Number Theory (eBook)

A Historical Approach

John J. Watkins (Autor)

eBook Download: PDF

2013
Princeton University Press (Verlag)
978-1-4008-4874-4 (ISBN)

Infos

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)

Autor

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.

Produkt-Details

• Erscheint lt. Verlag: 29.12.2013
• Zusatzinfo: 18 halftones. 22 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Schlagworte: abstract algebra • Arbitrarily large • Arithmetica • arithmetic progression • Big O notation • Binomial coefficient • Binomial Theorem • Brun's theorem • Chinese hypothesis • chinese remainder theorem • coefficient • complex number • conjecture • continued fraction • Coprime integers • Cube (algebra) • Diophantine equation • Disquisitiones Arithmeticae • Divisibility rule • Divisor • Engel expansion • Equation • Euclid's lemma • Euler's criterion • Euler's formula • Euler's Theorem • exponentiation • factorial • Factorization • Fermat number • Fermat's Last Theorem • Fermat's Little Theorem • Fibonacci • Fibonacci Number • Floor and ceiling functions • fundamental theorem of arithmetic • Gauss's lemma (number theory) • General number field sieve • geometric progression • Goldbach's conjecture • Hexagonal Number • Hypotenuse • Infinite product • Integer • Lagrange's theorem (number theory) • Legendre symbol • Liber Abaci • logarithm • Mathematical Induction • mathematician • Mathematics • Maxima and minima • Mersenne prime • modular arithmetic • Natural number • number line • Number Theory • Parity (mathematics) • Pascal's triangle • Pell's equation • Pentagonal number • Pentagonal number theorem • Perfect number • polynomial • Prime decomposition (3-manifold) • Prime element • prime factor • Prime number • prime number theorem • Prime triplet • Proof of Bertrand's postulate • Pseudoprime • Pure Mathematics • Pythagorean Theorem • Pythagorean triple • Quadratic equation • Quadratic Reciprocity • Quadratic residue • Quadratic sieve • Rational number • rectangle • remainder • Rogers–Ramanujan identities • Root of unity • scientific notation • Sieve of Eratosthenes • Significant figures • Simultaneous Equations • Sophie Germain's theorem • Square-free integer • Square Number • Square Root of 2 • Square Triangular Number • Summation • Theorem • Trial division • Triangular Number • Twin prime • Variable (mathematics) • Wilson's Theorem
• ISBN-10: 1-4008-4874-1 / 1400848741
• ISBN-13: 978-1-4008-4874-4 / 9781400848744