MAA Basic Library List Last Updated 1/23/18 Contact Darren Glass ([email protected]) with Questions
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Geometric Algebra for Vector Fields Analysis and Visualization: Mathematical Settings, Overview and Applications Chantal Oberson Ausoni, Pascal Frey
Geometric algebra for vector fields analysis and visualization: mathematical settings, overview and applications Chantal Oberson Ausoni, Pascal Frey To cite this version: Chantal Oberson Ausoni, Pascal Frey. Geometric algebra for vector fields analysis and visualization: mathematical settings, overview and applications. 2014. hal-00920544v2 HAL Id: hal-00920544 https://hal.sorbonne-universite.fr/hal-00920544v2 Preprint submitted on 18 Sep 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Geometric algebra for vector field analysis and visualization: mathematical settings, overview and applications Chantal Oberson Ausoni and Pascal Frey Abstract The formal language of Clifford’s algebras is attracting an increasingly large community of mathematicians, physicists and software developers seduced by the conciseness and the efficiency of this compelling system of mathematics. This contribution will suggest how these concepts can be used to serve the purpose of scientific visualization and more specifically to reveal the general structure of complex vector fields. We will emphasize the elegance and the ubiquitous nature of the geometric algebra approach, as well as point out the computational issues at stake. 1 Introduction Nowadays, complex numerical simulations (e.g. in climate modelling, weather fore- cast, aeronautics, genomics, etc.) produce very large data sets, often several ter- abytes, that become almost impossible to process in a reasonable amount of time. -
Amie Wilkinson 1
Amie Wilkinson 1 Amie Wilkinson Department of Mathematics, University of Chicago 5734 S. University Avenue Chicago, Illinois 60637 (773) 702-7337 [email protected] ACADEMIC POSITIONS • Professor of Mathematics, University of Chicago, 2012 { present. • Professor of Mathematics, Northwestern University, 2005 { 2012. • Associate Professor of Mathematics, Northwestern University, 2002 { 2005. • Assistant Professor of Mathematics, Northwestern University, 1999 { 2002. • Boas Assistant Professor of Mathematics, Northwestern University, 1996 { 1999. • Benjamin Peirce Instructor, Harvard University, 1995 { 1996. Visiting Positions • Visiting Professor, University of Chicago, Fall and Spring Quarters 2003{2004, Fall Quarter 2011. • Professeur Invit´e, Universit´ede Bourgogne, May 2002 and Sept 2003. • Member, Institut des Hautes Etudes Scientifiques (IHES), Summer 1993, 1996, 1998. • Visitor, IBM T.J. Watson Labs, Yorktown NY, Winter 1992 and 1994, Summer 1997, 1998, 2000, and 2001. • Graduate Research Assistant, The Center for Nonlinear Studies, Los Alamos National Laboratories, Summer, 1992. EDUCATION • Ph.D. in Mathematics, University of California, Berkeley, May 1995 • A.B. in Mathematics, Harvard University, June 1989 DATE OF BIRTH April, 1968. U.S. citizen. Amie Wilkinson 2 RESEARCH INTERESTS • Ergodic theory and smooth dynamical systems • Geometry and regularity of foliations • Actions of discrete groups on manifolds • Dynamical systems of geometric origin GRANTS, FELLOWSHIPS AND AWARDS • Levi L. Conant Prize, 2020. • Foreign Member, Academia Europaea, 2019. • Fellow of the American Mathematical Society, 2013. • Ruth Lyttle Satter Prize, 2011. • NSF Grant \Ergodicity, Rigidity, and the Interplay Between Chaotic and Regular Dynamics" $758,242, 2018{2021. • NSF Grant \Innovations in Bright Beam Science" (co-PI) $680,000, 2015{2018. • NSF Grant \RTG: Geometry and topology at the University of Chicago" (co-PI) $1,377,340, 2014{2019. -
Exploring Physics with Geometric Algebra, Book II., , C December 2016 COPYRIGHT
peeter joot [email protected] EXPLORINGPHYSICSWITHGEOMETRICALGEBRA,BOOKII. EXPLORINGPHYSICSWITHGEOMETRICALGEBRA,BOOKII. peeter joot [email protected] December 2016 – version v.1.3 Peeter Joot [email protected]: Exploring physics with Geometric Algebra, Book II., , c December 2016 COPYRIGHT Copyright c 2016 Peeter Joot All Rights Reserved This book may be reproduced and distributed in whole or in part, without fee, subject to the following conditions: • The copyright notice above and this permission notice must be preserved complete on all complete or partial copies. • Any translation or derived work must be approved by the author in writing before distri- bution. • If you distribute this work in part, instructions for obtaining the complete version of this document must be included, and a means for obtaining a complete version provided. • Small portions may be reproduced as illustrations for reviews or quotes in other works without this permission notice if proper citation is given. Exceptions to these rules may be granted for academic purposes: Write to the author and ask. Disclaimer: I confess to violating somebody’s copyright when I copied this copyright state- ment. v DOCUMENTVERSION Version 0.6465 Sources for this notes compilation can be found in the github repository https://github.com/peeterjoot/physicsplay The last commit (Dec/5/2016), associated with this pdf was 595cc0ba1748328b765c9dea0767b85311a26b3d vii Dedicated to: Aurora and Lance, my awesome kids, and Sofia, who not only tolerates and encourages my studies, but is also awesome enough to think that math is sexy. PREFACE This is an exploratory collection of notes containing worked examples of more advanced appli- cations of Geometric Algebra (GA), also known as Clifford Algebra. -
A Historical Perspective of Spectrum Estimation
PROCEEDINGSIEEE, OF THE VOL. 70, NO. 9, SEPTEMBER885 1982 A Historical Perspective of Spectrum Estimation ENDERS A. ROBINSON Invited Paper Alwhrct-The prehistory of spectral estimation has its mots in an- times, credit for the empirical discovery of spectra goes to the cient times with the development of the calendar and the clock The diversified genius of Sir Isaac Newton [ 11. But the great in- work of F’ythagom in 600 B.C. on the laws of musical harmony found mathematical expression in the eighteenthcentury in terms of the wave terest in spectral analysis made its appearanceonly a little equation. The strueto understand the solution of the wave equation more than a century ago. The prominent German chemist was fhlly resolved by Jean Baptiste Joseph de Fourier in 1807 with Robert Wilhelm Bunsen (18 1 1-1899) repeated Newton’s his introduction of the Fourier series TheFourier theory was ex- experiment of the glass prism. Only Bunsen did not use the tended to the case of arbitrary orthogollpl functions by Stmn and sun’s rays Newton did. Newtonhad found that aray of Liowillein 1836. The Stum+Liouville theory led to the greatest as empirical sum of spectral analysis yet obbhed, namely the formulo sunlight is expanded into a band of many colors, the spectrum tion of quantum mechnnics as given by Heisenberg and SchrMngm in of the rainbow. In Bunsen’s experiment, the role of pure sun- 1925 and 1926. In 1929 John von Neumann put the spectral theory of light was replaced by the burning of an old rag that had been the atom on a Turn mathematical foundation in his spectral represent, soaked in a salt solution (sodium chloride). -
Curriculum Vitae
Curriculum Vitae Larry Guth Education B.S. Mathematics, Yale University, 2000 PhD Mathematics, MIT, 2005 Employment Samelson Fellow, Stanford University 2005-6 Szego Assistant Professor, Stanford University, 2006 - 2008 National Science Foundation Postdoctoral Fellow, 2006 - 2008 Tenure-stream Assistant Professor, University of Toronto, 2008 - 2011 Member, Institute for Advanced Study, 2010 - 2011 Professor, New York University, 2011 - 2012 Professor, MIT, 2012 - Fellowships National Science Foundation Graduate Fellowship, 2001 - 2003 National Science Foundation Postdoctoral Fellowship , 2006 - 2008 Alfred P. Sloan Research Fellowship, 2010 - 2014 Simons Investigator, 2014 - Honors Salem prize 2013 Invited talks Invited sectional speaker at the 2010 International Congress of Mathematics Marston Morse lectures, IAS, 2013 Namboodiri lectures, University of Chicago, 2015 1 Selected publications 1. Lipshitz maps from surfaces, Geom. Funct. Anal. 15 (2005), no. 5, 1052-109 2. The width-volume inequality, Geom. Funct. Anal. 17 (2007) no. 4, 1139-1179 3. Notes on Gromov's systolic estimate, Geom. Dedicata 123 (2006) 113-129 4. Symplectic embeddings of polydisks, Invent. Math. 172 (2008) no. 3, 477-489 5. Minimax problems related to cup powers and Steenrod squares, Geom. Funct. Anal. 18 (2009), no. 6, 1917{1987 6. The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture, Acta Math. 205 (2010), no. 2, 263-286. 7. Systolic inequalities and minimal hypersurfaces, Geom. Funct. Anal. 19 (2010), no. 6, 1688-1692. 8. Volumes of balls in large Riemannian manifolds, Ann. of Math. (2) 173 (2011), no. 1, 5176. 9. Area-expanding embeddings of rectangles, preprint 10. Algebraic methods in discrete analogs of the Kakeya problem (joint with Nets Katz), Adv. -
Donald Knuth Fletcher Jones Professor of Computer Science, Emeritus Curriculum Vitae Available Online
Donald Knuth Fletcher Jones Professor of Computer Science, Emeritus Curriculum Vitae available Online Bio BIO Donald Ervin Knuth is an American computer scientist, mathematician, and Professor Emeritus at Stanford University. He is the author of the multi-volume work The Art of Computer Programming and has been called the "father" of the analysis of algorithms. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar,[4] Knuth created the WEB and CWEB computer programming systems designed to encourage and facilitate literate programming, and designed the MIX/MMIX instruction set architectures. As a member of the academic and scientific community, Knuth is strongly opposed to the policy of granting software patents. He has expressed his disagreement directly to the patent offices of the United States and Europe. (via Wikipedia) ACADEMIC APPOINTMENTS • Professor Emeritus, Computer Science HONORS AND AWARDS • Grace Murray Hopper Award, ACM (1971) • Member, American Academy of Arts and Sciences (1973) • Turing Award, ACM (1974) • Lester R Ford Award, Mathematical Association of America (1975) • Member, National Academy of Sciences (1975) 5 OF 44 PROFESSIONAL EDUCATION • PhD, California Institute of Technology , Mathematics (1963) PATENTS • Donald Knuth, Stephen N Schiller. "United States Patent 5,305,118 Methods of controlling dot size in digital half toning with multi-cell threshold arrays", Adobe Systems, Apr 19, 1994 • Donald Knuth, LeRoy R Guck, Lawrence G Hanson. -
CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA
A MERICAN M ATHEMATICAL S OCIETY CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA 1:00 PM Carina Curto, Pennsylvania State University What can topology tell us about the neural code? Surprising new applications of what used to be thought of as “pure” mathematics. 2:00 PM Yuval Peres, Microsoft Research and University of California, Berkeley, and Lionel Levine, Cornell University Laplacian growth, sandpiles and scaling limits Striking large-scale structure arising from simple cellular automata. 3:00 PM Timothy Gowers, Cambridge University Probabilistic combinatorics and the recent work of Peter Keevash The major existence conjecture for combinatorial designs has been proven! 4:00 PM Amie Wilkinson, University of Chicago What are Lyapunov exponents, and why are they interesting? A basic tool in understanding the predictability of physical systems, explained. Organized by David Eisenbud, Mathematical Sciences Research Institute Introduction to the Current Events Bulletin Will the Riemann Hypothesis be proved this week? What is the Geometric Langlands Conjecture about? How could you best exploit a stream of data flowing by too fast to capture? I think we mathematicians are provoked to ask such questions by our sense that underneath the vastness of mathematics is a fundamental unity allowing us to look into many different corners -- though we couldn't possibly work in all of them. I love the idea of having an expert explain such things to me in a brief, accessible way. And I, like most of us, love common-room gossip. -
Defence Strategic Communications
Defence Strategic Communications | Volume 5 | Autumn 2018 DEFENCE STRATEGIC COMMUNICATIONS DEFENCE STRATEGIC 12 Volume 5 | Autumn 2018 DEFENCE STRATEGIC COMMUNICATIONS The official journal of the NATO Strategic Communications Centre of Excellence AUTUMN 2018 The Acoustic World of Influence: How Musicology Illuminates Strategic Communications Hostile Gatekeeping: the Strategy of Engaging With Journalists in Extremism Reporting The ‘Fake News’ Label and Politicisation of Malaysia’s Elections Brand Putin: an Analysis of Vladimir Putin’s Projected Images What Does it Mean for a Communication to be Trusted? Strategic Communications at the Pyeongchang Winter Olympics: a Groundwork Study ISSN: 2500-9486 DOI: 10.30966/2018.RIGA.5. Defence Strategic Communications | Volume 5 | Autumn 2018 DOI 10.30966/2018.RIGA.5.5 WHAT DOES IT MEAN 171 FOR A COMMUNICATION TO BE TRUSTED? Francesca Granelli Abstract Despite following best practice, most governments fail in their strategic communications. There is a missing ‘X’ factor: trust. This offers a quick win to strategic communicators, provided they understand what the phenomenon involves. Moreover, it allows practitioners to avoid the risk of citizens feeling betrayed when their government fails to deliver. Keywords: trust, communications, impersonal trust, distrust, reliance, co-operation, strategic communications About the author Dr Francesca Granelli is a Teaching Fellow at King’s College London, where her research focuses on trust. Her forthcoming book is Trust, Politics and Revolution: A European History. Defence Strategic Communications | Volume 5 | Autumn 2018 DOI 10.30966/2018.RIGA.5.5 172 Introduction Governments, politicians, and commentators are worried. The ‘crisis of trust’ is now a common refrain, which draws upon a mountain of apparent evidence.1 Edelman’s Trust Barometer, for instance, points to declining levels of trust in governments, NGOs, businesses, and the media across most countries each year. -
Modified Moments for Indefinite Weight Functions [2Mm] (A Tribute
Modified Moments for Indefinite Weight Functions (a Tribute to a Fruitful Collaboration with Gene H. Golub) Martin H. Gutknecht Seminar for Applied Mathematics ETH Zurich Remembering Gene Golub Around the World Leuven, February 29, 2008 Martin H. Gutknecht Modified Moments for Indefinite Weight Functions My education in numerical analysis at ETH Zurich My teachers of numerical analysis: Eduard Stiefel [1909–1978] (first, basic NA course, 1964) Peter Läuchli [b. 1928] (ALGOL, 1965) Hans-Rudolf Schwarz [b. 1930] (numerical linear algebra, 1966) Heinz Rutishauser [1917–1970] (follow-up numerical analysis course; “selected chapters of NM” [several courses]; computer hands-on training) Peter Henrici [1923–1987] (computational complex analysis [many courses]) The best of all worlds? Martin H. Gutknecht Modified Moments for Indefinite Weight Functions My education in numerical analysis (cont’d) What did I learn? Gauss elimination, simplex alg., interpolation, quadrature, conjugate gradients, ODEs, FDM for PDEs, ... qd algorithm [often], LR algorithm, continued fractions, ... many topics in computational complex analysis, e.g., numerical conformal mapping What did I miss to learn? (numerical linear algebra only) QR algorithm nonsymmetric eigenvalue problems SVD (theory, algorithms, applications) Lanczos algorithm (sym., nonsym.) Padé approximation, rational interpolation Martin H. Gutknecht Modified Moments for Indefinite Weight Functions My first encounters with Gene H. Golub Gene’s first two talks at ETH Zurich (probably) 4 June 1971: “Some modified eigenvalue problems” 28 Nov. 1974: “The block Lanczos algorithm” Gene was one of many famous visitors Peter Henrici attracted. Fall 1974: GHG on sabbatical at ETH Zurich. I had just finished editing the “Lectures of Numerical Mathematics” of Heinz Rutishauser (1917–1970). -
Pursuit of Genius: Flexner, Einstein, and the Early Faculty at the Institute
i i i i PURSUIT OF GENIUS i i i i i i i i PURSUIT OF GENIUS Flexner, Einstein,and the Early Faculty at the Institute for Advanced Study Steve Batterson Emory University A K Peters, Ltd. Natick, Massachusetts i i i i i i i i Editorial, Sales, and Customer Service Office A K Peters, Ltd. 5 Commonwealth Road, Suite 2C Natick, MA 01760 www.akpeters.com Copyright ⃝c 2006 by A K Peters, Ltd. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form, electronic or mechanical, including photocopy- ing, recording, or by any information storage and retrieval system, without written permission from the copyright owner. Library of Congress Cataloging-in-Publication Data Batterson, Steve, 1950– Pursuit of genius : Flexner, Einstein, and the early faculty at the Institute for Advanced Study / Steve Batterson. p. cm. Includes bibliographical references and index. ISBN 13: 978-1-56881-259-5 (alk. paper) ISBN 10: 1-56881-259-0 (alk. paper) 1. Mathematics–Study and teaching (Higher)–New Jersey–Princeton–History. 2. Institute for Advanced Study (Princeton, N.J.). School of Mathematics–History. 3. Institute for Advanced Study (Princeton, N.J.). School of Mathematics–Faculty. I Title. QA13.5.N383 I583 2006 510.7’0749652--dc22 2005057416 Cover Photographs: Front cover: Clockwise from upper left: Hermann Weyl (1930s, cour- tesy of Nina Weyl), James Alexander (from the Archives of the Institute for Advanced Study), Marston Morse (photo courtesy of the American Mathematical Society), Albert Einstein (1932, The New York Times), John von Neumann (courtesy of Marina von Neumann Whitman), Oswald Veblen (early 1930s, from the Archives of the Institute for Advanced Study). -
Martin Gardner Receives JPBM Communications Award
THE NEWSLETTER OF THE MATHEMATICAL ASSOCIAnON OF AMERICA Martin Gardner Receives JPBM voIome 14, Number 4 Communications Award Martin Gardner has been named the 1994 the United States Navy recipient of the Joint Policy Board for Math and served until the end ematics Communications Award. Author of of the Second World In this Issue numerous books and articles about mathemat War. He began his Sci ics' Gardner isbest known for thelong-running entific Americancolumn "Mathematical Games" column in Scientific in December 1956. 4 CD-ROM American. For nearly forty years, Gardner, The MAA is proud to count Gardneras one of its Textbooks and through his column and books, has exertedan authors. He has published four books with the enormous influence on mathematicians and Calculus Association, with three more in thepipeline. This students of mathematics. September, he begins "Gardner's Gatherings," 6 Open Secrets When asked about the appeal of mathemat a new column in Math Horizons. ics, Gardner said, "It's just the patterns, and Previous JPBM Communications Awards have their order-and their beauty: the way it all gone to James Gleick, author of Chaos; Hugh 8 Section Awards fits together so it all comes out right in the Whitemore for the play Breaking the Code; Ivars end." for Distinguished Peterson, author of several books and associate Teaching Gardner graduated Phi Beta Kappa in phi editor of Science News; and Joel Schneider, losophy from the University of Chicago in content director for the Children's Television 10 Personal Opinion 1936, and then pursued graduate work in the Workshop's Square One TV. -
Boletín De La RSME
Boletín de la RSME Número 297, 16 de enero de 2012 Sumario Noticias de la RSME Noticias de la RSME Encuentro Conjunto RSME-SMM. Antonio Campillo. Torremolinos, Málaga, 17-20 de enero El programa científico consta de veinticuatro • Encuentro Conjunto RSME- La Real Sociedad Matemática Española y la sesiones especiales, ocho conferencias ple- SMM. Torremolinos, Málaga, Sociedad Matemática Mexicana celebran el narias y la conferencia de clausura del profe- 17-20 de enero Segundo Encuentro Conjunto RSME-SMM en sor Federico Mayor Zaragoza con el título preciso “La comunidad científica ante los de- • Noticias del CIMPA el Hotel Meliá Costa del Sol de Torremolinos (Málaga) los próximos días 17, 18, 19 y 20 de safíos presentes”. Como en la primera edi- • Acuerdo entre cuatro insti- enero. El Primer Encuentro Conjunto se ce- ción, el congreso ha programado alrededor tuciones para la creación del lebró en Oaxaca en julio de 2009 y la serie de doscientas conferencias invitadas, la mitad IEMath. Documento de In- continuará cada tres años a partir de 2014, de las cuales corresponden a la parte mexi- cana y la otra mitad a la española. vestigación de la RSME año en el que está prevista la tercera edición en México. El comité organizador está presi- Las conferencias plenarias están a cargo de • Ampliación del orden del dido por Daniel Girela, e integrado por José Samuel Gitler, José Luis Alías, José María día de la Junta General Ordi- Luis Flores, Cristóbal González, Francisco Pérez Izquierdo, Jorge Velasco, María Emilia naria de la RSME Javier Martín Reyes, María Lina Martínez, Caballero, Javier Fernández de Bobadilla, Francisco José Palma, José Ángel Peláez y • Noticia de la COSCE: Nue- Xavier Gómez-Mont y Eulalia Nulart.