Algebraic Analytic And Computational Number Theory And Its Applications
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Algebraic Analytic And Computational Number Theory And Its Applications
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Author : Diana Savin
language : en
Publisher: Mdpi AG
Release Date : 2024-01-16
Algebraic Analytic And Computational Number Theory And Its Applications written by Diana Savin and has been published by Mdpi AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-16 with Computers categories.
Analytic number theory is a branch of number theory which uses methods from mathematical analysis in order to solve difficult problems about integers. Analytic number theory can be split into two major areas: multiplicative number theory and additive number theory. Bernhard Riemann made some very important contributions to the field of analytic number theory; among others, he investigated the Riemann zeta function, and he established its importance for understanding the distribution of prime numbers. A typical problem of analytic number theory is the enumeration of number-theoretic objects like primes, solutions of Diophantine equations, etc. Algebraic number theory on the other hand studies the arithmetic of algebraic number fields, i.e., the ring of integers of arbitrary number fields. It embraces, among others, the study of the ideals and of the group of units in the ring of integers and the extent to which unique factorization holds. The purpose and scope of this ''Special Issue" were to collect new results in algebraic number theory and analytic number theory (namely in the areas of ramification theory in algebraic number fields, class field theory, arithmetic functions, L-functions, modular forms and elliptic curves) and in some similar research areas (namely associative algebras, logical algebras, elementary number theory, combinatorics, difference equations, group rings and algebraic hyper-structures).
Algebraic Function Fields And Codes
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Author : Henning Stichtenoth
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Algebraic Function Fields And Codes written by Henning Stichtenoth 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 2009-02-11 with Mathematics categories.
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
A Course In Functional Analysis
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Author : John B Conway
language : en
Publisher: Springer
Release Date : 2019-03-09
A Course In Functional Analysis written by John B Conway and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-09 with Mathematics categories.
Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.
Abstract Algebra
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Author : Pierre Antoine Grillet
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-21
Abstract Algebra written by Pierre Antoine Grillet 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 2007-07-21 with Mathematics categories.
A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories.
Algebra
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-21
Algebra written by Serge Lang 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 2005-06-21 with Mathematics categories.
This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."
Algebraic Geometry
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Author : Robin Hartshorne
language : en
Publisher: Springer Science & Business Media
Release Date : 1977-12-19
Algebraic Geometry written by Robin Hartshorne 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 1977-12-19 with Mathematics categories.
This book provides an introduction to abstract algebraic geometry. It includes more than 400 exercises that offer specific examples as well as more specialized topics. From the reviews: "Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions." --MATHEMATICAL REVIEWS
Algebra
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Author : Thomas W. Hungerford
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebra written by Thomas W. Hungerford 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 2012-12-06 with Mathematics categories.
Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents. The guiding philosophical principle throughout the text is that the material should be presented in the maximum usable generality consistent with good pedagogy. Therefore it is essentially self-contained, stresses clarity rather than brevity and contains an unusually large number of illustrative exercises. The book covers major areas of modern algebra, which is a necessity for most mathematics students in sufficient breadth and depth.
Algebraic Topology
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Author : William Fulton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Algebraic Topology written by William Fulton 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 2013-12-01 with Mathematics categories.
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups
Harmonic Function Theory
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Author : Sheldon Axler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Harmonic Function Theory written by Sheldon Axler 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 2013-11-11 with Mathematics categories.
This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.
Algebraic Geometry
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Author : Joe Harris
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-09-17
Algebraic Geometry written by Joe Harris 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 1992-09-17 with Mathematics categories.
This textbook is an introduction to algebraic geometry that emphasizes the classical roots of the subject, avoiding the technical details better treated with the most recent methods. It provides a basis for understanding the developments of the last half century which have put the subject on a radically new footing. Based on lectures given at Brown and Harvard, the book retains an informal style and stresses examples. Annotation copyright by Book News, Inc., Portland, OR