Series: London Mathematical Society Student Texts
Hardback (ISBN-13: 9780521882187)
Paperback (ISBN-13: 9780521708760)
The final part of a three-volume set providing a modern account
of the representation theory of finite dimensional associative
algebras over an algebraically closed field. The subject is
presented from the perspective of linear representations of
quivers and homological algebra.
This volume provides an introduction to the representation theory
of representation-infinite tilted algebras from the point of view
of the time-wild dichotomy. Also included is a collection of
selected results relating to the material discussed in all three
volumes.
The book is primarily addressed to a graduate student starting
research in the representation theory of algebras, but will also
be of interest to mathematicians in other fields. Proofs are
presented in complete detail, and the text includes many
illustrative examples and a large number of exercises at the end
of each chapter, making the book suitable for courses, seminars,
and self-study.
* Self contained, only knowledge from the first two volumes is
required for volume three
* Finishes with a collection of result bringing together material
from all three volumes
* Class tested in courses given by the authors
Contents
Introduction; 15. Tubular extensions and tubular coextensions; 16.
Branch algebras; 17. Tilted algebras of Euclidean type; 18. Wild
hereditary algebras and tilted algebras of wild type; 19. Tame
and wild representation type of algebras; 20. Perspectives;
Bibliography; Index; List of symbols.
Hardback (ISBN-13: 9780521872652)
Paperback (ISBN-13: 9780521694247)
Learn programming in the language you want: R! Until now a gap
has separated generalised introductory computer programming and
the application of these programming skills specifically to
statistics and data analysis. This textbook bridges that gap with
a self-contained first course in statistical computing. The book
uses the open-source R statistical package to introduce students
to basic programming notions common to most computing languages.
The basics of R syntax and statistical graphics are explained,
and elementary programming is discussed, including how to develop
complex projects reliably. Programming applications in simulation
and optimization as well as numerical linear algebra are
introduced. Real code in R is shown and all examples are drawn
from statistical applications. Unlike other introductory books on
the ground-breaking R system, this book emphasizes programming.
Particularly useful for those studying statistics, biostatistics
and econometrics, it is accessible to any student familiar with
the basics of probability.
* First book to teach basic computer programming in R, the
language of choice for statistics and data analysis
* Authors recognized and trusted: John Braun is co-author of the
successful book Data Analysis and Graphics Using R; Duncan
Murdoch is a member of the R Core Development Team
* End-of-chapter review questions plus over 150 exercises; data
sets and solutions all available on web
Contents
1. Getting started; 2. Introduction to the R language; 3.
Programming statistical graphics; 4. Programming with R; 5.
Simulation; 6. Computational linear algebra; 7. Numerical
optimization; Appendix. Review of random variables and
distributions; Index.
Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-13: 9780521876766)
This book is an introduction to the Schwinger action principle in
quantum mechanics and quantum field theory, with applications to
a variety of different models including Bose-Einstein
condensation, the Casimir effect, and trapped Fermi gases. The
book begins with a brief review of the action principle in
classical mechanics and classical field theory. It then moves on
to quantum field theory, focussing on the effective action method.
This is introduced as simply as possible by using the zero-point
energy of the simple harmonic oscillator as the starting point.
The book concludes with a more complete definition of the
effective action, and demonstrates how the provisional definition
used earlier is the first term in the systematic loop expansion.
The renormalization of interacting scalar field theory is
presented to two-loop order. This book will interest graduate
students and researchers in theoretical physics who are familiar
with quantum mechanics.
* Self-contained, making it ideal for self-study
* Includes applications of the Schwinger action principle to a
variety of different models, not only those of particle physics
Contents
Preface; 1. Action principle in classical mechanics; 2. Action
principle in classical field theory; 3. Action principle in
quantum theory; 4. The effective action; 5. Quantum statistical
mechanics; 6. Effective action at finite temperature; 7. Further
applications of the Schwinger action principle; 8. General
definition of the effective action; Appendices; References; Index.
Series: Cambridge Tracts in Mathematics vol. 173)
Hardback (ISBN-13: 9780521882170)
How many groups of order n are there? This is a natural question
for anyone studying group theory, and this Tract provides an
exhaustive and up-to-date account of research into this question
spanning almost fifty years. The authors presuppose an
undergraduate knowledge of group theory, up to and including
Sylow's Theorems, a little knowledge of how a group may be
presented by generators and relations, a very little
representation theory from the perspective of module theory, and
a very little cohomology theory - but most of the basics are
expounded here and the book is more or less self-contained.
Although it is principally devoted to a connected exposition of
an agreeable theory, the book does also contain some material
that has not hitherto been published. It is designed to be used
as a graduate text but also as a handbook for established
research workers in group theory.
* The first book devoted to this exciting and vigorous area of
modern group-theoretic research
* Written by leading specialists in the field; contains hitherto
unpublished material
* Includes many open problems - ideal for graduate students in
group theory
Contents
1. Introduction; Part I. Elementary Results: 2. Some basic
observations; Part II. Groups of Prime Power Order: 3.
Preliminaries; 4. Enumerating p-groups: a lower bound; 5.
Enumerating p-groups: upper bounds; Part III. Pyber’s Theorem:
6. Some more preliminaries; 7. Group extensions and cohomology; 8.
Some representation theory; 9. Primitive soluble linear groups;
10. The orders of groups; 11. Conjugacy classes of maximal
soluble subgroups of symmetric groups; 12. Enumeration of finite
groups with abelian Sylow subgroups; 13. Maximal soluble linear
groups; 14. Conjugacy classes of maximal soluble subgroups of the
general linear group; 15. Pyber’s theorem: the soluble case; 16.
Pyber’s theorem: the general case; Part IV. Other Topics: 17.
Enumeration within varieties of abelian groups; 18. Enumeration
within small varieties of A-groups; 19. Enumeration within small
varieties of p-groups; 20. Miscellanea; 21. Survey of other
results; 22. Some open problems; Appendix A. Maximising two
equations.
Series: Discrete Mathematics and Its Applications
ISBN: 9781584888383
ISBN 10: 1584888385
Publication Date: 6/1/2007
Number of Pages: 328
Covers classical designs such as Latin squares, balanced
incomplete block designs, and finite projective and affine planes
Introduces modern extensions of design theory, including one-factorizations,
Room squares, tournament designs, and nested designs
Features applications in several areas, including cryptography,
computer science, experimental design, and communications theory
Includes instructive examples and theorems with every topic
Provides exercises in each section, select answers in the back of
the book, and more complete solutions on the author's website
Contains references to classical literature to put results in a
historical perspective
Combinatorial theory is one of the fastest growing areas of
modern mathematics. Focusing on a major part of this subject,
Introduction to Combinatorial Designs, Second Edition provides a
solid foundation in the classical areas of design theory as well
as in more contemporary designs based on applications in a
variety of fields.
After an overview of basic concepts, the text introduces balanced
designs and finite geometries. The author then delves into
balanced incomplete block designs, covering difference methods,
residual and derived designs, and resolvability. Following a
chapter on the existence theorem of Bruck, Ryser, and Chowla, the
book discusses Latin squares, one-factorizations, triple systems,
Hadamard matrices, and Room squares. It concludes with a number
of statistical applications of designs.
Reflecting recent results in design theory and outlining several
applications, this new edition of a standard text presents a
comprehensive look at the combinatorial theory of experimental
design. Suitable for a one-semester course or for self-study, it
will prepare readers for further exploration in the field.
Contents