Post Modern Algebra

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Post-Modern Algebra

Jonathan D. H. Smith,Anna B. Romanowska
Post Modern Algebra Book PDF

Author : Jonathan D. H. Smith,Anna B. Romanowska
Publisher : John Wiley & Sons
Page : 386 pages
File Size : 40,6 Mb
Release : 2011-09-30
Category : Mathematics
ISBN : 9781118030837

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Post-Modern Algebra by Jonathan D. H. Smith,Anna B. Romanowska Pdf

Advanced algebra in the service of contemporary mathematicalresearch-- a unique introduction. This volume takes an altogether new approach to advanced algebra.Its intriguing title, inspired by the term postmodernism, denotes adeparture from van der Waerden's Modern Algebra--a book that hasdominated the field for nearly seventy years. Post-Modern Algebraoffers a truly up-to-date alternative to the standard approach,explaining topics from an applications-based perspective ratherthan by abstract principles alone. The book broadens the field ofstudy to include algebraic structures and methods used in currentand emerging mathematical research, and describes the powerful yetsubtle techniques of universal algebra and category theory.Classical algebraic areas of groups, rings, fields, and vectorspaces are bolstered by such topics as ordered sets, monoids,monoid actions, quasigroups, loops, lattices, Boolean algebras,categories, and Heyting algebras. The text features: * A clear and concise treatment at an introductory level, tested inuniversity courses. * A wealth of exercises illustrating concepts and their practicalapplication. * Effective techniques for solving research problems in the realworld. * Flexibility of presentation, making it easy to tailor material tospecific needs. * Help with elementary proofs and algebraic notations for studentsof varying abilities. Post-Modern Algebra is an excellent primary or supplementary textfor graduate-level algebra courses. It is also an extremely usefulresource for professionals and researchers in many areas who musttackle abstract, linear, or universal algebra in the course oftheir work.

The Proceedings of the 12th International Congress on Mathematical Education

Sung Je Cho
The Proceedings of the 12th International Congress on Mathematical Education Book PDF

Author : Sung Je Cho
Publisher : Springer
Page : 617 pages
File Size : 43,8 Mb
Release : 2015-02-10
Category : Education
ISBN : 9783319126883

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The Proceedings of the 12th International Congress on Mathematical Education by Sung Je Cho Pdf

This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.

Advanced Modern Algebra

Joseph J. Rotman
Advanced Modern Algebra Book PDF

Author : Joseph J. Rotman
Publisher : American Mathematical Society
Page : 570 pages
File Size : 55,5 Mb
Release : 2023-02-22
Category : Mathematics
ISBN : 9781470472757

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Advanced Modern Algebra by Joseph J. Rotman Pdf

This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

Algebra: Chapter 0

Paolo Aluffi
Algebra Chapter 0 Book PDF

Author : Paolo Aluffi
Publisher : American Mathematical Soc.
Page : 713 pages
File Size : 51,6 Mb
Release : 2021-11-09
Category : Education
ISBN : 9781470465711

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Algebra: Chapter 0 by Paolo Aluffi Pdf

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

A Book of Abstract Algebra

Charles C Pinter
A Book of Abstract Algebra Book PDF

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 41,6 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9780486474175

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A Book of Abstract Algebra by Charles C Pinter Pdf

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Modern Algebra

B S Vatssa
Modern Algebra Book PDF

Author : B S Vatssa
Publisher : New Age International
Page : 384 pages
File Size : 51,5 Mb
Release : 1999
Category : Algebra
ISBN : 8122411916

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Modern Algebra by B S Vatssa Pdf

This Book Is Meant To Provide A Text For The Graduate And Post-Graduate Classes On Modern Algebra At All Indian Universities And At The Institutes Of Technology, But Is Also Intended To Be Useful For All Competitive Examinations Such As I.A.S., Net Etc.This Book Presents Basic And More Important Results In Group Theory, Ring Theory, Linear Algebra And Field Theory. It Is A Self-Contained Book And Also Provides An Understanding Of Basic Mathematical Concepts To Science, Engineering And Social Science Students.There Is Always A Danger Of Introducing The Abstract Concepts Too Suddenly And Without Sufficient Base Of Examples. In Order To Mitigate It The Concepts Have Been Motivated Beforehand. The Topics Have Been Presented In A Simple, Clear And Coherent Style With A Number Of Examples And Exercises. Exercises Of Various Levels Of Difficulty Are Given At The End Each Section.

Undergraduate Algebra

Serge Lang
Undergraduate Algebra Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 44,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475768985

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Undergraduate Algebra by Serge Lang Pdf

The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

A Course in Algebra

Ėrnest Borisovich Vinberg
A Course in Algebra Book PDF

Author : Ėrnest Borisovich Vinberg
Publisher : American Mathematical Soc.
Page : 526 pages
File Size : 50,6 Mb
Release : 2003
Category : Algebra
ISBN : 9780821833186

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A Course in Algebra by Ėrnest Borisovich Vinberg Pdf

Great book! The author's teaching experinece shows in every chapter. --Efim Zelmanov, University of California, San Diego Vinberg has written an algebra book that is excellent, both as a classroom text or for self-study. It is plain that years of teaching abstract algebra have enabled him to say the right thing at the right time. --Irving Kaplansky, MSRI This is a comprehensive text on modern algebra written for advanced undergraduate and basic graduate algebra classes. The book is based on courses taught by the author at the Mechanics and Mathematics Department of Moscow State University and at the Mathematical College of the Independent University of Moscow. The unique feature of the book is that it contains almost no technically difficult proofs. Following his point of view on mathematics, the author tried, whenever possible, to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. Another important feature is that the book presents most of the topics on several levels, allowing the student to move smoothly from initial acquaintance to thorough study and deeper understanding of the subject. Presented are basic topics in algebra such as algebraic structures, linear algebra, polynomials, groups, as well as more advanced topics like affine and projective spaces, tensor algebra, Galois theory, Lie groups, associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. Written with extreme care and supplied with more than 200 exercises and 70 figures, the book is also an excellent text for independent study.

Advanced Modern Algebra

Joseph J. Rotman
Advanced Modern Algebra Book PDF

Author : Joseph J. Rotman
Publisher : American Mathematical Soc.
Page : 1026 pages
File Size : 52,8 Mb
Release : 2010-08-11
Category : Mathematics
ISBN : 9780821847411

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Advanced Modern Algebra by Joseph J. Rotman Pdf

"This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free). The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Gr'obner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn-Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra. Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic K-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization."--Publisher's description.

Basic Modern Algebra with Applications

Mahima Ranjan Adhikari,Avishek Adhikari
Basic Modern Algebra with Applications Book PDF

Author : Mahima Ranjan Adhikari,Avishek Adhikari
Publisher : Springer Science & Business Media
Page : 637 pages
File Size : 42,5 Mb
Release : 2013-12-08
Category : Mathematics
ISBN : 9788132215998

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Basic Modern Algebra with Applications by Mahima Ranjan Adhikari,Avishek Adhikari Pdf

The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.

Mathematics and the Roots of Postmodern Thought

Vladimir Tasic
Mathematics and the Roots of Postmodern Thought Book PDF

Author : Vladimir Tasic
Publisher : Oxford University Press
Page : 200 pages
File Size : 52,9 Mb
Release : 2001-08-30
Category : Mathematics
ISBN : 9780199881512

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Mathematics and the Roots of Postmodern Thought by Vladimir Tasic Pdf

This is a charming and insightful contribution to an understanding of the "Science Wars" between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy. It traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century, then compares developments in mathematics to what took place in the arts and humanities, discussing issues as diverse as literary theory, arts, and artificial intelligence. This is a straightforward, easily understood presentation of what can be difficult theoretical concepts It demonstrates that a pattern of misreading mathematics can be seen both on the part of science and on the part of postmodern thinking. This is a humorous, playful yet deeply serious look at the intellectual foundations of mathematics for those in the humanities and the perfect critical introduction to the bases of modernism and postmodernism for those in the sciences.

A First Course in Abstract Algebra

Joseph J. Rotman
A First Course in Abstract Algebra Book PDF

Author : Joseph J. Rotman
Publisher : Unknown
Page : 552 pages
File Size : 43,5 Mb
Release : 2000
Category : Mathematics
ISBN : STANFORD:36105028605132

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A First Course in Abstract Algebra by Joseph J. Rotman Pdf

For one-semester or two-semester undergraduate courses in Abstract Algebra. This new edition has been completely rewritten. The four chapters from the first edition are expanded, from 257 pages in first edition to 384 in the second. Two new chapters have been added: the first 3 chapters are a text for a one-semester course; the last 3 chapters are a text for a second semester. The new Chapter 5, Groups II, contains the fundamental theorem of finite abelian groups, the Sylow theorems, the Jordan-Holder theorem and solvable groups, and presentations of groups (including a careful construction of free groups). The new Chapter 6, Commutative Rings II, introduces prime and maximal ideals, unique factorization in polynomial rings in several variables, noetherian rings and the Hilbert basis theorem, affine varieties (including a proof of Hilbert's Nullstellensatz over the complex numbers and irreducible components), and Grobner bases, including the generalized division algorithm and Buchberger's algorithm.

Modern Computer Algebra

Joachim von zur Gathen,Jürgen Gerhard
Modern Computer Algebra Book PDF

Author : Joachim von zur Gathen,Jürgen Gerhard
Publisher : Cambridge University Press
Page : 811 pages
File Size : 46,8 Mb
Release : 2013-04-25
Category : Computers
ISBN : 9781107039032

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Modern Computer Algebra by Joachim von zur Gathen,Jürgen Gerhard Pdf

Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.

Category Theory in Context

Emily Riehl
Category Theory in Context Book PDF

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 54,7 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820804

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Category Theory in Context by Emily Riehl Pdf

Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Abstract Algebra

Derek J.S. Robinson
Abstract Algebra Book PDF

Author : Derek J.S. Robinson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 347 pages
File Size : 50,6 Mb
Release : 2015-05-19
Category : Mathematics
ISBN : 9783110340877

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Abstract Algebra by Derek J.S. Robinson Pdf

This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for students in the third or fourth year of study at a North American university or in the second or third year at a university in Europe, and should ease the transition to (post)graduate studies.