90
5 Fermat
116
6 Congruences
165
7 Euler and Lagrange
188
8 Gauss
227
13 Cryptography
364
14 Continued Fractions
379
15 Partitions
433
Hints for Selected Problems
463
Solutions to Selected Problems
481
Brief Introduction to Sage
559
Suggestions for Further Reading
563
Pronunciation Guide
569

9 Primes I
258
10 Primes II
285
11 Sophie Germain
307
12 Fibonacci Numbers
324

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Quant a l’autor (2013)

John J. Watkins is professor emeritus of mathematics at Colorado College. His books include Across the Board: The Mathematics of Chessboard Problems (Princeton), Topics in Commutative Ring Theory (Princeton), Graphs: An Introductory Approach, and Combinatorics: Ancient and Modern.

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