• Mathematics

Twelve Sporadic Groups


Author: Robert L. Jr. Griess
Publisher: Springer Science & Business Media
ISBN: 3662035162
Category: Mathematics
Page: 169
View: 3671
The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. This book is a leisurely and rigorous study of two of their three generations. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.

    • Mathematics

Algebra

A Teaching and Source Book
Author: Ernest Shult,David Surowski
Publisher: Springer
ISBN: 3319197347
Category: Mathematics
Page: 539
View: 7193
This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.

    • Finite simple groups

Applying the Classification of Finite Simple Groups: A User’s Guide


Author: Stephen D. Smith
Publisher: American Mathematical Soc.
ISBN: 1470442914
Category: Finite simple groups
Page: 231
View: 7386
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.

    • Mathematics

Recent Developments in Lie Algebras, Groups, and Representation Theory

2009-2011 Southeastern Lie Theory Workshop Series : Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University : Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia : Finite and Algebraic Groups, June 1-4, 2011, University of Virginia
Author: Kailash C. Misra,Daniel Ken Nakano,Brian Parshall
Publisher: American Mathematical Soc.
ISBN: 0821869175
Category: Mathematics
Page: 310
View: 327
This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.

    • Mathematics

Diagram Geometry

Related to Classical Groups and Buildings
Author: Francis Buekenhout,Arjeh M. Cohen
Publisher: Springer Science & Business Media
ISBN: 3642344534
Category: Mathematics
Page: 594
View: 5349
This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective. Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.

    • Mathematics

The Finite Simple Groups


Author: Robert Wilson
Publisher: Springer Science & Business Media
ISBN: 1848009879
Category: Mathematics
Page: 298
View: 705
Here, a thorough grounding in the theory of alternating and classical groups is followed by discussion of exceptional groups (classed as automorphism groups of multilinear forms), sporadic and Chevalley groups, as well as the theory of Lie algebras.

    • Mathematics

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 5446

    • Mathematics

Newsletter


Author: New Zealand Mathematical Society
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9038

    • Science

Basic Concepts of String Theory


Author: Ralph Blumenhagen,Dieter Lüst,Stefan Theisen
Publisher: Springer Science & Business Media
ISBN: 3642294979
Category: Science
Page: 784
View: 3593
The purpose of this book is to thoroughly prepare the reader for research in string theory at an intermediate level. As such it is not a compendium of results but intended as textbook in the sense that most of the material is organized in a pedagogical and self-contained fashion. Beyond the basics, a number of more advanced topics are introduced, such as conformal field theory, superstrings and string dualities - the text does not cover applications to black hole physics and cosmology, nor strings theory at finite temperatures. End-of-chapter references have been added to guide the reader wishing to pursue further studies or to start research in well-defined topics covered by this book.

    • Mathematics

Algebraic Topology

An Intuitive Approach
Author: Hajime Satō
Publisher: American Mathematical Soc.
ISBN: 9780821810460
Category: Mathematics
Page: 118
View: 5322
The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Mobius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.

    • Science

Moonshine beyond the Monster

The Bridge Connecting Algebra, Modular Forms and Physics
Author: Terry Gannon
Publisher: Cambridge University Press
ISBN: 9781139457804
Category: Science
Page: N.A
View: 4337
This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

    • Science

Scientific American


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Science
Page: N.A
View: 1868

    • Mathematics

Analysis and Algebra on Differentiable Manifolds

A Workbook for Students and Teachers
Author: Pedro M. Gadea,Jaime Muñoz Masqué,Ihor V. Mykytyuk
Publisher: Springer Science & Business Media
ISBN: 9400759525
Category: Mathematics
Page: 618
View: 5950
This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. In this 2nd edition: • 76 new problems • a section devoted to a generalization of Gauss’ Lemma • a short novel section dealing with some properties of the energy of Hopf vector fields • an expanded collection of formulae and tables • an extended bibliography Audience This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.

    • Mathematics

Counting Surfaces

CRM Aisenstadt Chair lectures
Author: Bertrand Eynard
Publisher: Springer Science & Business Media
ISBN: 3764387971
Category: Mathematics
Page: 414
View: 1136
The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. More generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and gives the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided.

    • Mathematics

The Theory of Finite Groups

An Introduction
Author: Hans Kurzweil,Bernd Stellmacher
Publisher: Springer Science & Business Media
ISBN: 0387217681
Category: Mathematics
Page: 388
View: 6736
From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews

    • Mathematics

On Thom Spectra, Orientability, and Cobordism


Author: Yu. B. Rudyak
Publisher: Springer Science & Business Media
ISBN: 3540777512
Category: Mathematics
Page: 590
View: 7269
Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.



    • Mathematics

Algebra VII

Combinatorial Group Theory Applications to Geometry
Author: D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang
Publisher: Springer Science & Business Media
ISBN: 3642580130
Category: Mathematics
Page: 242
View: 6245
From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996

    • Mathematics

Research Problems in Discrete Geometry


Author: Peter Brass,William O. J. Moser,János Pach
Publisher: Springer Science & Business Media
ISBN: 0387238158
Category: Mathematics
Page: 499
View: 1694
This book is a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems.