A Classical Introduction to Modern Number Theory

Author:   Kenneth Ireland ,  Michael Rosen
Publisher:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 2nd ed. 1990
Volume:   84
ISBN:  

9781441930941


Pages:   394
Publication Date:   01 December 2010
Format:   Paperback
Availability:   In Print   Availability explained
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A Classical Introduction to Modern Number Theory


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Author:   Kenneth Ireland ,  Michael Rosen
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 2nd ed. 1990
Volume:   84
Dimensions:   Width: 15.50cm , Height: 2.10cm , Length: 23.50cm
Weight:   1.260kg
ISBN:  

9781441930941


ISBN 10:   1441930949
Pages:   394
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

1 Unique Factorization.- 2 Applications of Unique Factorization.- 3 Congruence.- 4 The Structure of U(?/n?).- 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.- Selected Hints for the Exercises.

Reviews

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)


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)


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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