number theory pure and applied mathematics

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Number Theory

Author : Don Redmond
ISBN : 0824796969
Genre : Mathematics
File Size : 75. 45 MB
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This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.

Algebraic Groups And Number Theory

Author : Vladimir Platonov
ISBN : 0080874592
Genre : Mathematics
File Size : 44. 73 MB
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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.

Number Theory And Its Applications

Author : Serguei Stepanov
ISBN : 0824719697
Genre : Mathematics
File Size : 57. 75 MB
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"Addresses contemporary developments in number theory and coding theory, originally presented as lectures at summer school held at Bilkent University, Ankara, Turkey. Includes many results in book form for the first time."

Number Theory

Author :
ISBN : 0080873324
Genre : Mathematics
File Size : 20. 35 MB
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This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.

Theory Of Codes

Author :
ISBN : 0080874363
Genre : Mathematics
File Size : 70. 26 MB
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Theory of Codes

Groups Rings And Group Rings

Author : A. Giambruno
ISBN : 9780821847718
Genre : Mathematics
File Size : 45. 9 MB
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This volume represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. Papers in this volume contain results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras. In particular, topics such as growth functions on varieties, groups of units in group rings, representation theory of Lie algebras, Jordan, alternative and Leibniz algebras, graded identities, automorphisms of trees, and partial actions, are discussed.

The Chebyshev Polynomials

Author : Theodore J. Rivlin
ISBN : MINN:319510004728748
Genre : Chebyshev polynomials
File Size : 88. 57 MB
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Factorization In Integral Domains

Author : Daniel Anderson
ISBN : 9781351448932
Genre : Mathematics
File Size : 26. 62 MB
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The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.

A Theory Of Sets

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ISBN : 0080873308
Genre : Mathematics
File Size : 55. 25 MB
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A Theory of Sets

Invariant Descriptive Set Theory

Author : Su Gao
ISBN : 158488794X
Genre : Mathematics
File Size : 31. 35 MB
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Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields. After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research.

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