Developed from the author’s popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.
Editorial Reviews
Review
‘[Baker] … possesses … powerful gifts for precision and concision … [the book] never seems rushed or artificially compressed. Highly recommended.’ D. V. Feldman, Choice
Book Description
The author’s classic concise introduction now fully updated and developed to suit courses extending from primers to introductions to research.
About the Author
Alan Baker is Emeritus Professor of Pure Mathematics in the University of Cambridge and Fellow of Trinity College, Cambridge. His many distinctions include the Fields Medal (1970) and the Adams Prize (1972).
Developed from the author’s popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.
Editorial Reviews
Review
“Now the idea of a 250-page “comprehensive” introduction to number theory may seem audacious, but among mathematical writers, Baker manifestly possesses the powerful gifts for precision and concision that could even make it possible. Such a book surely demands very careful study, but amazingly never seems rushed or artificially compressed. Highly recommended.” D.V. Feldman, University of New Hampshire for Choice Magazine
“Any competent instructor could use this as the starting point of a valuable course.” Richard T. Bumby, Mathematical Reviews
Book Description
The author’s classic concise introduction now fully updated and developed to suit courses extending from primers to introductions to research.
About the Author
Alan Baker is Emeritus Professor of Pure Mathematics in the University of Cambridge and Fellow of Trinity College, Cambridge. His many distinctions include the Fields Medal (1970) and the Adams Prize (1972).
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