The Mathematics Of Frobenius In Context
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The Mathematics Of Frobenius In Context
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Author : Thomas Hawkins
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-23
The Mathematics Of Frobenius In Context written by Thomas Hawkins 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 2013-07-23 with Mathematics categories.
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.
Emergence Of The Theory Of Lie Groups
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Author : Thomas Hawkins
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Emergence Of The Theory Of Lie Groups written by Thomas Hawkins 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.
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.
Group Matrices Group Determinants And Representation Theory
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Author : Kenneth W. Johnson
language : en
Publisher: Springer Nature
Release Date : 2019-11-08
Group Matrices Group Determinants And Representation Theory written by Kenneth W. Johnson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-08 with Mathematics categories.
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.
Frobenius Categories Versus Brauer Blocks
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Author : Lluís Puig
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-22
Frobenius Categories Versus Brauer Blocks written by Lluís Puig 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 2009-06-22 with Mathematics categories.
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.
The Diophantine Frobenius Problem
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Author : Jorge L. Ramírez Alfonsín
language : en
Publisher: OUP Oxford
Release Date : 2005-12-01
The Diophantine Frobenius Problem written by Jorge L. Ramírez Alfonsín and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-01 with Mathematics categories.
During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,...,an, find the largest natural number (called the Frobenius number and denoted by g(a1,...,an) that is not representable as a nonnegative integer combination of a1,...,an, . At first glance FP may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.
Writing Small Omegas
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Author : Alberto Cogliati
language : en
Publisher: Academic Press
Release Date : 2017-10-31
Writing Small Omegas written by Alberto Cogliati and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-31 with Mathematics categories.
Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 provides a general account of Lie’s theory of finite continuous groups, critically examining Cartan’s doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters. It evaluates pioneering attempts to generalize Lie's classical ideas to the infinite-dimensional case in the works of Lie, Engel, Medolaghi and Vessiot. Within this context, Cartan’s groundbreaking contributions in continuous group theory, particularly in his characteristic and unique recourse to exterior differential calculus, are introduced and discussed at length. The work concludes by discussing Cartan’s contributions to the structural theory of infinite continuous groups, his method of moving frames, and the genesis of his geometrical theory of Lie groups. Discusses the origins of the theory of moving frames and the geometrical theory of Lie groups Reviews Cartan’s revolutionary contributions to Lie group theory and differential geometry Evaluates many unpublished sources that shed light on important aspects of the historical development of Lie algebras
A Richer Picture Of Mathematics
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Author : David E. Rowe
language : en
Publisher: Springer
Release Date : 2018-02-13
A Richer Picture Of Mathematics written by David E. Rowe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-13 with Mathematics categories.
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.
Numerical Analysis
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Author : Brian Sutton
language : en
Publisher: SIAM
Release Date : 2019-04-18
Numerical Analysis written by Brian Sutton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-18 with Mathematics categories.
This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.
Operator Theory
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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-04
Operator Theory written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-04 with Mathematics categories.
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.
Actions Of Groups
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Author : John McCleary
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-31
Actions Of Groups written by John McCleary 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 2022-12-31 with Mathematics categories.
An undergraduate text with an active learning approach introducing representation theory and Galois theory topics using group actions.