I, Mathematician

Author: Peter Casazza,Steven G. Krantz,Randi D. Ruden

Publisher: The Mathematical Association of America

ISBN: 0883855852

Category: Mathematics

Page: 320

View: 3719

Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking. Not all respondents addressed the question directly. Michael Atiyah reflects on the tension between truth and beauty in mathematics. T.W. Körner, Alan Schoenfeld and Hyman Bass chose to write, reflectively and thoughtfully, about teaching and learning. Others, including Ian Stewart and Jane Hawkins, write about the sociology of our community. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here.

E.E. Slutsky as Economist and Mathematician

Crossing the Limits of Knowledge

Author: Vincent Barnett

Publisher: Routledge

ISBN: 1136737316

Category: Business & Economics

Page: 224

View: 7019

E.E. Slutsky is perhaps the Russian/Ukrainian economist most quoted by mainstream economists today. This is the first research monograph to examine the life and work of the internationally-renowned economist and mathematician. It does so from both a ‘history of economics’ perspective and a ‘history of science’ perspective, bringing these two strands together in order to demonstrate Slutsky’s enduring legacy as an innovative researcher and an influential intellectual. It also presents some of Slutsky’s lesser-known (and hitherto-unavailable) works in English translation.

Methods of Spectral Analysis in Mathematical Physics

Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2006, Lund, Sweden

Author: Jan Janas,Pavel Kurasov,A. Laptev,Sergei Naboko,Gunter Stolz

Publisher: Springer Science & Business Media

ISBN: 3764387556

Category: Science

Page: 444

View: 7657

The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.

Mathematics Education

A Spectrum of Work in Mathematical Sciences Departments

Author: Jacqueline Dewar,Pao-sheng Hsu,Harriet Pollatsek

Publisher: Springer

ISBN: 3319449508

Category: Mathematics

Page: 391

View: 2703

Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its value in the mathematical community. The writing is expository, not technical, and should be accessible and informative to a diverse audience. The primary readership includes all those in departments of mathematical sciences in two or four year colleges and universities, and their administrators, as well as graduate students. Researchers in education may also find topics of interest. Other potential readers include those doing work in mathematics education in schools of education, and teachers of secondary or middle school mathematics as well as those involved in their professional development.

European Congress of Mathematics

Barcelona, July 10–14, 2000

Author: Carles Casacuberta,Rosa Maria Miro-Roig,Joan Verdera,Sebastia Xambo-Descamps

Publisher: Birkhäuser

ISBN: 3034882688

Category: Mathematics

Page: 582

View: 7099


A Mathematical spectrum miscellany

selections from Mathematical spectrum, 1967-1994

Author: Applied Probability Trust

Publisher: N.A

ISBN: 9780902016057

Category: Mathematics

Page: 198

View: 8396


Microlocal Analysis and Precise Spectral Asymptotics

Author: Victor Ivrii

Publisher: Springer Science & Business Media

ISBN: 9783540627807

Category: Mathematics

Page: 731

View: 1222

Devoted to the methods of microlocal analysis applied to spectral asymptotics with accurate remainder estimates, this long awaited book develops the very powerful machinery of local and microlocal semiclassical spectral asymptotics, as well as methods of combining these asymptotics with spectral estimates. The rescaling technique, an easy to use and very powerful tool, is presented. Many theorems, considered till now as independent and difficult, are now just special cases of easy corollaries of the theorems proved in this book. Most of the results and their proofs are as yet unpublished. Part 1 considers semiclassical microlocal analysis and propagation of singularities inside the domain and near the boundary. Part 2 is on local and microlocal semiclassical spectral asymptotics for general operators and Schrödinger and Dirac operators. After a synthesis in Part 3, the real fun begins in Part 4: the main theorems are applied and numerous results, both known and new, are recovered with little effort. Then, in Chapter 12, non-Weyl asymptotics are obtained for operators in domains with thick cusps, degenerate operators, for spectral Riesz means for operators with singularities. Most of the results and almost all the proofs were never published.

Autism Spectrum Disorders

Psychological Theory and Research

Author: Dermot Bowler

Publisher: John Wiley & Sons

ISBN: 047003503X

Category: Education

Page: 318

View: 2302

Psychological research into autism spectrum disorders (ASD) has increased exponentially in the last two decades. Much of this work has been led by various theorists who claim to have identified processes that hold the key to understanding the condition. As a consequence, newcomers to the field feel that they have to opt for one or more of the competing approaches and to neglect the remainder as being in some way wrong. In fact, the different theoretical perspectives are just that - different points of view on the same phenomenon - each with its own insights to offer. This is not to say that understanding ASD in psychological terms is just a matter of choosing a perspective and that all perspectives are of equal value. Clearly they are not. This book, in addition to providing an outline of what current perspectives have to offer, also provides a framework to help readers to decide which aspects of psychological research into ASD contribute to our understanding of the field and how these can be integrated in a way that enables research to be taken forward.

Ultrafilters Across Mathematics

International Congress, Ultramath 2008, Applications of Ultrafilters and Ultraproducts in Mathematics, June 1-7, 2008, Pisa, Italy

Author: Vitaly Bergelson

Publisher: American Mathematical Soc.

ISBN: 082184833X

Category: Mathematics

Page: 200

View: 6597

This volume originated from the International Congress ``ULTRAMATH: Applications of Ultrafilters and Ultraproducts in Mathematics'', which was held in Pisa, Italy, from June 1-7, 2008. The volume aims to present the state-of-the-art of applications in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts. It contains two general surveys on ultrafilters in set theory and on the ultraproduct construction, as well as papers that cover additive and combinatorial number theory, nonstandard methods and stochastic differential equations, measure theory, dynamics, Ramsey theory, algebra in the space of ultrafilters, and large cardinals. The papers are intended to be accessible and interesting for mathematicians who are not experts on ultrafilters and ultraproducts. Greater prominence has been given to results that can be formulated and presented in non-special terms and be, in principle, understandable by any mathematician, and to those results that connect different areas of mathematics, revealing new facets of known important topics.

Spectral Theory and Quantum Mechanics

With an Introduction to the Algebraic Formulation

Author: Valter Moretti

Publisher: Springer Science & Business Media

ISBN: 8847028353

Category: Mathematics

Page: 728

View: 946

This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out to Master's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.

Fünf Minuten Mathematik

100 Beiträge der Mathematik-Kolumne der Zeitung DIE WELT

Author: Ehrhard Behrends

Publisher: Springer-Verlag

ISBN: 3658009985

Category: Mathematics

Page: 262

View: 6053

Das Buch enthält einen Querschnitt durch die moderne und alltägliche Mathematik. Die 100 Beiträge sind aus der Kolumne "Fünf Minuten Mathematik" hervorgegangen, in der verschiedene mathematische Gebiete in einer für Laien verständlichen Sprache behandelt wurden. Der Leser findet hier den mathematischen Hintergrund und viele attraktive Fotos zur Veranschaulichung der Mathematik. Für die Neuauflage wurde der Text aktualisiert und ergänzt; anhand von QR-Codes können zu verschiedenen Themen kurze Filme bei Youtube abgerufen werden.

Mathematics in Historical Context

Author: Jeff Suzuki

Publisher: MAA

ISBN: 9780883855706

Category: Mathematics

Page: 409

View: 476

What would Newton see if he looked out his bedroom window? This book describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected by the outside world, and at the same time how the outside world was affected by mathematics and mathematicians. Part biography, part mathematics, and part history, this book provides the interested layperson the background to understand mathematics and the history of mathematics, and is suitable for supplemental reading in any history of mathematics course.

Spectral Theory of Operators on Hilbert Spaces

Author: Carlos S. Kubrusly

Publisher: Springer Science & Business Media

ISBN: 0817683283

Category: Mathematics

Page: 197

View: 8989

This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to apply spectral theory to their field. ​

Wavelets Through a Looking Glass

The World of the Spectrum

Author: Ola Bratteli,Palle E. T. Jørgensen

Publisher: Springer Science & Business Media

ISBN: 9780817642808

Category: Computers

Page: 398

View: 2579

This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectral-theoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics. This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory.

Mathematical Apocrypha

Stories and Anecdotes of Mathematicians and the Mathematical

Author: Steven G. Krantz

Publisher: MAA

ISBN: 9780883855393

Category: Mathematics

Page: 214

View: 1724

Collection of stories about famous contemporary mathematicians, with illustrations.

History of Mathematics

Highways and Byways

Author: Amy Dahan,Jeanne Peiffer

Publisher: MAA

ISBN: 0883855623

Category: Mathematics

Page: 330

View: 7437

This book is arranged to show the development of the different branches of mathematics over time and contains many illustrations to support the text. In all, a short, innovative and easy-to-read history of mathematics.

Differential Operators and Spectral Theory

M. Sh. Birman's 70th Anniversary Collection

Author: Margarita Solomyak,Dmitriĭ Rauelʹevich I͡Afaev

Publisher: American Mathematical Soc.

ISBN: 9780821813874

Category: Mathematics

Page: 285

View: 3208

This volume contains a collection of original papers in mathematical physics, spectral theory, and differential equations. The papers are dedicated to the outstanding mathematician, Professor M. Sh. Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional colleagues of Birman. The main topics discussed are spectral and scattering theory of differential operators, trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrodinger operator, which is within Birman's current scope of interests and recently has been studied extensively. Included is a detailed survey of his mathematical work and an updated list of his publications.This book is aimed at graduate students and specialists in the above-mentioned branches of mathematics and theoretical physicists. The biographical section will be of interest to readers concerned with the scientific activities of Birman and the history of those branches of analysis and spectral theory where his contributions were important and often decisive. Features: The first detailed survey of Birman's mathematical work; includes an updated bibliography. New material on the history of some branches of analysis. Prominent authors: Lieb, Agmon, Deift, Simon, Ladyzhenskaya, and others. All original works, containing new results in fields of great current interest.

Expeditions in Mathematics

Author: Tatiana Shubin

Publisher: MAA

ISBN: 0883855712

Category: Mathematics

Page: 312

View: 6352

Collection of lectures, aimed at high school students and presented by prominent mathematicians as part of the Bay Area Mathematical Adventures program.