Groups Modular Mathematics Series

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Groups Modular Mathematics Series

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Author : Camilla Jordan
language : en
Publisher: Butterworth-Heinemann
Release Date : 1994-07-01

Groups Modular Mathematics Series written by Camilla Jordan and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-01 with Mathematics categories.

This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.

Linear Algebra

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Author : Reg Allenby
language : en
Publisher: Butterworth-Heinemann
Release Date : 1995-01-05

Linear Algebra written by Reg Allenby and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-05 with Mathematics categories.

As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.

Groups Rings And Fields

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Author : David A.R. Wallace
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-22

Groups Rings And Fields written by David A.R. Wallace 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 2001-06-22 with Mathematics categories.

This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.

Modular Functions And Dirichlet Series In Number Theory

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Author : Tom M. Apostol
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Modular Functions And Dirichlet Series In Number Theory written by Tom M. Apostol 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.

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj( r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T. M. A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory.

Rings Fields And Groups

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Author : R. B. J. T. Allenby
language : en
Publisher: Butterworth-Heinemann
Release Date : 1991

Rings Fields And Groups written by R. B. J. T. Allenby and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses

Quaternion Algebras

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Author : John Voight
language : en
Publisher: Springer Nature
Release Date : 2021-06-28

Quaternion Algebras written by John Voight and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Mathematics categories.

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

Modular Forms And Galois Cohomology

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Author : Haruzo Hida
language : en
Publisher: Cambridge University Press
Release Date : 2000-06-29

Modular Forms And Galois Cohomology written by Haruzo Hida 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 2000-06-29 with Mathematics categories.

Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.

Modular Invariant Theory

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Author : H.E.A. Eddy Campbell
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-12

Modular Invariant Theory written by H.E.A. Eddy Campbell 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 2011-01-12 with Mathematics categories.

This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.

Abstract Algebra

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Author : Gregory T. Lee
language : en
Publisher: Springer
Release Date : 2018-04-13

Abstract Algebra written by Gregory T. Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-13 with Mathematics categories.

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.

Resources In Education

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Author :
language : en
Publisher:
Release Date : 1980

Resources In Education written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Education categories.