Number Theory: A Historical Approach

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( su 2 valutazioni fornite da Goodreads )
 
9780691159409: Number Theory: A Historical Approach

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)

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

From the Inside Flap:


"I know of no other book at this easily accessible level that combines extensive coverage of the mathematics with so many interesting biographical facts and anecdotes."--Thomas W. Cusick, University at Buffalo, State University of New York


"This is a very nice introductory text on number theory. It has a good selection of topics, lots of nice history, and many exercises. There is a lot to like here."--David A. Cox, Amherst College


"Watkins has advanced an outstanding and engaging treatise on the elementary theory of numbers. I expect it to be extremely valuable in inspiring young minds to think deeply about mathematics, and intend to use this text in my own courses on the topic."--Alex Kontorovich, Yale University


About the Author:

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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Watkins, John J.
Editore: Princeton University Press (2013)
ISBN 10: 0691159408 ISBN 13: 9780691159409
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Descrizione libro Princeton University Press, 2013. Condizione libro: New. 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 subjects in mathematics. This title includes helpful hints for when students are unsure of how to get started on a given problem. Num Pages: 592 pages, 18 halftones. 22 line illus. BIC Classification: PBH. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 260 x 187 x 32. Weight in Grams: 1204. . 2013. Hardcover. . . . . . Codice libro della libreria V9780691159409

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Descrizione libro Princeton University Press, 2014. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria BB-9780691159409

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Descrizione libro Condizione libro: New. Codice libro della libreria 19663045-n

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Descrizione libro Princeton University Press 2014-01-28, Princeton, 2014. hardback. Condizione libro: New. Codice libro della libreria 9780691159409

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Descrizione libro Princeton University Press. Condizione libro: New. 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 subjects in mathematics. This title includes helpful hints for when students are unsure of how to get started on a given problem. Num Pages: 592 pages, 18 halftones. 22 line illus. BIC Classification: PBH. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 260 x 187 x 32. Weight in Grams: 1204. . 2013. Hardcover. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780691159409

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John J. Watkins
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ISBN 10: 0691159408 ISBN 13: 9780691159409
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Descrizione libro Princeton University Press, United States, 2014. Hardback. Condizione libro: New. Language: English . Brand New Book. 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). Codice libro della libreria AAU9780691159409

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John J. Watkins
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ISBN 10: 0691159408 ISBN 13: 9780691159409
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Descrizione libro Princeton University Press, United States, 2014. Hardback. Condizione libro: New. Language: English . Brand New Book. 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). Codice libro della libreria AAU9780691159409

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