An Invitation To Representation Theory

Download An Invitation To Representation Theory full books in PDF, epub, and Kindle. Read online An Invitation To Representation Theory ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

An Invitation to Representation Theory

Author : R. Michael Howe
Publisher : Springer Nature
ISBN 13 : 3030980251
Total Pages : 236 pages
Book Rating : 4.0/5 (39 download)

DOWNLOAD NOW!

Book Synopsis An Invitation to Representation Theory by : R. Michael Howe

Download or read book An Invitation to Representation Theory written by R. Michael Howe and published by Springer Nature. This book was released on 2022-05-28 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Invitation to Representation Theory offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory. The subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently. With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study.

Representation Theory of Finite Groups

Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461407761
Total Pages : 166 pages
Book Rating : 4.4/5 (614 download)

DOWNLOAD NOW!

Book Synopsis Representation Theory of Finite Groups by : Benjamin Steinberg

Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space

Author : Konrad Schmüdgen
Publisher : Springer Nature
ISBN 13 : 3030463664
Total Pages : 388 pages
Book Rating : 4.0/5 (34 download)

DOWNLOAD NOW!

Book Synopsis An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space by : Konrad Schmüdgen

Download or read book An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space written by Konrad Schmüdgen and published by Springer Nature. This book was released on 2020-07-28 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

Representation Theory

Author : William Fulton
Publisher : Springer Science & Business Media
ISBN 13 : 9780387974958
Total Pages : 616 pages
Book Rating : 4.9/5 (749 download)

DOWNLOAD NOW!

Book Synopsis Representation Theory by : William Fulton

Download or read book Representation Theory written by William Fulton and published by Springer Science & Business Media. This book was released on 1991 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.

Invitation to Nonlinear Algebra

Author : Mateusz Michałek
Publisher : American Mathematical Society
ISBN 13 : 1470453673
Total Pages : 226 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Invitation to Nonlinear Algebra by : Mateusz Michałek

Download or read book Invitation to Nonlinear Algebra written by Mateusz Michałek and published by American Mathematical Society. This book was released on 2021-03-05 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.

Classical Lie Algebras at Infinity

Author : Ivan Penkov
Publisher : Springer Nature
ISBN 13 : 3030896609
Total Pages : 245 pages
Book Rating : 4.0/5 (38 download)

DOWNLOAD NOW!

Book Synopsis Classical Lie Algebras at Infinity by : Ivan Penkov

Download or read book Classical Lie Algebras at Infinity written by Ivan Penkov and published by Springer Nature. This book was released on 2022-01-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.

An Invitation to C*-Algebras

Author : W. Arveson
Publisher : Springer Science & Business Media
ISBN 13 : 1461263719
Total Pages : 117 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis An Invitation to C*-Algebras by : W. Arveson

Download or read book An Invitation to C*-Algebras written by W. Arveson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to C*-algebras and their representations on Hilbert spaces. We have tried to present only what we believe are the most basic ideas, as simply and concretely as we could. So whenever it is convenient (and it usually is), Hilbert spaces become separable and C*-algebras become GCR. This practice probably creates an impression that nothing of value is known about other C*-algebras. Of course that is not true. But insofar as representations are con cerned, we can point to the empirical fact that to this day no one has given a concrete parametric description of even the irreducible representations of any C*-algebra which is not GCR. Indeed, there is metamathematical evidence which strongly suggests that no one ever will (see the discussion at the end of Section 3. 4). Occasionally, when the idea behind the proof of a general theorem is exposed very clearly in a special case, we prove only the special case and relegate generalizations to the exercises. In effect, we have systematically eschewed the Bourbaki tradition. We have also tried to take into account the interests of a variety of readers. For example, the multiplicity theory for normal operators is contained in Sections 2. 1 and 2. 2. (it would be desirable but not necessary to include Section 1. 1 as well), whereas someone interested in Borel structures could read Chapter 3 separately. Chapter I could be used as a bare-bones introduction to C*-algebras. Sections 2.

An Invitation to Applied Category Theory

Author : Brendan Fong
Publisher : Cambridge University Press
ISBN 13 : 1108582249
Total Pages : 351 pages
Book Rating : 4.1/5 (85 download)

DOWNLOAD NOW!

Book Synopsis An Invitation to Applied Category Theory by : Brendan Fong

Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.

Invitation to the Mathematics of Fermat-Wiles

Author : Yves Hellegouarch
Publisher : Elsevier
ISBN 13 : 0080478778
Total Pages : 395 pages
Book Rating : 4.0/5 (84 download)

DOWNLOAD NOW!

Book Synopsis Invitation to the Mathematics of Fermat-Wiles by : Yves Hellegouarch

Download or read book Invitation to the Mathematics of Fermat-Wiles written by Yves Hellegouarch and published by Elsevier. This book was released on 2001-09-24 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles' extraordinary proof. Furthermore, it places these concepts in their historical context. This book can be used in introduction to mathematics theories courses and in special topics courses on Fermat's last theorem. It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically informed reader intrigued by the unraveling of this fascinating puzzle. Rigorously presents the concepts required to understand Wiles' proof, assuming only modest undergraduate level math Sets the math in its historical context Contains several themes that could be further developed by student research and numerous exercises and problems Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat's last theorem

Quadratic Number Theory

Author : J. L. Lehman
Publisher : American Mathematical Soc.
ISBN 13 : 1470447371
Total Pages : 410 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Quadratic Number Theory by : J. L. Lehman

Download or read book Quadratic Number Theory written by J. L. Lehman and published by American Mathematical Soc.. This book was released on 2019-02-13 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text. Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and this notation, serve the author's historical purpose as well; ideals can be seen as number-like objects, as Kummer and Dedekind conceived of them. The notation can be adapted to quadratic forms and provides insight into the connection between quadratic forms and ideals. The computation of class groups and continued fraction representations are featured—the author's notation makes these computations particularly illuminating. Quadratic Number Theory, with its exceptionally clear prose, hundreds of exercises, and historical motivation, would make an excellent textbook for a second undergraduate course in number theory. The clarity of the exposition would also make it a terrific choice for independent reading. It will be exceptionally useful as a fruitful launching pad for undergraduate research projects in algebraic number theory.

An Invitation To Noncommutative Geometry

Author : Matilde Marcolli
Publisher : World Scientific
ISBN 13 : 9814475629
Total Pages : 515 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!

Book Synopsis An Invitation To Noncommutative Geometry by : Matilde Marcolli

Download or read book An Invitation To Noncommutative Geometry written by Matilde Marcolli and published by World Scientific. This book was released on 2008-02-11 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.

An Invitation to Abstract Mathematics

Author : Béla Bajnok
Publisher : Springer Nature
ISBN 13 : 3030561747
Total Pages : 443 pages
Book Rating : 4.0/5 (35 download)

DOWNLOAD NOW!

Book Synopsis An Invitation to Abstract Mathematics by : Béla Bajnok

Download or read book An Invitation to Abstract Mathematics written by Béla Bajnok and published by Springer Nature. This book was released on 2020-10-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH

An Invitation to Modern Number Theory

Author : Steven J. Miller
Publisher : Princeton University Press
ISBN 13 : 0691215979
Total Pages : 526 pages
Book Rating : 4.6/5 (912 download)

DOWNLOAD NOW!

Book Synopsis An Invitation to Modern Number Theory by : Steven J. Miller

Download or read book An Invitation to Modern Number Theory written by Steven J. Miller and published by Princeton University Press. This book was released on 2020-07-21 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.

Noncommutative Algebra

Author : Benson Farb
Publisher : Springer Science & Business Media
ISBN 13 : 1461208890
Total Pages : 229 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!

Book Synopsis Noncommutative Algebra by : Benson Farb

Download or read book Noncommutative Algebra written by Benson Farb and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: About This Book This book is meant to be used by beginning graduate students. It covers basic material needed by any student of algebra, and is essential to those specializing in ring theory, homological algebra, representation theory and K-theory, among others. It will also be of interest to students of algebraic topology, functional analysis, differential geometry and number theory. Our approach is more homological than ring-theoretic, as this leads the to many important areas of mathematics. This ap student more quickly proach is also, we believe, cleaner and easier to understand. However, the more classical, ring-theoretic approach, as well as modern extensions, are also presented via several exercises and sections in Chapter Five. We have tried not to leave any gaps on the paths to proving the main theorem- at most we ask the reader to fill in details for some of the sideline results; indeed this can be a fruitful way of solidifying one's understanding.

Invitation to C*-algebras and Topological Dynamics

Author : Jun Tomiyama
Publisher : World Scientific
ISBN 13 : 9789971503383
Total Pages : 180 pages
Book Rating : 4.5/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Invitation to C*-algebras and Topological Dynamics by : Jun Tomiyama

Download or read book Invitation to C*-algebras and Topological Dynamics written by Jun Tomiyama and published by World Scientific. This book was released on 1987 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition on the interesting interplay between topological dynamics and the theory of C*-algebras. Researchers working in topological dynamics from various fields in mathematics are becoming more and more interested in this kind of algebraic approach of dynamics. This book is designed to present to the readers the subject in an elementary way, including also results of recent developments.

Basic Category Theory

Author : Tom Leinster
Publisher : Cambridge University Press
ISBN 13 : 1107044243
Total Pages : 193 pages
Book Rating : 4.1/5 (7 download)

DOWNLOAD NOW!

Book Synopsis Basic Category Theory by : Tom Leinster

Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.

Group Theory in a Nutshell for Physicists

Author : A. Zee
Publisher : Princeton University Press
ISBN 13 : 1400881188
Total Pages : 632 pages
Book Rating : 4.4/5 (8 download)

DOWNLOAD NOW!

Book Synopsis Group Theory in a Nutshell for Physicists by : A. Zee

Download or read book Group Theory in a Nutshell for Physicists written by A. Zee and published by Princeton University Press. This book was released on 2016-03-29 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)