Problems In Algebraic Number Theory

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Problems In Algebraic Number Theory

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Author : M. Ram Murty
language : en
Publisher: Springer Science & Business Media
Release Date : 2005

Problems In Algebraic Number Theory written by M. Ram Murty and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved

Computational Problems Methods And Results In Algebraic Number Theory

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Author : H. G. Zimmer
language : en
Publisher: Springer
Release Date : 2006-11-15

Computational Problems Methods And Results In Algebraic Number Theory written by H. G. Zimmer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Algebraic Number Theory

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Author : J.S. Chahal
language : en
Publisher: CRC Press
Release Date : 2021-07-21

Algebraic Number Theory written by J.S. Chahal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Mathematics categories.

This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic. The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material, then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields, and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry. About the Author Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies, he likes to travel and hike. His book, Fundamentals of Linear Algebra, is also published by CRC Press.

Solved And Unsolved Problems In Number Theory

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Author : Daniel Shanks
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-24

Solved And Unsolved Problems In Number Theory written by Daniel Shanks and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-24 with Mathematics categories.

The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers.

Algebraic Number Theory For Beginners

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Author : John Stillwell
language : en
Publisher: Cambridge University Press
Release Date : 2022-08-11

Algebraic Number Theory For Beginners written by John Stillwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-11 with Mathematics categories.

A concise and well-motivated introduction to algebraic number theory, following the evolution of unique prime factorization through history.

Algebraic Number Theory And Fermat S Last Theorem

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Author : Ian Stewart
language : en
Publisher: CRC Press
Release Date : 2025-02-07

Algebraic Number Theory And Fermat S Last Theorem written by Ian Stewart and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-07 with Mathematics categories.

Updated to reflect current research and extended to cover more advanced topics as well as the basics, Algebraic Number Theory and Fermat’s Last Theorem, Fifth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers, initially from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work. New to the Fifth Edition Pell's Equation x^2-dy^2=1: all solutions can be obtained from a single `fundamental' solution, which can be found using continued fractions. Galois theory of number field extensions, relating the field structure to that of the group of automorphisms. More material on cyclotomic fields, and some results on cubic fields. Advanced properties of prime ideals, including the valuation of a fractional ideal relative to a prime ideal, localisation at a prime ideal, and discrete valuation rings. Ramification theory, which discusses how a prime ideal factorises when the number field is extended to a larger one. A short proof of the Quadratic Reciprocity Law based on properties of cyclotomic fields. This Valuations and p-adic numbers. Topology of the p-adic integers. Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.

A Textbook Of Algebraic Number Theory

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Author : Sudesh Kaur Khanduja
language : en
Publisher: Springer Nature
Release Date : 2022-04-26

A Textbook Of Algebraic Number Theory written by Sudesh Kaur Khanduja and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-26 with Mathematics categories.

This self-contained and comprehensive textbook of algebraic number theory is useful for advanced undergraduate and graduate students of mathematics. The book discusses proofs of almost all basic significant theorems of algebraic number theory including Dedekind’s theorem on splitting of primes, Dirichlet’s unit theorem, Minkowski’s convex body theorem, Dedekind’s discriminant theorem, Hermite’s theorem on discriminant, Dirichlet’s class number formula, and Dirichlet’s theorem on primes in arithmetic progressions. A few research problems arising out of these results are mentioned together with the progress made in the direction of each problem. Following the classical approach of Dedekind’s theory of ideals, the book aims at arousing the reader’s interest in the current research being held in the subject area. It not only proves basic results but pairs them with recent developments, making the book relevant and thought-provoking. Historical notes are given at various places. Featured with numerous related exercises and examples, this book is of significant value to students and researchers associated with the field. The book also is suitable for independent study. The only prerequisite is basic knowledge of abstract algebra and elementary number theory.

Algebraic Number Theory

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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-04-06

Algebraic Number Theory written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-06 with Mathematics categories.

EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.

Algebraic Number Theory

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Author : H. Koch
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-09-12

Algebraic Number Theory written by H. Koch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-12 with Mathematics categories.

From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993

Algebraic Groups And Number Theory

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Author : Vladimir Platonov
language : en
Publisher: Academic Press
Release Date : 1993-12-07

Algebraic Groups And Number Theory written by Vladimir Platonov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-07 with Mathematics categories.

This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.