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*FORMER LIBRARY BOOK* Book is in good condition. Front and back cover may contain minimal damage. Readable copy. LIGHTNING FAST SHIPPING!!* *FORMER LIBRARY BOOK* Book is in good condition. Front and back cover may contain minimal damage. Readable copy. LIGHTNING FAST SHIPPING!!* See less
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Neal Koblitz
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Introduction to Elliptic Curves and Modular Forms (Graduate Texts in Mathematics, 97) 2nd Edition

by Neal I. Koblitz (Author)
4.4 4.4 out of 5 stars 16 ratings
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This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find it hard to read more advanced or more algebraically oriented treatments. At the same time I want to introduce topics which are at the forefront of current research. Down-to-earth examples are given in the text and exercises, with the aim of making the material readable and interesting to mathematicians in fields far removed from the subject of the book. With numerous exercises (and answers) included, the textbook is also intended for graduate students who have completed the standard first-year courses in real and complex analysis and algebra. Such students would learn applications of techniques from those courses. thereby solidifying their under­ standing of some basic tools used throughout mathematics. Graduate stu­ dents wanting to work in number theory or algebraic geometry would get a motivational, example-oriented introduction. In addition, advanced under­ graduates could use the book for independent study projects, senior theses, and seminar work.
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  1. ISBN-10
    0387979662
  2. ISBN-13
    978-0387979663
  3. Edition
    2nd
  4. Publisher
    Springer
  5. Publication date
    April 29, 1993
  6. Language
    English
  7. Dimensions
    6.04 x 0.69 x 9.44 inches
  8. Print length
    262 pages
  9. See all details
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The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics, 106)
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Product details

  • Publisher ‏ : ‎ Springer; 2nd edition (April 29, 1993)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 262 pages
  • ISBN-10 ‏ : ‎ 0387979662
  • ISBN-13 ‏ : ‎ 978-0387979663
  • Item Weight ‏ : ‎ 2.31 pounds
  • Dimensions ‏ : ‎ 6.04 x 0.69 x 9.44 inches
  • Customer Reviews:
    4.4 4.4 out of 5 stars 16 ratings

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Neal Koblitz

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4.4 out of 5 stars
16 global ratings

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Top reviews from the United States

  • Revanchist
    5.0 out of 5 stars Well-deserved accolades
    Reviewed in the United States on October 6, 2012
    There are several other excellent works in the field of elliptic curves and in modular forms. However, there are several features about this book that make it truly unique. Of all the works that I've seen in the area, I have found Koblitz's work to be the most accessible and easy to follow. Among the many plus points of the book, are the large number of problems that are presented and the answers to selected problems that are available at the end of the book. For a graduate student in the field, it is invaluable to work out a good number of problems and Koblitz's book is ideal for undertaking such a task.

    The book is divided into four major sections. The first, quite interestingly, develops the theory of elliptic curves starting from congruent numbers. The discussion on elliptic functions, the Weierstrass form, etc are all very nicely done. The second section involves looking at the Hasse-Weil L-function of an elliptic curve. The discussion on the Riemann zeta function and the functional equation of the Hasse-Weil L-function were very informative and easy to understand, without sacrificing rigour. The last two sections deal with modular forms. The first of the two involves studying the SL(2,Z) group, developing modular forms for this group and a brief discussion of theta functions and Hecke operators. The last section is in many ways the most interesting, dealing with modular forms of half-integer weight and finishing with the theorems by Shimura, Tunnell, etc.

    For a book that is barely 200 pages long, there is a good range of topics covered, and the presentation is very elegant. The book maintains a high standard of rigour throughout and deserves all the praise that it has rightfully earned. My only crib, and it is a minor one, is that the transition from elliptic curves to modular forms is not an entirely seamless one.
    10 people found this helpful
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  • Rodolfo Riverol
    5.0 out of 5 stars Great intro to 1/2 weight modular forms. A must read for anyone interestested in the congruent number problem, modular forms
    Reviewed in the United States on January 9, 2011
    This is a very well thought out and accessible introduction to modular forms that paves the way to further study and research. While not as general as Miyake and others, it explains the fundamental concepts and driving ideas behind modular forms and elliptic curves in a down to earth fashion not seen in modern text. The author uses Tunnell's groundbreaking work on the congruent number problem to bridge the gap between modular forms and elliptic curves. Tunnell's theorem, which uses Shimura's deep connection between half integer weight and full integer weight modular forms and also employs the Swinnerton-Dyer conjecture on elliptic curves, is fully laid out in the last chapter. Motivated by the classical and beautiful congruent number problem the author has provided a wonderful path through modular forms and elliptic curves. A real gem, a must read.
    4 people found this helpful
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  • Les
    5.0 out of 5 stars Brilliant Exposition
    Reviewed in the United States on September 26, 2007
    Koblitz is in his element with this text. Much like Daniel Marcus's Number Fields, Koblitz develops a ground work to begin the study of elliptic curves. Here he builds upon the ancient problem of congruent numbers to help develop motivation for an in depth study of elliptic curves and modular forms. Not for the faint of (mathematical) heart, but a truly brilliant piece added to the number theoretic literature. A must own for those interested in advanced ideas behind elliptic curves.
    11 people found this helpful
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  • P. J. Gies
    5.0 out of 5 stars Clearly the best
    Reviewed in the United States on November 5, 2001
    This is not an easy book---it's certainly intended for graduate students---but it's also clearly the best introduction to the mathematics that give rise to the Taniyama-Shimura conjecture and the ideas that underlie the Wiles proof of Fermat's Last Theorem, and as such it deserves a prominent place in the world's intellectual life. And you have to love a math text that has a beautiful frontispiece (a sketch by Fomenko whose mathematical meaning I am still trying to work out).
    19 people found this helpful
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  • Alan Wong
    5.0 out of 5 stars Organized and Wonderful
    Reviewed in the United States on July 28, 2002
    The book provides an excellent and readable introduction to elliptic curves, using the complex analysis approach. It gives detailed proof to many theorems, and the exercises for each chapter are wonderful. It is a good supplement for those who use another book by Koblitz: Algebraic Aspects of Cryptography (AAC). It is funny that Koblitz has copied and pasted some of the paragraphs from Introduction to Elliptic Curves and Modular Forms to AAC!
    13 people found this helpful
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Top reviews from other countries

  • R. Carling
    5.0 out of 5 stars The Riemann Zeta-Function and Modular Forms
    Reviewed in Canada on March 27, 2024
    Verified Purchase
    I bought the book in order to find out the connection between the Riemann Zeta-Function and Modular Forms. The subject matter presented in chapters two, three and four of the book clearly explain the relation between the Riemann Zeta-Function and an important class of modular forms.
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  • Nikola Adzaga
    4.0 out of 5 stars Good for motivation
    Reviewed in the United Kingdom on August 13, 2017
    Verified Purchase
    A somewhat unusual book, I like it even though I haven't learned the material systematically through it. The writing style is interesting (even fun at times) and it does a good job at motivating both elliptic curves and modular forms through a seemingly simple problem.
    One person found this helpful
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