Contemporary Mathematics, Volume: 504
2009; 254 pp; softcover
ISBN-13: 978-0-8218-4839-5
Expected publication date is December 27, 2009.
This volume contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008.
This volume includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus, on localization techniques and on string topology--offering a broad perspective of modern algebraic topology.
Graduate students and research mathematicians interested in various aspects of modern algebraic topology.
A. Baker -- L-complete Hopf algebroids and their comodules
M. A. Batanin and C. Berger -- The lattice path operad and Hochschild cochains
A. J. Blumberg, R. L. Cohen, and C. Teleman -- Open-closed field theories, string topology, and Hochschild homology
W. Chacholski, E. D. Farjoun, R. Gobel, and Y. Segev -- Cellular covers of divisible abelian groups
A. Dessai -- Some geometric properties of the Witten genus
W. G. Dwyer and E. D. Farjoun -- Localization and cellularization of principal fibrations
B. Fresse -- Operadic cobar constructions, cylinder objects and homotopy morphisms of algebras over operads
B. Jahren -- Involutions on the rational K-theory of group rings of finite groups
J. A. Neisendorfer -- A quick trip through localization
B. Richter -- Divided power structures and chain complexes
2010; approx. 331 pp; hardcover
ISBN-13: 978-0-8218-4761-9
Expected publication date is January 29, 2010.
This is an unusual and unusually fascinating book.
Readers who never thought about mathematics after their school years will be amazed to discover how many habits of mind, ideas, and even material objects that are inherently mathematical serve as building blocks of our civilization and everyday life.
A professional mathematician, reluctantly breaking the daily routine, or pondering on some resisting problem, will open this book and enjoy a sudden return to his or her young days when mathematics was fresh, exciting, and holding all promises.
And do not take the word "microscope" in the title too literally: in fact, the author looks around, in time and space, focusing in turn on a tremendous variety of motives, from mathematical "memes" (genes of culture) to an unusual life of a Hollywood star.
--Yuri I. Manin, Max-Planck Institute of Mathematics, Bonn, and Northwestern University
It is an unusual book that casts new and paradoxical light on the nature of mathematics.
This book will be interesting--perhaps for different reasons--to school teachers of mathematics, to math majors at universities, to graduate students in mathematics and computer science, to research mathematicians and computer scientists, to philosophers and historians of mathematics, and to psychologists and neurophysiologists.
The author's goal is to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts more intuitive than others? To what extent does the "small scale" structure of mathematical concepts and algorithms reflect the workings of the human brain? What are the "elementary particles" of mathematics that build up the mathematical universe?
One of the principal points of the book is the essential vertical unity of mathematics, the natural integration of its simplest objects and concepts into the complex hierarchy of mathematics as a whole. The same ideas and patterns of thinking can be found in elementary school arithmetic and in cutting-edge mathematical theories. There are no boundaries between "recreational", "elementary", "undergraduate", and "research" mathematics; the book freely moves throughout the whole range. Nevertheless, the author takes great care in keeping the book as non-technical as possible.
The book is saturated with amusing examples from a wide range of disciplines--from turbulence to error-correcting codes to logic--as well as with just puzzles and brainteasers. Despite the very serious subject matter, the author's approach is lighthearted and entertaining.
Undergraduate students and mathematicians interested in cognitive aspects of mathematics.
Simple things: How structures of human cognition reveal themselves in mathematics
A taste of things to come
What you see is what you get
The wing of the hummingbird
Simple things
Infinity and beyond
Encapsulation of actual infinity
Mathematical reasoning
What is it that makes a mathematician?
"Kolmogorov's logic" and heuristic reasoning
Recovery vs. discovery
The line of sight
History and philosophy
The ultimate replicating machines
The vivisection of the Cheshire Cat
References
Index
2010; 241 pp; hardcover
ISBN-13: 978-0-8218-4925-5
Expected publication date is January 13, 2010. S
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering.
The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Graduate students and research mathematicians interested in topology, algorithms, and applications to science and engineering.
Computational geometric topology
Graphs
Surfaces
Complexes
Computational algebraic topology
Homology
Duality
Morse functions
Computational persistent topology
Persistence
Stability
Applications
References
Index
Mathematical Surveys and Monographs, Volume: 157
2010; approx. 357 pp; hardcover
ISBN-13: 978-0-8218-4820-3
Expected publication date is January 15, 2010.
The material covered in this book involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry. The development carefully provides the basic definitions of mutual intersection and self-intersection local times for Brownian motions and the accompanying large deviation results. The book then proceeds to the analogues of these concepts and results for random walks on lattices of R^d. This includes suitable integrability and large deviation results for these models and some applications. Moreover, the notes and comments at the end of the chapters provide interesting remarks and references to various related results, as well as a good number of exercises. The author provides a beautiful development of these subtle topics at a level accessible to advanced graduate students.
Graduate students and research mathematicians interested in probability and statistical physics.
Basics on large deviations
Brownian intersection local times
Mutual intersection: large deviations
Self-intersection: large deviations
Intersections on lattices: weak convergence
Inequalities and integrabilities
Independent random walks: large deviations
Single random walk: large deviations
Green's function
Fourier transformation
Constant kappa(d,p) and related variations
Regularity of stochastic processes
Self-adjoint operators
Bibliography
List of general notations
Index
Approx. 832 pages
Trim size 7 1/2 X 9 1/4 in
Copyright 2010
Expected Release Date: Mar 2010
Description
This updated text provides a superior introduction to applied probability and statistics for engineering or science majors. Ross emphasizes the manner in which probability yields insight into statistical problems; ultimately resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and scientists. Real data sets are incorporated in a wide variety of exercises and examples throughout the book, and this emphasis on data motivates the probability coverage.
As with the previous editions, Ross' text has tremendously clear exposition, plus real-data examples and exercises throughout the text. Numerous exercises, examples, and applications apply probability theory to everyday statistical problems and situations.
This text is written for the introductory non-calculus based statistics course offered in mathematics and/or statistics departments for undergraduate students of any major who take a semester course in basic Statistics or a year course in Probability and Statistics.
Preface
Introduction to Statistics
Describing Data Sets Using Statistics to Summarize
Data Sets Probability
Discrete Random Variables
Normal Random Variables
Distributions of Sampling
Statistics Estimation Testing
Statistical Hypotheses
Hypothesis Tests Concerning Two Populations
Analysis of Variance Linear Regression
Chi-Squared Goodness of Fit Tests
Nonparametric Hypotheses
Tests
Quality Control
Appendices