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| Author | : Martyn R. Dixon |
| Publisher | : John Wiley & Sons |
| Total Pages | : 544 |
| Release | : 2011-07-15 |
| Genre | : Mathematics |
| ISBN | : 9780470640531 |
Download Algebra and Number Theory Book in PDF, ePub and Kindle
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.
| Author | : Edwin Weiss |
| Publisher | : Courier Corporation |
| Total Pages | : 308 |
| Release | : 2012-01-27 |
| Genre | : Mathematics |
| ISBN | : 048615436X |
Download Algebraic Number Theory Book in PDF, ePub and Kindle
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 | : Ian Stewart |
| Publisher | : Springer |
| Total Pages | : 257 |
| Release | : 1979-05-31 |
| Genre | : Science |
| ISBN | : 9780412138409 |
Download Algebraic Number Theory Book in PDF, ePub and Kindle
The title of this book may be read in two ways. One is 'algebraic number-theory', that is, the theory of numbers viewed algebraically; the other, 'algebraic-number theory', the study of algebraic numbers. Both readings are compatible with our aims, and both are perhaps misleading. Misleading, because a proper coverage of either topic would require more space than is available, and demand more of the reader than we wish to; compatible, because our aim is to illustrate how some of the basic notions of the theory of algebraic numbers may be applied to problems in number theory. Algebra is an easy subject to compartmentalize, with topics such as 'groups', 'rings' or 'modules' being taught in comparative isolation. Many students view it this way. While it would be easy to exaggerate this tendency, it is not an especially desirable one. The leading mathematicians of the nineteenth and early twentieth centuries developed and used most of the basic results and techniques of linear algebra for perhaps a hundred years, without ever defining an abstract vector space: nor is there anything to suggest that they suf fered thereby. This historical fact may indicate that abstrac tion is not always as necessary as one commonly imagines; on the other hand the axiomatization of mathematics has led to enormous organizational and conceptual gains.
| Author | : Harry Pollard |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 1975-12-31 |
| Genre | : Algebraic number theory |
| ISBN | : 1614440093 |
Download The Theory of Algebraic Numbers: Second Edition Book in PDF, ePub and Kindle
This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
| Author | : Ian Stewart |
| Publisher | : CRC Press |
| Total Pages | : 334 |
| Release | : 2001-12-12 |
| Genre | : Mathematics |
| ISBN | : 143986408X |
Download Algebraic Number Theory and Fermat's Last Theorem Book in PDF, ePub and Kindle
First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it
| Author | : Benjamin Fine |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 342 |
| Release | : 2017-09-11 |
| Genre | : Mathematics |
| ISBN | : 3110516144 |
Download Algebra and Number Theory Book in PDF, ePub and Kindle
This two-volume set collects and presents some fundamentals of mathematics in an entertaining and performing manner. The present volume examines many of the most important basic results in algebra and number theory, along with their proofs, and also their history. Contents The natural, integral and rational numbers Division and factorization in the integers Modular arithmetic Exceptional numbers Pythagorean triples and sums of squares Polynomials and unique factorization Field extensions and splitting fields Permutations and symmetric polynomials Real numbers The complex numbers, the Fundamental Theorem of Algebra and polynomial equations Quadratic number fields and Pell’s equation Transcendental numbers and the numbers e and π Compass and straightedge constructions and the classical problems Euclidean vector spaces
| Author | : Fedor Bogomolov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 365 |
| Release | : 2006-06-22 |
| Genre | : Mathematics |
| ISBN | : 0817644172 |
Download Geometric Methods in Algebra and Number Theory Book in PDF, ePub and Kindle
* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry
| Author | : Henri Cohen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 556 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662029456 |
Download A Course in Computational Algebraic Number Theory Book in PDF, ePub and Kindle
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
| Author | : Serge Lang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 146120853X |
Download Algebraic Number Theory Book in PDF, ePub and Kindle
This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—-MATHEMATICAL REVIEWS
| Author | : Frazer Jarvis |
| Publisher | : Springer |
| Total Pages | : 298 |
| Release | : 2014-06-23 |
| Genre | : Mathematics |
| ISBN | : 3319075454 |
Download Algebraic Number Theory Book in PDF, ePub and Kindle
This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.
