I, Mathematician

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

Publisher: The Mathematical Association of America

ISBN: 0883855852

Category: Mathematics

Page: 320

View: 3211

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: 9455

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,Günter Stolz

Publisher: Springer Science & Business Media

ISBN: 3764387556

Category: Science

Page: 444

View: 2446

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.

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: 5679

This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabré, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. Föllmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Simó, B. Tóth, E. van den Ban, M.-F. Vignéras, O. Viro.

Microlocal Analysis and Precise Spectral Asymptotics

Author: Victor Ivrii

Publisher: Springer Science & Business Media

ISBN: 9783540627807

Category: Mathematics

Page: 731

View: 5634

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: 7163

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.

Expeditions in Mathematics

Author: Tatiana Shubin

Publisher: MAA

ISBN: 0883855712

Category: Mathematics

Page: 312

View: 8720

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

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: 4340

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.

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: 7104

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.

Spectral Theory of Operators on Hilbert Spaces

Author: Carlos S. Kubrusly

Publisher: Springer Science & Business Media

ISBN: 0817683283

Category: Mathematics

Page: 197

View: 8666

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. ​

Full Spectrum Intelligence

A Practical Course on Behaving Wisely and Well

Author: Chris Thomson

Publisher: John Hunt Publishing

ISBN: 1782796924

Category: Body, Mind & Spirit

Page: 205

View: 6494

A practical course in how to become more intelligent, in the widest sense, where intelligence is defined as "behaving wisely and well". It covers six main forms of intelligence, from physical to spiritual, as well as your "other senses". The book emphasises the relationship between the state of the world today and the need for us to become much more intelligent.

Stationary Stochastic Processes for Scientists and Engineers

Author: Georg Lindgren,Holger Rootzen,Maria Sandsten

Publisher: CRC Press

ISBN: 1466586192

Category: Mathematics

Page: 330

View: 5617

Stochastic processes are indispensable tools for development and research in signal and image processing, automatic control, oceanography, structural reliability, environmetrics, climatology, econometrics, and many other areas of science and engineering. Suitable for a one-semester course, Stationary Stochastic Processes for Scientists and Engineers teaches students how to use these processes efficiently. Carefully balancing mathematical rigor and ease of exposition, the book provides students with a sufficient understanding of the theory and a practical appreciation of how it is used in real-life situations. Special emphasis is on the interpretation of various statistical models and concepts as well as the types of questions statistical analysis can answer. The text first introduces numerous examples from signal processing, economics, and general natural sciences and technology. It then covers the estimation of mean value and covariance functions, properties of stationary Poisson processes, Fourier analysis of the covariance function (spectral analysis), and the Gaussian distribution. The book also focuses on input-output relations in linear filters, describes discrete-time auto-regressive and moving average processes, and explains how to solve linear stochastic differential equations. It concludes with frequency analysis and estimation of spectral densities. With a focus on model building and interpreting the statistical concepts, this classroom-tested book conveys a broad understanding of the mechanisms that generate stationary stochastic processes. By combining theory and applications, the text gives students a well-rounded introduction to these processes. To enable hands-on practice, MATLAB® code is available online.

The Basics of Spectroscopy

Author: David Warren Ball

Publisher: SPIE Press

ISBN: 9780819441041

Category: Technology & Engineering

Page: 122

View: 4285

Spectroscopy--the study of matter using electromagnetic radiation--and its applications as a scientific tool are the focus of this tutorial. Topics covered include the interaction of light with matter, spectrometer fundamentals, quantum mechanics, selection rules, and experimental factors.

Fünf Minuten Mathematik

100 Beiträge der Mathematik-Kolumne der Zeitung DIE WELT

Author: Ehrhard Behrends

Publisher: Springer-Verlag

ISBN: 3834890138

Category: Mathematics

Page: 254

View: 2323

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. Diese Beiträge wurden für das Buch überarbeitet, stark erweitert und mit Illustrationen versehen. Der Leser findet hier den mathematischen Hintergrund und viele attraktive Fotos zur Veranschaulichung der Mathematik.

Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations

Author: M. Sh Birman

Publisher: American Mathematical Soc.

ISBN: 9780821841068

Category: Differential equations

Page: 204

View: 3429

The Leningrad Seminar on mathematical physics, begun in 1947 by V. I. Smirnov and now run by O. A. Ladyzhenskaya, is sponsored by Leningrad University and the Leningrad Branch of the Steklov Mathematical Institute of the Academy of Sciences of the USSR. The main topics of the seminar center on the theory of boundary value problems and related questions of analysis and mathematical physics. This volume contains adaptations of lectures presented at the seminar during the academic year 1989-1990. For the most part, the papers are devoted to investigations of the spectrum of the Schrödinger operator (or its generalizations) perturbed by some relatively compact operator. The book studies the discrete spectrum that emerges in the spectral gaps of the nonperturbed operator, and considers the corresponding estimates and asymptotic formulas for spectrum distribution functions in the large-coupling-constant limit. The starting point here is the opening paper, which is devoted to the important case of a semi-infinite gap. The book also covers the case of inner gaps, related questions in the theory of functions, and an integral equation with difference kernel on a finite interval. The collection concludes with a paper focusing on the classical problem of constructing scattering theory for the Schrödinger operator with potential decreasing faster than the Coulomb potential

Quantum Field Theory I: Basics in Mathematics and Physics

A Bridge between Mathematicians and Physicists

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 354034764X

Category: Science

Page: 1051

View: 7433

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Women Becoming Mathematicians

Creating a Professional Identity in Post-World War II America

Author: Margaret A. M. Murray

Publisher: MIT Press

ISBN: 9780262632461

Category: Science

Page: 277

View: 8980

Women mathematicians of the 1950s, 1960s, and 1970s and how they built professional identities in the face of social and institutional obstacles.

Orthogonal Polynomials on the Unit Circle: Spectral theory

Author: Barry Simon

Publisher: American Mathematical Soc.

ISBN: 9780821836750

Category: Science

Page: 1044

View: 7477

This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegö's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by z (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.