Elliptic Curves: Function Theory, Geometry, Arithmetic

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9780521658171: Elliptic Curves: Function Theory, Geometry, Arithmetic

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, whose masters were Abel, Gauss, Jacobi, and Legendre. This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows a historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. The many exercises with hints scattered throughout the text give the reader a glimpse of further developments. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics.

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Book Description:

The subject of elliptic curves is one of the jewels of 19th century mathematics, whose masters were Abel, Gauss, Jacobi, and Legendre. This book presents account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic.Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics. The many exercises with hints scattered throughout the text give the reader a glimpse of further developments.

Review:

"...undergraduates will find that McKean and Moll's book...offers more diverse viewpoints [than other books on elliptic curves]. Highly recommended."
Choice

"...this is a wonderful book that should reward those who have the background for it with immense joy and insight."
SIAM Review

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Henry McKean; Victor Moll
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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2011. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****. The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This 1997 book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text. Bookseller Inventory # AAV9780521658171

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2011. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****.The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This 1997 book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text. Bookseller Inventory # AAV9780521658171

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