Contemporary Mathematics Volume: 701
2018; 232 pp; Softcover
MSC: Primary 11; 14;
Print ISBN: 978-1-4704-1991-2
This volume contains the proceedings of the Barcelona-Boston-Tokyo Number Theory Seminar, which was held in memory of Fumiyuki Momose, a distinguished number theorist from Chuo University in Tokyo.
Momose, who was a student of Yasutaka Ihara, made important contributions to the theory of Galois representations attached to modular forms, rational points on elliptic and modular curves, modularity of some families of Abelian varieties, and applications of arithmetic geometry to cryptography.
Papers contained in this volume cover these general themes in addition to discussing Momose's contributions as well as recent work and new results.
Graduate students and research mathematicians interested in number theory and arithmetic geometry.
Mathematical Surveys and Monographs Volume: 40
344 pp; Hardcover
MSC: Primary 20;
Print ISBN: 978-0-8218-4069-6
The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1-40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4?40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13.
The book is suitable for graduate students and researchers interested in the theory of finite groups.
Readership
Graduate students and researchers interested in the theory of finite groups.
Mathematical Surveys and Monographs Volume: 228
2018; 336 pp; Hardcover
MSC: Primary 14; 17;
Print ISBN: 978-1-4704-4188-3
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes
The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.
Readership
Graduate students and researchers interested in algebraic geometry.
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Mathematical Surveys and Monographs Volume: 229
2018; 304 pp; Hardcover
MSC: Primary 17; 16;
Print ISBN: 978-1-4704-3659-9
The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras.
The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical
W-algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations.
An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical W-algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
Graduate students and researchers interested in algebraic aspects of representation theory and applications to mathematical physics.
Pure and Applied Undergraduate Texts Volume: 28
2018; 820 pp; Hardcover
MSC: Primary 62;
Print ISBN: 978-1-4704-2848-8
Foundations and Applications of Statistics simultaneously emphasizes both the foundational and the computational aspects of modern statistics. Engaging and accessible, this book is useful to undergraduate students with a wide range of backgrounds and career goals.
The exposition immediately begins with statistics, presenting concepts and results from probability along the way. Hypothesis testing is introduced very early, and the motivation for several probability distributions comes from p-value computations. Pruim develops the students' practical statistical reasoning through explicit examples and through numerical and graphical summaries of data that allow intuitive inferences before introducing the formal machinery. The topics have been selected to reflect the current practice in statistics, where computation is an indispensible tool. In this vein, the statistical computing environment R is used throughout the text and is integral to the exposition. Attention is paid to developing students' mathematical and computational skills as well as their statistical reasoning. Linear models, such as regression and ANOVA, are treated with explicit reference to the underlying linear algebra, which is motivated geometrically.
Foundations and Applications of Statistics discusses both the mathematical theory underlying statistics and practical applications that make it a powerful tool across disciplines. The book contains ample material for a two-semester course in undergraduate probability and statistics. A one-semester course based on the book will cover hypothesis testing and confidence intervals for the most common situations.
In the second edition, the R code has been updated throughout to take advantage of new R packages and to illustrate better coding style. New sections have been added covering bootstrap methods, multinomial and multivariate normal distributions, the delta method, numerical methods for Bayesian inference, and nonlinear least squares. Also, the use of matrix algebra has been expanded, but remains optional, providing instructors with more options regarding the amount of linear algebra required.
Undergraduate and graduate students interested in teaching and learning mathematical statistics.