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Mathematics Into Type by Ellen Swanson

Title Mathematics Into Type
Author Ellen Swanson
Publisher American Mathematical Soc.
Release Date 1999-01-01
Category Language Arts & Disciplines
Total Pages 102
ISBN 0821897322
Language English, Spanish, and French
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Book Summary:

This edition, updated by Arlene O'Sean and Antoinette Schleyer of the American Mathematical Society, brings Ms. Swanson's work up to date, reflecting the more technical reality of publishing today. While it includes information for copy editors, proofreaders, and production staff to do a thorough, traditional copyediting and proofreading of a manuscript and proof copy, it is increasingly more useful to authors, who have become intricately involved with the typesetting of their manuscripts.

Introduction To Approximate Groups by Matthew C. H. Tointon

Title Introduction to Approximate Groups
Author Matthew C. H. Tointon
Publisher Cambridge University Press
Release Date 2019-11-14
Category Mathematics
Total Pages 86
ISBN 9781108571609
Language English, Spanish, and French
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Book Summary:

Approximate groups have shot to prominence in recent years, driven both by rapid progress in the field itself and by a varied and expanding range of applications. This text collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction. The author presents a number of recent developments in the field, including an exposition of his recent result classifying nilpotent approximate groups. The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples. It closes with a substantial chapter on applications, including an exposition of Breuillard, Green and Tao's celebrated approximate-group proof of Gromov's theorem on groups of polynomial growth. Written by an author who is at the forefront of both researching and teaching this topic, this text will be useful to advanced students and to researchers working in approximate groups and related areas.

Title Fourier Restriction Decoupling and Applications
Author Ciprian Demeter
Publisher Cambridge University Press
Release Date 2020-01-31
Category Mathematics
Total Pages 357
ISBN 9781108499705
Language English, Spanish, and French
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Book Summary:

Comprehensive coverage of recent, exciting developments in Fourier restriction theory, including applications to number theory and PDEs.

Title Mathematical Biology Modeling and Analysis
Author Avner Friedman
Publisher American Mathematical Soc.
Release Date 2018-06-14
Category Biology
Total Pages 100
ISBN 9781470447151
Language English, Spanish, and French
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Book Summary:

The fast growing field of mathematical biology addresses biological questions using mathematical models from areas such as dynamical systems, probability, statistics, and discrete mathematics. This book considers models that are described by systems of partial differential equations, and it focuses on modeling, rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing. A rich variety of open problems demonstrates the exciting challenges and opportunities for research at the interface of mathematics and biology. This book primarily addresses students and researchers in mathematics who do not necessarily have any background in biology and who may have had little exposure to PDEs.

Title Topics in Classical Automorphic Forms
Author Henryk Iwaniec
Publisher American Mathematical Soc.
Release Date 1997
Category Mathematics
Total Pages 259
ISBN 9780821807774
Language English, Spanish, and French
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Book Summary:

The main purpose of the book is to present the reader with various perspectives of the theory of automorphic forms. In addition to detailed and often nonstandard exposition of familiar topics of the theory, with a particular emphasis on analytic aspects, special attention is paid to such subjects as theta-functions and representations of integers by quadratic forms.

Title Fundamentals of the Theory of Operator Algebras
Author Richard V. Kadison
Publisher American Mathematical Soc.
Release Date 1998
Category Mathematics
Total Pages 859
ISBN 0821809911
Language English, Spanish, and French
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Book Summary:

This volume is the companion volume to Fundamentals of the Theory of Operator Algebras - Volume I: Elementary Theory. The goal of the text is to teach the subject and lead readers to where the literature - in the subject specifically and in its many applications - becomes accessible. The choice of material was made from among the fundamentals of what may be called the classical theory of operator algebras. This volume contains written solutions to the exercises in the Fundamentals of the Theory of Operator Algebras. Volume I: Elementary Theory.

A Course In Operator Theory by John B. Conway

Title A Course in Operator Theory
Author John B. Conway
Publisher American Mathematical Soc.
Release Date 2000
Category Mathematics
Total Pages 372
ISBN 9780821820650
Language English, Spanish, and French
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Book Summary:

Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, mathematical physics, and more. This text covers the central themes of operator theory, presented with the excellent clarity and style that readers have come to associate with Conway's writing. Early chapters introduce and review material on $C^*$-algebras, normal operators, compact operators, and non-normal operators. Some of the major topics covered are the spectral theorem, the functional calculus, and the Fredholm index. In addition, some deep connections between operator theory and analytic functions are presented. Later chapters cover more advanced topics, such as representations of $C^*$-algebras, compact perturbations, and von Neumann algebras. Major results, such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem, and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory. The last chapter gives an introduction to reflexive subspaces, which along with hyperreflexive spaces, are one of the more successful episodes in the modern study of asymmetric algebras. Professor Conway's authoritative treatment makes this a compelling and rigorous course text, suitable for graduate students who have had a standard course in functional analysis.

Title John Von Neumann 1903 1957
Author J. C. Oxtoby
Publisher American Mathematical Soc.
Release Date 1966-12-31
Category
Total Pages 129
ISBN 0821896792
Language English, Spanish, and French
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Book Summary:

This is Bulletin , Volume 64, Number 3, Part II, May 1958. A memorial to the late John von Neumann edited by J. C. Oxtoby, B. J. Pettis and E. B. Price.

Title Introduction to the Mathematics of Finance
Author Ruth J. Williams
Publisher American Mathematical Soc.
Release Date 2006
Category Business & Economics
Total Pages 150
ISBN 9780821839034
Language English, Spanish, and French
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Book Summary:

The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions.

A Course In Convexity by Alexander Barvinok

Title A Course in Convexity
Author Alexander Barvinok
Publisher American Mathematical Soc.
Release Date 2002-11-19
Category Mathematics
Total Pages 366
ISBN 9780821829684
Language English, Spanish, and French
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Book Summary:

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.

Differential Topology by Victor Guillemin

Title Differential Topology
Author Victor Guillemin
Publisher American Mathematical Soc.
Release Date 2010
Category Mathematics
Total Pages 222
ISBN 9780821851937
Language English, Spanish, and French
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Book Summary:

Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.

The Noether Theorems by Yvette Kosmann-Schwarzbach

Title The Noether Theorems
Author Yvette Kosmann-Schwarzbach
Publisher Springer Science & Business Media
Release Date 2010-11-17
Category Mathematics
Total Pages 205
ISBN 0387878688
Language English, Spanish, and French
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Book Summary:

In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether's achievements were remembered, and sometimes figure in quick historical accounts of the time. This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether's results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.

Lectures On Matrices by J. H. M. Wedderburn

Title Lectures on Matrices
Author J. H. M. Wedderburn
Publisher American Mathematical Soc.
Release Date 1934-12-31
Category Mathematics
Total Pages 205
ISBN 9780821846100
Language English, Spanish, and French
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Book Summary:

It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of results--the subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion. --Bulletin of the American Mathematical Society The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory. --Jahrbuch uber die Fortschritte der Mathematik In 1937, the theory of matrices was seventy-five years old. However, many results had only recently evolved from special cases to true general theorems. With the publication of his Colloquium Lectures, Wedderburn provided one of the first great syntheses of the subject. Much of the material in the early chapters is now familiar from textbooks on linear algebra. Wedderburn discusses topics such as vectors, bases, adjoints, eigenvalues and the characteristic polynomials, up to and including the properties of Hermitian and orthogonal matrices. Later chapters bring in special results on commuting families of matrices, functions of matrices--including elements of the differential and integral calculus sometimes known as matrix analysis, and transformations of bilinear forms. The final chapter treats associative algebras, culminating with the well-known Wedderburn-Artin theorem that simple algebras are necessarily isomorphic to matrix algebras. Wedderburn ends with an appendix of historical notes on the development of the theory of matrices, and a bibliography that emphasizes the history of the subject.

Common Sense Mathematics by Ethan D. Bolker

Title Common Sense Mathematics
Author Ethan D. Bolker
Publisher The Mathematical Association of America
Release Date 2016-05-04
Category Mathematics
Total Pages 326
ISBN 9781939512109
Language English, Spanish, and French
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Book Summary:

Common Sense Mathematics is a text for a one semester college-level course in quantitative literacy. The text emphasizes common sense and common knowledge in approaching real problems through popular news items and finding useful mathematical tools and frames with which to address those questions. We asked ourselves what we hoped our students would remember about this course in ten year’s time. From that ten year perspective thoughts about syllabus–“what topics should we cover?"–seemed much too narrow. What matters more is our wish to change the way our students' minds work–the way they approach a problem, or, more generally, the way they approach the world. Most people “skip the numbers" in newspapers, magazines, on the web and (more importantly) even in financial information. We hope that in ten years our students will follow the news, confident in their ability to make sense of the numbers they find there and in their daily lives. Most quantitative reasoning texts are arranged by mathematical topics to be mastered. Since the mathematics is only a part of what we hope students learn, we've chosen another strategy. We look at real life stories that can be best understood with careful reading and a little mathematics.

Spectral Graph Theory by Fan R. K. Chung

Title Spectral Graph Theory
Author Fan R. K. Chung
Publisher American Mathematical Soc.
Release Date 1997
Category Mathematics
Total Pages 207
ISBN 9780821803158
Language English, Spanish, and French
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Book Summary:

Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's well-written exposition can be likened to a conversation with a good teacher--one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics.

Title Geometric Nonlinear Functional Analysis
Author Yoav Benyamini
Publisher American Mathematical Soc.
Release Date 2000
Category Nonlinear functional analysis
Total Pages 488
ISBN 9780821808351
Language English, Spanish, and French
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Book Summary:

This book presents a systematic and unified study of geometric nonlinear functional analysis. This is a very active research area and has connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. Students and instructors alike benefit from examples and complete proofs.

Bulletin by New York Mathematical Society

Title Bulletin
Author New York Mathematical Society
Publisher Unknown
Release Date 1894
Category
Total Pages 86
ISBN UCSC:32106020204878
Language English, Spanish, and French
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Book Summary:

Global Analysis by Shiing-Shen Chern

Title Global Analysis
Author Shiing-Shen Chern
Publisher American Mathematical Soc.
Release Date 1970-12-31
Category Mathematics
Total Pages 367
ISBN 9780821814147
Language English, Spanish, and French
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Book Summary:

Includes bibliographical references.

Fundamental Algebraic Geometry by Barbara Fantechi

Title Fundamental Algebraic Geometry
Author Barbara Fantechi
Publisher American Mathematical Soc.
Release Date 2005
Category Mathematics
Total Pages 339
ISBN 9780821842454
Language English, Spanish, and French
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Book Summary:

Alexander Grothendieck introduced many concepts into algebraic geometry; they turned out to be astoundingly powerful and productive and truly revolutionized the subject. Grothendieck sketched his new theories in a series of talks at the Seminaire Bourbaki between 1957 and 1962 and collected his write-ups in a volume entitled ``Fondements de la Geometrie Algebrique,'' known as FGA. Much of FGA is now common knowledge; however, some of FGA is less well known, and its full scope is familiar to few. The present book resulted from the 2003 ``Advanced School in Basic Algebraic Geometry'' at the ICTP in Trieste, Italy. The book aims to fill in Grothendieck's brief sketches. There are four themes: descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. Most results are proved in full detail; furthermore, newer ideas are introduced to promote understanding, and many connections are drawn to newer developments. The main prerequisite is a thorough acquaintance with basic scheme theory. Thus this book is a valuable resource for anyone doing algebraic geometry.

Title Pioneering Women in American Mathematics
Author Judy Green
Publisher American Mathematical Soc.
Release Date 2009-01
Category Mathematics
Total Pages 349
ISBN 9780821843765
Language English, Spanish, and French
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Book Summary:

More than 14 percent of the PhD's awarded in the United States during the first four decades of the twentieth century went to women, a proportion not achieved again until the 1980s. This book is the result of a study in which the authors identified all of the American women who earned PhD's in mathematics before 1940, and collected extensive biographical and bibliographical information about each of them. By reconstructing as complete a picture as possible of this group of women, Green and LaDuke reveal insights into the larger scientific and cultural communities in which they lived and worked. The book contains an extended introductory essay, as well as biographical entries for each of the 228 women in the study. The authors examine family backgrounds, education, careers, and other professional activities. They show that there were many more women earning PhD's in mathematics before 1940 than is commonly thought. Extended biographies and bibliographical information are available from the companion website for the book: www.ams.org/bookpages/hmath-34. The material will be of interest to researchers, teachers, and students in mathematics, history of mathematics, history of science, women's studies, and sociology. The data presented about each of the 228 individual members of the group will support additional study and analysis by scholars in a large number of disciplines.