I, Mathematician

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

Publisher: The Mathematical Association of America

ISBN: 0883855852

Category: Mathematics

Page: 320

View: 9315

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: 7005

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: 1141

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: 1417

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: 3068

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.

Introduction to Hilbert Space and the Theory of Spectral Multiplicity

Second Edition

Author: Paul R. Halmos

Publisher: Courier Dover Publications

ISBN: 048682683X

Category: Mathematics

Page: 128

View: 7086

Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.

Microlocal Analysis and Precise Spectral Asymptotics

Author: Victor Ivrii

Publisher: Springer Science & Business Media

ISBN: 9783540627807

Category: Mathematics

Page: 731

View: 4591

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: 5963

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.

Beautiful Mathematics

Author: Martin Erickson

Publisher: MAA

ISBN: 0883855763

Category: Mathematics

Page: 177

View: 1290

This book is about beautiful mathematical concepts and creations. Mathematical ideas have an aesthetic appeal that can be appreciated by those who have the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. Readers will investigate exciting mathematical topics ranging from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared.Do you know that a lemniscate curve is the circular inversion of a hyperbola? That Sierpinski's triangle has fractal dimension 1.585….? That a regular septagon can be constructed with straightedge, compass, and an angle trisector? Do you know how to prove Lagrange's theorem that every positive integer is the sum of four squares? Can you find the first three digits of the millionth Fibonacci number? Discover the keys to these and many other mathematical problems. In each case, the mathematics is compelling, elegant, simple, and beautiful.Who should read this book? There is something new for any mathematically-minded person. High school and college students will find motivation for their mathematical studies. Professional mathematicians will find fresh examples of mathematical beauty to pass along to others. Within each chapter, the topics require progressively more prerequisite knowledge. An appendix gives background definitions and theorems, while another gives challenging exercises (with solutions).

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: 3125

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.

Wavelets Through a Looking Glass

The World of the Spectrum

Author: Ola Bratteli,Palle E. T. Jørgensen,Palle Jorgensen

Publisher: Springer Science & Business Media

ISBN: 9780817642808

Category: Computers

Page: 398

View: 4974

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.

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: 2478

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.

Voronezh Winter Mathematical Schools

Dedicated to Selim Krein

Author: Selim Grigorʹevich Kreĭn,Peter Kuchment,Vladimir Lin

Publisher: American Mathematical Soc.

ISBN: 9780821809761

Category: Mathematics

Page: 263

View: 4787

This volume is devoted to the 25-year-old Voronezh Winter Mathematical School and to the scientific work of its founder, Selim Krein. The Voronezh Winter Mathematical School was a unique annual event in the scientific life of the former Soviet Union. Over the years it attracted thousands of mathematicians, from undergraduates to world-renowned experts, and played a major role in spreading information about cutting edge results of mathematical research, triggering cooperation and educating new generations of mathematicians. The articles in this book, written by prominent mathematicians and former lecturers and participants of the school, cover a wide range of subjects in analysis and geometry, including global analysis, harmonic analysis, function theory, operator theory, spectral theory, dynamical systems, mathematical physics, homogenization, algebraic geometry, differential geometry, and geometric analysis.

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: 4831

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.

Mathematical Apocrypha

Stories and Anecdotes of Mathematicians and the Mathematical

Author: Steven G. Krantz

Publisher: MAA

ISBN: 9780883855393

Category: Mathematics

Page: 214

View: 1170

Collection of stories about famous contemporary mathematicians, with illustrations.

Spectral Theory of Operators on Hilbert Spaces

Author: Carlos S. Kubrusly

Publisher: Springer Science & Business Media

ISBN: 0817683283

Category: Mathematics

Page: 197

View: 7584

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. ​

Expeditions in Mathematics

Author: Tatiana Shubin

Publisher: MAA

ISBN: 0883855712

Category: Mathematics

Page: 312

View: 9370

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

A Mathematical spectrum miscellany

selections from Mathematical spectrum, 1967-1994

Author: Applied Probability Trust

Publisher: N.A

ISBN: 9780902016057

Category: Mathematics

Page: 198

View: 7306