Series: Universitext
2011, XIV, 158 p. 4 illus.
Softcover, ISBN 978-1-4614-0775-1
Due: August 5, 2011
Concise focus enables the author to avoid prerequisites in analysis and topology
Provides a simple context for students to understand group representation theory
Author provides a gentle approach for students as well as the necessary motivation and exercises
Representation Theory of Finite Groups presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linear algebra, group theory, and very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted. Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader.
The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside's pq-theorem and the dimension theorem, permutation representations, induced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probability and statistics, a chapter on random walks on finite groups serves as an illustration to link finite stochastics and representation theory. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject and the author provides motivation and a gentle style throughout the text. A number of exercises add greater dimension to the understanding of the subject and some aspects of a combinatorial nature are clearly shown in diagrams.
This text will engage a broad readership due to the significance of representation theory in diverse branches of mathematics, engineering, and physics, to name a few. Its primary intended use is as a one semester textbook for a third or fourth year undergraduate course or an introductory graduate course on group representation theory. The content can also be of use as a reference to researchers in all areas of mathematics, statistics, and several mathematical sciences.
-Preface.-Introduction.-Review of Linear Algebra.-Group Representations.-Character Theory.-Fourier Analysis on Finite Groups.-Burnside's Theorem.-Permutation Representations.-Induced Representations.-Another Theorem of Burnside.-The Symmetric Group.-Bibliography.-Index
Series: Springer Texts in Statistics
2011, XVI, 753 p. 183 illus., 148 in color.
Hardcover, ISBN 978-1-4614-0393-7
Due: August 28, 2011
The text addresses the needs of the vibrant and rapidly growing engineering fields, bioengineering and biomedical engineering
Implements software with which engineers are familiar
Incorporates substantial coverage of Bayesian approaches to statistical inference
Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing engineering fields, bioengineering and biomedical engineering, while implementing software that engineers are familiar with.
The author integrates introductory statistics for engineers and introductory biostatistics as a single textbook heavily oriented to computation and hands on approaches. For example, topics ranging from the aspects of disease and device testing, Sensitivity, Specificity and ROC curves, Epidemiological Risk Theory, Survival Analysis, or Logistic and Poisson Regressions are covered.
In addition to the synergy of engineering and biostatistical approaches, the novelty of this book is in the substantial coverage of Bayesian approaches to statistical inference. Many examples in this text are solved using both the traditional and Bayesian methods, and the results are compared and commented.
Introduction.- The Sample and Its Properties.- Probability, Conditional Probability, and Bayes' Rule.- Sensitivity, Specificity, and Relatives.- Random Variables.- Normal Distribution.- Point and Interval Estimators.- Bayesian Approach to Inference.- Testing Statistical Hypotheses.- Two Samples.- ANOVA and Elements of Experimental Design.- Distribution-Free Tests.- Goodness-of-Fit Tests.- Models for Tables.- Correlation.- Regression.- Regression for Binary and Count Data.- Inference for Censored Data and Survival Analysis.- Bayesian Inference Using Gibbs Sampling - BUGS Project.
Series: Algebra and Applications, Vol. 16
2011, X, 262 p. 1 illus.
Hardcover, ISBN 978-0-85729-849-2
Due: September 30, 2011
The theory of table algebras was introduced in 1991 by Z. Arad and H.Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with various applications, including the representation theory of finite groups, algebraic combinatorics and fusion rules algebras.
This book presents the latest developments in this area. Its main goal is to give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification approach, while remaining parts separately treat special cases that appear during classification. A particularly unique contribution to the field, can be found in part four, whereby a number of the algebras are linked to the polynomial irreducible representations of the group SL3(C).
This book will be of interest to research mathematicians and PhD students working in table algebras, group representation theory, algebraic combinatorics and integral fusion rule algebras.
Introduction.- Splitting the Main Problem into Four Sub-cases.- A Proof of a Non-existence Sub-case (2).- Preliminary Classification of Sub-case (2).- Finishing the Proofs of the Main Results
Series: Developments in Mathematics, Vol. 23
2011, X, 202 p.
Hardcover, ISBN 978-1-4614-0027-1
Due: August 29, 2011
This book contains a unique collection of both research and survey papers written by an international group of some of the world's experts on partitions, q-series, and modular forms, as outgrowths of a conference held at the University of Florida, Gainesville in March 2008. The success of this conference has led to annual year-long programs in Algebra, Number Theory, and Combinatorics (ANTC) at the university.
A common theme in the book is the study of q-series, an area which in recent years has witnessed dramatic advances having significant impact on a variety of fields within and outside of mathematics such as physics. Most major aspects of the modern theory of q-series and how they relate to number theory, combinatorics, and special functions are represented in this volume. Topics include the theory of partitions via computer algebra, elementary asymptotic methods; expositions on Ramanujan's mock theta-functions emphasizing the classical aspects as well as the recent exciting connections with the theory of harmonic Maass forms; congruences for modular forms; a study of theta-functions from elementary, function-theoretic and Riemann surface viewpoints; and a systematic analysis of multiple basic hypergeometric functions associated with root systems of Lie algebras.
The broad range of topics covered in this volume will be of interest to both researchers and graduate students who want to learn of recent developments in the theory of partitions, q-series and modular forms and their far reaching impact on diverse areas of mathematics.
-Preface (K. Alladi and F. Garvan).- 1. MacMahon's dream (G. E. Andrews).- 2. Ramanujan's elementary method in partition congruences (B. Berndt, C. Gugg, and S. Kim).- 3. Coefficients of harmonic Maass forms (K. Bringmann and K. Ono).- 4. On the growth of restricted partition functions (E. R. Canfield and H. Wilf).- 5. On applications of roots of unity to product identities (Z. Cao).- 6. Lecture hall sequences, q-series, and asymmetric partition identities (S. Corteel, C. Savage and A. Sills).- 7. Generalizations of Hutchinson's curve and the Thomae formula (H. Farkas).- 8. On the parity of the Rogers-Ramanujan coefficients (B. Gordon).- 9. A survey of the classical mock theta functions (B. Gordon and R. McIntosh).- 10. An application of the Cauchy-Sylvester theorem on compound determinants to a BC_n Jackson integral (M. Ito and S. Okada).- 11. Multiple generalizations of q-series identities found in Ramanujan's Lost Notebook (Y. Kajihara).- 12. Non-terminating q-Whipple transformations for basic hypergeometric series in U(n) (S. C. Milne and J. W. Newcomb).
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
Series of Modern Surveys in Mathematics, Vol. 55
2011, 630 p.
Hardcover, ISBN 978-3-642-22252-8
Due: September 30, 2011
Content Level ≫ Research
Keywords ≫ Disordered Systems - Hopfield Model - Mean Field Models - Random Structures - Sherrington Kirkpatrick Model
Related subjects ≫ Materials - Probability Theory and Stochastic Processes - Theoretical, Mathematical & Computational Physics
Part I. Advanced Replica-Symmetry. - The Gardener Formula for the sphere. - The Gardener Formula for the Discrete Cube. - The Hopfield Model. - The SK Model Without External Field. - Part II. Low Temperature. - The Ghirlanda-Guerra Identities. - The High-Temperature Region of the SK Model. - The Parisi Formula. - The Parisi Solution. - The p-spin Interaction Model. - Appendix: Elements of Probability Theory. - References. - Index.