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ISBN: 9780511791260 9780521832502 9780521540117 0511166095 9780511166099 9780511164149 0511164149 0521832500 0521540119 0511791267 9780511164941 0511164947 0511164149 0521832500 0521540119 1107148855 9781107148857 0511566808 9780511566806 Year: 2004 Publisher: Cambridge New York Cambridge University Press
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Algebraic number theory is a subject which came into being through the attempts of mathematicians to try to prove Fermat's last theorem and which now has a wealth of applications to diophantine equations, cryptography, factoring, primality testing and public-key cryptosystems. This book provides an introduction to the subject suitable for senior undergraduates and beginning graduate students in mathematics. The material is presented in a straightforward, clear and elementary fashion, and the approach is hands on, with an explicit computational flavour. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested reading and to the biographies of mathematicians who have contributed to the development of algebraic number theory are given at the end of each chapter. There are over 320 exercises, an extensive index, and helpful location guides to theorems and lemmas in the text.
Algebraic number theory. --- Number theory. --- Number study --- Numbers, Theory of --- Algebra --- Number theory --- Algebraic number theory --- Théorie des nombres algébriques
ISBN: 9780521720083 0521720087 9780511721564 9781107363052 1107363055 9780511893834 0511893833 1139886797 9781139886796 1107367964 9781107367968 1107372496 9781107372498 1107365503 9781107365506 0511721560 129940555X Year: 2009 Publisher: Cambridge, U.K. New York Cambridge University Press
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Integration of differential equations is a central problem in mathematics and several approaches have been developed by studying analytic, algebraic, and algorithmic aspects of the subject. One of these is Differential Galois Theory, developed by Kolchin and his school, and another originates from the Soliton Theory and Inverse Spectral Transform method, which was born in the works of Kruskal, Zabusky, Gardner, Green and Miura. Many other approaches have also been developed, but there has so far been no intersection between them. This unique introduction to the subject finally brings them together, with the aim of initiating interaction and collaboration between these various mathematical communities. The collection includes a LMS Invited Lecture Course by Michael F. Singer, together with some shorter lecture courses and review articles, all based upon a mini-programme held at the International Centre for Mathematical Sciences (ICMS) in Edinburgh.
Differential equations --- Algebraic number theory --- Differential calculus --- Differential algebra --- Equations différentielles --- Théorie des nombres algébriques --- Calcul différentiel --- Algèbre différentielle --- Congresses --- Congrès --- Algebraic theory --- Calculus, Differential --- Calculus --- 517.91 Differential equations --- Algebra, Differential --- Differential fields --- Algebraic fields
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