Leslie Hogben Iowa State University, Ames, Iowa, USA

Handbook of Linear Algebra

Series: Discrete Mathematics and Its Applications Volume: 39
ISBN: 1584885106
Publication Date: 11/2/2006
Number of Pages: 1400

・Presents basic as well as advanced linear algebra concepts, such as matrix perturbation theory and inverse eigenvalue 　problems
・Features matrix notation throughout the text
・Cvers combinatorial and numerical linear algebra-two important branches of linear algebra
・Explores both mathematical and nonmathematical applications, such as quantum computing, control theory, signal processing, 　and computational biology
・Discusses software packages useful for linear algebra computations, including MATLABｮ, Maple・ and Mathematicaｮ
・Provides numerous references for additional information along with a glossary that covers all major linear algebra 　terminology

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research.

The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts.

Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical problems.

Contents

Charles J. Colbourn Arizona State University, Phoenix, Arizona, USA
Jeffrey H. Dinitz University of Vermont, Burlington, Vermont, USA

Handbook of Combinatorial Designs, Second Edition

Series: Discrete Mathematics and Its Applications Volume: 42

ISBN: 1584885068
Publication Date: 11/2/2006
Number of Pages: 1016

・Presents the latest as well as basic information pertaining to the construction, existence, and uses of combinatorial 　designs
・Supplies extensive tables and examples of Latin squares, orthogonal arrays, balanced incomplete block designs, t-designs, 　pairwise balanced designs, and Hadamard matrices
・Includes many applications to be used in statistics, cryptography, coding theory, graph theory, computer science, 　information theory, and mathematical finance
・Contains a state-of-the-art description of the computational methods used to construct and classify combinatorial designs

Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence results.

Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors' expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory.

New to the Second Edition

* An introductory part that provides a general overview and a historical perspective of the area
* New chapters on the history of design theory, various codes, bent functions, and numerous types of designs
* Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices
* Nearly 2,200 references in a single bibliographic section

Contents

Pierre Binetruy

Supersymmetry
Theory, Experiment, and Cosmology

(Hardback)
ISBN-10: 0-19-850954-5
ISBN-13: 978-0-19-850954-7
Publication date: 9 November 2006
536 pages, 75 line drawings and 5 halftones, 246x171 mm
Series: Oxford Graduate Texts

Reviews

'... introduces the formalism with nice intuitive and physical explanations.' - Mary K. Gaillard, University of California at Berkeley

Description

First textbook after the limits on supersymmetry have been set by the LEP high energy collider

3 different tracks for 3 different kinds of readers: theorists, experimentalists, cosmologists
Based on teaching, directed at graduate students and tested at various universities

Includes exercises and graded problem sets with detailed hints
Extensive appendices to endorse various aspects of the subject

This book describes the basic concepts of supersymmetric theories. It is aimed at theorists, experimentalists and cosmologists interested in supersymmetry, and its content is correspondingly divided into three distinct tracks of study. The topics covered include a discussion of the motivation for supersymmetry in fundamental physics, a description of the minimal supersymmetric model as well as models of grand unification and string models, a presentation of the main scenarios for supersymmetry breaking, including the concepts and results of dynamical breaking. On the astrophysics/cosmology side, the book includes discussions of supersymmetric dark matter candidates, inflation, dark energy, and the cosmological constant problem. Some very basic knowledge of quantum field theory is needed and extensive appendices (in particular an introduction to the Standard Model of fundamental interactions) allow the reader to refresh and complete their notions.

Readership: Primary: physics or astrophysics graduate students, theoretical physicists, experimental high energy physicists, cosmologists and astrophysicists. Secondary: mathematicians interested in the concepts developed in fundamental physics.

Contents
1. The problems of the Standard Model
2. The singular role of supersymmetry
3. Basic supermultiplets
4. The supersymmetry algebra and its representations
5. The minimal supersymmetric model
6. Supergravity
7. Phenomenology of supersymmetric models: supersymmetry at the quantum level
8. Dynamical breaking. Duality.
9. Supersymmetric grand unification
10. An overview of string theory and string models
11. Supersymmetry and the early universe
12. The challenges of supersymmetry
A. A review of the Standard Model and of various notions of quantum field theory
B. Spinors
C. Superfields
D. An introduction to cosmology
E. Renormalization group equations

Andrew H. Wallace

Differential Topology: First Steps

ISBN: 0486453170
Page Count: 144
Dimensions: 5 3/8 x 8 1/2

Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds. 1968 edition.

Francois Viete
T. Richard Witmer

The Analytic Art

ISBN: 0486453480
Page Count: 464
Dimensions: 5 3/8 x 8 1/2


This historic work consists of several treatises that developed the first consistent, coherent, and systematic conception of algebraic equations. Originally published in 1591, it pioneered the notion of using symbols of one kind (vowels) for unknowns and of another kind (consonants) for known quantities.

E. B. Dynkin
D. E. Brown
T. Kovary

Theory of Markov Processes

ISBN: 0486453057
Page Count: 224
Dimensions: 5 3/8 x 8 1/2


An investigation of the logical foundations of the theory behind Markov random processes, this text explores subprocesses, transition functions, and conditions for boundedness and continuity. Rather than focusing on probability measures individually, the work explores connections between functions. An elementary grasp of the theory of Markov processes is assumed. 1961 edition.