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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.
This book shows how the ADE Coxeter graphs unify at least 20 different types of mathematical structures. These mathematical structures are of great utility in unified field theory, string theory, and other areas of physics.
Authors: Fomenko, Anatoly, Fuchs, DmitryUpdates a popular textbook from the golden era of the Moscow school of I. M. GelfandPresents material concisely but rigorouslyIlluminates the subject matter with a range of technical and artistic illustrations, along with a wealth of examples and computations meant to provide a treatment of the topic that is both deep and broadContains an entirely new chapter on K-theory and the Riemann-Roch theoremThis textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I.
With the advent of computers that can handle symbolic manipulations, abstract algebra can now be applied. In this book David Joyner, Richard Kreminski, and Joann Turisco introduce a wide range of abstract algebra with relevant and interesting applications, from error-correcting codes to cryptography to the group theory of Rubik’s cube. They cover basic topics such as the Euclidean algorithm, encryption, and permutations. Hamming codes and Reed-Solomon codes used on today’s CDs are also discussed.
Passage to Abstract Mathematics facilitates the transition from introductory mathematics courses to the more abstract work that occurs in advanced courses. This text covers logic, proofs, numbers, sets, induction, functions, and more–material which instructors of upper-level courses often presume their students have already mastered but are in fact missing from lower-level courses. Students will learn how to read and write mathematics–especially proofs–the way that mathematicians do. The text emphasizes the use of complete, correct definitions and mathematical syntax.
Authors: Barbeau, Edward J.Includes problems that are prime for standard assignments and more advanced problems for eager studentsProvides a model for institutions who may wish to establish math competitionsPrepares students for the Putnam mathematics competitionsAbout this TextbookThis text records the problems given for the first 15 annual undergraduate mathematics competitions, held in March each year since 2001 at the University of Toronto. Problems cover areas of single-variable differential and integral calculus, linear algebra, advanced algebra, analytic geometry, combinatorics, basic group theory, and number theory.
Authors: Jones, Gareth A., Wolfart, JürgenProvides basic material about maps and hypermaps on Riemann surfacesPresents many elementary and less elementary examples of Galois actions on dessins and their algebraic curves Emphasises the role of group theory in the classification of regular maps, regular dessins, and quasiplatonic surfaces Explains the links between the theory of dessins and other areas of arithmetic and geometryThis volume provides an introduction to dessins d’enfants and embeddings of bipartite graphs in compact Riemann surfaces.
"This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications." – "Electric Review"A comprehensive introduction, "Linear Algebra: Ideas and Applications, Fourth Edition "provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts.
For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book.
The study of Hopf algebras spans many fields in mathematics including topology, algebraic geometry, algebraic number theory, Galois module theory, cohomology of groups, and formal groups and has wide-ranging connections to fields from theoretical physics to computer science. This text is unique in making this engaging subject accessible to advanced graduate and beginning graduate students and focuses on applications of Hopf algebras to algebraic number theory and Galois module theory, providing a smooth transition from modern algebra to Hopf algebras.
After providing an introduction to the spectrum of a ring and the Zariski topology, the text treats presheaves, sheaves, and representable group functors. In this way the student transitions smoothly from basic algebraic geometry to Hopf algebras. The importance of Hopf orders is underscored with applications to algebraic number theory, Galois module theory and the theory of formal groups. By the end of the book, readers will be familiar with established results in the field and ready to pose research questions of their own.
An exercise set is included in each of twelve chapters with questions ranging in difficulty. Open problems and research questions are presented in the last chapter. Prerequisites include an understanding of the material on groups, rings, and fields normally covered in a basic course in modern algebra.
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject.
Discusses latest results in the subjects of computation, cryptography and network securityContains discussion from a converging range of interdisciplinary fields with a large breadth of technological applicationsDevelops courses of action or methodologies to reconcile the issues identifiedFrom the Back CoverAnalysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April 2013 at the Hellenic Military Academy, and brings together a broad variety of mathematical methods and theories with several applications.
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