An Introduction to the Theory of Numbers

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Oxford University Press, Oct 29, 2008 - Mathematics - 621 pages
6 Reviews
An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory.
Updates include a chapter by J. H. Silverman on one of the most important developments in number theory - modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader.
The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.
Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor of
Pure Mathematics at Oxford University. He works in analytic number
theory, and in particular on its applications to prime numbers and to
Diophantine equations.

Preface to the sixth edition Andrew Wiles


Preface to the fifth edition


1. The Series of Primes (1)


2. The Series of Primes (2)


3. Farey Series and a Theorem of Minkowski


4. Irrational Numbers


5. Congruences and Residues


6. Fermat's Theorem and its Consequences


7. General Properties of Congruences


8. Congruences to Composite Moduli


9. The Representation of Numbers by Decimals


10. Continued Fractions


11. Approximation of Irrationals by Rationals


12. The Fundamental Theorem of Arithmetic in k(l), k(i), and k(p)


13. Some Diophantine Equations


14. Quadratic Fields (1)


15. Quadratic Fields (2)


16. The Arithmetical Functions (n), m(n), d(n), σ(n), r(n)


17. Generating Functions of Arithmetical Functions


18. The Order of Magnitude of Arithmetical Functions


19. Partitions


20. The Representation of a Number by Two or Four Squares


21. Representation by Cubes and Higher Powers


22. The Series of Primes (3)


23. Kronecker's Theorem


24. Geometry of Numbers


25. Elliptic Curves, Joseph H. Silverman


Appendix


List of Books


Index of Special Symbols and Words


Index of Names


General Index


From inside the book

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Review: An Introduction to the Theory of Numbers

User Review  - Mikesokolov - Goodreads

I got a lot out of it, but ultimately didn't finish.. can't say why really; maybe the same reason I didn't get a graduate math degree Read full review

Review: An Introduction to the Theory of Numbers

User Review  - Joey Comeau - Goodreads

I read a two sentence review of this once that has really stuck with me. It went along the lines of "If I could bring only one book with me to a desert island, it would be [some other book] if I ... Read full review

Contents

THE SERIES OF PRIMES 1
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Copyright

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About the author (2008)


Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor of
Pure Mathematics at Oxford University. He works in analytic number
theory, and in particular on its applications to prime numbers and to
Diophantine equations.

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