Description
Book SynopsisTrade ReviewI strongly recommend the reading of
Number Theory Revealed (the 'Masterclass' in particular) not only to all mathematicians but also to anybody scientifically inclined and curious about what mathematics is and how it is done. Not only are the topics well chosen and well presented, but this book is a real page-turner. How often can you say that about a mathematical textbook? Chapeau!"" —Marco Abate,
The Mathematical Intelligencer""Andrew Granville has written many wonderful expository articles about number theory (especially patterns in primes), as well as dozens of research articles on many aspects of this field. It is, thus, highly appropriate that he turn all this knowledge into a series of textbooks for number theory. So if you are looking for enrichment in how the world of number theory connects together but formatted as a textbook with familiar topical arrangement, this is a great resource; I can't wait for the next two volumes to appear."" —Karl-Dieter Crisman,
MAA ReviewsTable of Contents
- Preliminary chapter on induction
- The Eulidean 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
- The anatomy of integers
- Counting integral and rational points on curves, modulo $p$
- Combinatorial number theory
- The $p$-adic numbers
- Rational points on elliptic curve
- Hints for exercises
- Recommended further reading
- Index
