The Mathematics Of Frobenius In Context

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The Mathematics of Frobenius in Context

Author : Thomas Hawkins
Publisher : Springer Science & Business Media
ISBN 13 : 1461463335
Total Pages : 698 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis The Mathematics of Frobenius in Context by : Thomas Hawkins

Download or read book The Mathematics of Frobenius in Context written by Thomas Hawkins and published by Springer Science & Business Media. This book was released on 2013-07-23 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discusses the Berlin school of mathematics and the guiding force of Weierstrass in that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laid the groundwork for Frobenius's work in linear algebra. The book concludes with a discussion of Frobenius's contribution to the theory of stochastic matrices.

Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer

Author : Charles W. Curtis
Publisher : American Mathematical Soc.
ISBN 13 : 0821826778
Total Pages : 308 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer by : Charles W. Curtis

Download or read book Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer written by Charles W. Curtis and published by American Mathematical Soc.. This book was released on 1999 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The AMS History of Mathematics series is one of the most popular items for bookstore sales. These books feature colorful, attractive covers that are perfect for face out displays. The topics will appeal to a broad audience in the mathematical and scientific communities.

Introduction to Applied Linear Algebra

Author : Stephen Boyd
Publisher : Cambridge University Press
ISBN 13 : 1316518965
Total Pages : 477 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Nonlinear Perron-Frobenius Theory

Author : Bas Lemmens
Publisher : Cambridge University Press
ISBN 13 : 0521898811
Total Pages : 337 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Nonlinear Perron-Frobenius Theory by : Bas Lemmens

Download or read book Nonlinear Perron-Frobenius Theory written by Bas Lemmens and published by Cambridge University Press. This book was released on 2012-05-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.

Frobenius Algebras and 2-D Topological Quantum Field Theories

Author : Joachim Kock
Publisher : Cambridge University Press
ISBN 13 : 9780521540315
Total Pages : 260 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Frobenius Algebras and 2-D Topological Quantum Field Theories by : Joachim Kock

Download or read book Frobenius Algebras and 2-D Topological Quantum Field Theories written by Joachim Kock and published by Cambridge University Press. This book was released on 2004 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.

Emergence of the Theory of Lie Groups

Author : Thomas Hawkins
Publisher : Springer Science & Business Media
ISBN 13 : 1461212022
Total Pages : 578 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Emergence of the Theory of Lie Groups by : Thomas Hawkins

Download or read book Emergence of the Theory of Lie Groups written by Thomas Hawkins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.

Category Theory in Context

Author : Emily Riehl
Publisher : Courier Dover Publications
ISBN 13 : 0486820807
Total Pages : 273 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Category Theory in Context by : Emily Riehl

Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Curvature in Mathematics and Physics

Author : Shlomo Sternberg
Publisher : Courier Corporation
ISBN 13 : 0486292711
Total Pages : 418 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Curvature in Mathematics and Physics by : Shlomo Sternberg

Download or read book Curvature in Mathematics and Physics written by Shlomo Sternberg and published by Courier Corporation. This book was released on 2013-04-17 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Frobenius Categories versus Brauer Blocks

Author : Lluís Puig
Publisher : Birkhäuser
ISBN 13 : 9783034600156
Total Pages : 498 pages
Book Rating : 4.6/5 (1 download)

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Book Synopsis Frobenius Categories versus Brauer Blocks by : Lluís Puig

Download or read book Frobenius Categories versus Brauer Blocks written by Lluís Puig and published by Birkhäuser. This book was released on 2009-08-29 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contributes to important questions in modern representation theory of finite groups. It introduces and develops the abstract setting of the Frobenius categories and gives the application of the abstract setting to the blocks.

Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces

Author : I︠U︡. I. Manin
Publisher : American Mathematical Soc.
ISBN 13 : 0821819178
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces by : I︠U︡. I. Manin

Download or read book Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces written by I︠U︡. I. Manin and published by American Mathematical Soc.. This book was released on 1999 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph dedicated to the systematic exposition of the whole variety of topics related to quantum cohomology. The subject first originated in theoretical physics (quantum string theory) and has continued to develop extensively over the last decade. The author's approach to quantum cohomology is based on the notion of the Frobenius manifold. The first part of the book is devoted to this notion and its extensive interconnections with algebraic formalism of operads, differential equations, perturbations, and geometry. In the second part of the book, the author describes the construction of quantum cohomology and reviews the algebraic geometry mechanisms involved in this construction (intersection and deformation theory of Deligne-Artin and Mumford stacks). Yuri Manin is currently the director of the Max-Planck-Institut für Mathematik in Bonn, Germany. He has authored and coauthored 10 monographs and almost 200 research articles in algebraic geometry, number theory, mathematical physics, history of culture, and psycholinguistics. Manin's books, such as Cubic Forms: Algebra, Geometry, and Arithmetic (1974), A Course in Mathematical Logic (1977), Gauge Field Theory and Complex Geometry (1988), Elementary Particles: Mathematics, Physics and Philosophy (1989, with I. Yu. Kobzarev), Topics in Non-commutative Geometry (1991), and Methods of Homological Algebra (1996, with S. I. Gelfand), secured for him solid recognition as an excellent expositor. Undoubtedly the present book will serve mathematicians for many years to come.

A Richer Picture of Mathematics

Author : David E. Rowe
Publisher : Springer
ISBN 13 : 3319678191
Total Pages : 448 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis A Richer Picture of Mathematics by : David E. Rowe

Download or read book A Richer Picture of Mathematics written by David E. Rowe and published by Springer. This book was released on 2018-02-13 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the “Years Ago” column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe’s various and many-faceted contributions to the history of mathematics. Centered on the Göttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow recount episodes relating to the section’s overall theme. All of the essays in this collection, with the exception of two, appeared over the course of more than 30 years in The Mathematical Intelligencer. Based largely on archival and primary sources, these vignettes offer unusual insights into behind-the-scenes events. Taken together, they aim to show how Göttingen managed to attract an extraordinary array of talented individuals, several of whom contributed to the development of a new mathematical culture during the first decades of the twentieth century.

Group Matrices, Group Determinants and Representation Theory

Author : Kenneth W. Johnson
Publisher : Springer Nature
ISBN 13 : 3030283003
Total Pages : 384 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Group Matrices, Group Determinants and Representation Theory by : Kenneth W. Johnson

Download or read book Group Matrices, Group Determinants and Representation Theory written by Kenneth W. Johnson and published by Springer Nature. This book was released on 2019-11-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science. The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.

Quasi-Frobenius Rings

Author : W. K. Nicholson
Publisher : Cambridge University Press
ISBN 13 : 9780521815932
Total Pages : 332 pages
Book Rating : 4.8/5 (159 download)

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Book Synopsis Quasi-Frobenius Rings by : W. K. Nicholson

Download or read book Quasi-Frobenius Rings written by W. K. Nicholson and published by Cambridge University Press. This book was released on 2003-09-08 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an elementary account of the basic facts about quasi-Frobenius rings.

Introduction to Noncommutative Algebra

Author : Matej Brešar
Publisher : Springer
ISBN 13 : 3319086936
Total Pages : 227 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Introduction to Noncommutative Algebra by : Matej Brešar

Download or read book Introduction to Noncommutative Algebra written by Matej Brešar and published by Springer. This book was released on 2014-10-14 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.

Operator Theory

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 1470411032
Total Pages : 769 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Operator Theory by : Barry Simon

Download or read book Operator Theory written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 4 focuses on operator theory, especially on a Hilbert space. Central topics are the spectral theorem, the theory of trace class and Fredholm determinants, and the study of unbounded self-adjoint operators. There is also an introduction to the theory of orthogonal polynomials and a long chapter on Banach algebras, including the commutative and non-commutative Gel'fand-Naimark theorems and Fourier analysis on general locally compact abelian groups.

Introduction to Representation Theory

Author : Pavel I. Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 0821853511
Total Pages : 240 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof

Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Actions of Groups

Author : John McCleary
Publisher : Cambridge University Press
ISBN 13 : 1009183877
Total Pages : 248 pages
Book Rating : 4.0/5 (91 download)

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Book Synopsis Actions of Groups by : John McCleary

Download or read book Actions of Groups written by John McCleary and published by Cambridge University Press. This book was released on 2022-12-31 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the unifying notion of group actions, this second course in modern algebra introduces the deeper algebraic tools needed to get into topics only hinted at in a first course, like the successful classification of finite simple groups and how groups play a role in the solutions of polynomial equations. Because groups may act as permutations of a set, as linear transformations on a vector space, or as automorphisms of a field, the deeper structure of a group may emerge from these viewpoints, two different groups can be distinguished, or a polynomial equation can be shown to be solvable by radicals. By developing the properties of these group actions, readers encounter essential algebra topics like the Sylow theorems and their applications, Galois theory, and representation theory. Warmup chapters that review and build on the first course and active learning modules help students transition to a deeper understanding of ideas.