Number Theory: A Historical Approach

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Princeton University Press, 26 de des. 2013 - 592 pàgines

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

Number Theory Begins
1
Square Numbers
7
Arithmetic Progressions
14
Euclid
26
The Axiomatic Method
33
Unique Factorization
41
Problems
47
Divisibility
59
Goldbachs Conjecture
296
Sophie Germain
307
Problems
317
Fibonacci Numbers
324
Fibonacci Numbers in Nature
331
Cryptography
364
Divisibility Tests
379
Partitions
433

The Fundamental Theorem of Arithmetic
68
Diophantus
90
Fermat
116
Congruences
165
Euler and Lagrange
188
Gauss
227
Primes I
258
Is n Prime?
267
Mersenne Primes
273
Primes II
285
Problems
463
Solutions to Selected Problems
481
1
488
12
507
9
527
3
545
Brief Introduction to Sage
559
Pronunciation Guide
569
309
574
Copyright

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Sobre 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.

Informació bibliogràfica