A Conversational Introduction To Algebraic Number Theory Arithmetic Beyond Z PDF Download
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Author | : Paul Pollack |
Publisher | : American Mathematical Soc. |
Total Pages | : 312 |
Release | : 2017-08-01 |
Genre | : Algebraic number theory |
ISBN | : 1470436531 |
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Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Author | : Edwin Weiss |
Publisher | : Courier Corporation |
Total Pages | : 308 |
Release | : 2012-01-27 |
Genre | : Mathematics |
ISBN | : 048615436X |
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Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
Author | : J. S. Chahal |
Publisher | : |
Total Pages | : 150 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : |
Download A Brief Introduction to Algebraic Number Theory Book in PDF, ePub and Kindle
Author | : Benjamin Fine |
Publisher | : Springer Science & Business Media |
Total Pages | : 342 |
Release | : 2007-06-04 |
Genre | : Mathematics |
ISBN | : 0817645411 |
Download Number Theory Book in PDF, ePub and Kindle
This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Analytic number theory and algebraic number theory both receive a solid introductory treatment. The book’s user-friendly style, historical context, and wide range of exercises make it ideal for self study and classroom use.
Author | : H. P. F. Swinnerton-Dyer |
Publisher | : Cambridge University Press |
Total Pages | : 164 |
Release | : 2001-02-22 |
Genre | : Mathematics |
ISBN | : 9780521004237 |
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Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author | : John W. S. Cassels |
Publisher | : |
Total Pages | : 366 |
Release | : 1987 |
Genre | : Algebraic number theory |
ISBN | : 9780121632519 |
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Author | : Zhang Xian Ke |
Publisher | : ALPHA SCIENCE INTERNATIONAL LIMITED |
Total Pages | : 416 |
Release | : 2016-03-14 |
Genre | : Mathematics |
ISBN | : 1783323094 |
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ALGEBRAIC NUMBER THEORY provides concisely both the fundamental and profound theory, starting from the succinct ideal theory (Chapters 1-3), turning then to valuation theory and local completion field (Chapters 4-5) which is the base of modern approach. After specific discussions on class numbers, units, quadratic and cyclotomic fields, and analytical theory (Chapters 6-8), the important Class Field Theory (Chapter 9) is expounded, and algebraic function field (Chapter 10) is sketched. This book is based on the study and lectures of the author at several universities.
Author | : Richard A. Mollin |
Publisher | : CRC Press |
Total Pages | : 504 |
Release | : 1999-03-16 |
Genre | : Mathematics |
ISBN | : 9780849339899 |
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From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems. A follow-up to Dr. Mollin's popular Fundamental Number Theory with Applications, Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead, it carefully leads the student through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theory, and closes with reciprocity laws. In each chapter the author includes a section on a cryptographic application of the ideas presented, effectively demonstrating the pragmatic side of theory. In this way Algebraic Number Theory provides a comprehensible yet thorough treatment of the material. Written for upper-level undergraduate and graduate courses in algebraic number theory, this one-of-a-kind text brings the subject matter to life with historical background and real-world practicality. It easily serves as the basis for a range of courses, from bare-bones algebraic number theory, to a course rich with cryptography applications, to a course using the basic theory to prove Fermat's Last Theorem for regular primes. Its offering of over 430 exercises with odd-numbered solutions provided in the back of the book and, even-numbered solutions available a separate manual makes this the ideal text for both students and instructors.
Author | : Robert L. Long |
Publisher | : |
Total Pages | : 216 |
Release | : 1977 |
Genre | : Mathematics |
ISBN | : |
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Author | : Ian Stewart |
Publisher | : Springer |
Total Pages | : 296 |
Release | : 1987-05-07 |
Genre | : Juvenile Nonfiction |
ISBN | : |
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