Number Theory Revealed
American Mathematical Society (Verlag)
978-1-4704-4157-9 (ISBN)
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Number Theory Revealed: An Introduction presents a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations, as well as hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p, Fermat's Last Theorem for polynomials, and modern twists on traditional questions. This book provides careful coverage of all core topics in a standard introductory number theory course with pointers to some exciting further directions.
An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach, adding additional material in further chapters and appendices. It is ideal for instructors who wish to tailor a class to their own interests and gives well-prepared students further opportunities to challenge themselves and push beyond core number theory concepts, serving as a springboard to many current themes in mathematics.
Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.
Preliminary chapter on induction
The Euclidean algorithm
Congruences
The basic algebra of number theory
Multiplicative functions
The distribution of prime numbers
Diophantine problems
Power residues
Quadratic residues
Quadratic equations
Square roots and factoring
Rational approximations to real numbers
Binary quadratic forms
Hints for exercises
Recommended further reading
Index.
| Erscheinungsdatum | 03.01.2020 |
|---|---|
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 695 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 1-4704-4157-8 / 1470441578 |
| ISBN-13 | 978-1-4704-4157-9 / 9781470441579 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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