A Classical Introduction to Modern Number Theory
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A Classical Introduction to Modern Number Theory

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Description

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
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Product details

  • Hardback | 394 pages
  • 155 x 235 x 23.88mm | 817g
  • New York, NY, United States
  • English
  • Revised
  • 2nd ed. 1990. Corr. 5th printing 1998
  • XIV, 394 p.
  • 038797329X
  • 9780387973296
  • 487,338

Table of contents

1: Unique Factorization. 2: Applications of Unique Factorization. 3: Congruence. 4: The Structure of U. 5: Quadratic Reciprocity. 6: Quadratic Gauss Sums. 7: Finite Fields. 8: Gauss and Jacobi Sums. 9: Cubic and Biquadratic Reciprocity. 10: Equations over Finite Fields. 11: The Zeta Function. 12: Algebraic Number Theory. 13: Quadratic and Cyclotomic Fields. 14: The Stickelberger Relation and the Eisenstein Reciprocity Law. 15: Bernoulli Numbers. 16: Dirichlet L-functions. 17: Diophantine Equations. 18: Elliptic Curves. 19: The Mordell-Weil Theorem. 20: New Progress in Arithmetic Geometry.
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Review Text

From the reviews of the second edition:

K. Ireland and M. Rosen

A Classical Introduction to Modern Number Theory

"Many mathematicians of this generation have reached the frontiers of research without having a good sense of the history of their subject. In number theory this historical ignorance is being alleviated by a number of fine recent books. This work stands among them as a unique and valuable contribution."

- MATHEMATICAL REVIEWS

"This is a great book, one that does exactly what it proposes to do, and does it well. For me, this is the go-to book whenever a student wants to do an advanced independent study project in number theory. ... for a student who wants to get started on the subject and has taken a basic course on elementary number theory and the standard abstract algebra course, this is perfect." (Fernando Q. Gouvêa, MathDL, January, 2006)
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Review quote

From the reviews of the second edition:


K. Ireland and M. Rosen


A Classical Introduction to Modern Number Theory


"Many mathematicians of this generation have reached the frontiers of research without having a good sense of the history of their subject. In number theory this historical ignorance is being alleviated by a number of fine recent books. This work stands among them as a unique and valuable contribution."


- MATHEMATICAL REVIEWS


"This is a great book, one that does exactly what it proposes to do, and does it well. For me, this is the go-to book whenever a student wants to do an advanced independent study project in number theory. ... for a student who wants to get started on the subject and has taken a basic course on elementary number theory and the standard abstract algebra course, this is perfect." (Fernando Q. Gouvea, MathDL, January, 2006)
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About Kenneth F. Ireland

Michael Rosen is a hugely bestselling author of poetry. Michael frequently appears on radio and gives talks. He is the Children's Laureate for 2007-2009 and the winner of the Eleanor Farjeon Award for services to children's literature. Michael lives in London.
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Rating details

36 ratings
4.47 out of 5 stars
5 56% (20)
4 36% (13)
3 8% (3)
2 0% (0)
1 0% (0)
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