Martin Gardner Papers SC0647
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Iterations of the Words-To-Numbers Function
1 2 Journal of Integer Sequences, Vol. 21 (2018), 3 Article 18.9.2 47 6 23 11 Iterations of the Words-to-Numbers Function Matthew E. Coppenbarger School of Mathematical Sciences 85 Lomb Memorial Drive Rochester Institute of Technology Rochester, NY 14623-5603 USA [email protected] Abstract The Words-to-Numbers function takes a nonnegative integer and maps it to the number of characters required to spell the number in English. For each k = 0, 1,..., 8, we determine the minimal nonnegative integer n such that the iterates of n converge to the fixed point (through the Words-to-Numbers function) in exactly k iterations. Our travels take us from some simple answers, to an etymology of the names of large numbers, to Conway/Guy’s established system representing the name of any integer, and finally use generating functions to arrive at a very large number. 1 Introduction and initial definitions The idea for the problem originates in a 1965 book [3, p. 243] by recreational linguistics icon Dmitri Borgmann (1927–85) and in a 1966 article [16] by another icon, recreational mathematician Martin Gardner (1914–2010). Gardner’s article appears again in a book [17, pp. 71–72, 265–267] containing reprinted Gardner articles from Scientific American along with his comments on his reader’s responses. Both Borgmann and Gardner identify the only English number that requires exactly the same number of characters to spell the number as the number represents. Borgmann goes further by identifying numbers in 16 other languages with this property. Borgmann calling such numbers truthful and Gardner calling them honest. -
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. -
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). -
Solving 8 × 8 Domineering
Theoretical Computer Science 230 (2000) 195–206 www.elsevier.com/locate/tcs View metadata, citation and similar papers at core.ac.uk brought to you by CORE Mathematical Games provided by Elsevier - Publisher Connector Solving 8 × 8 Domineering D.M. Breuker, J.W.H.M. Uiterwijk ∗, H.J. van den Herik Department of Computer Science, MATRIKS Research Institute, Universiteit Maastricht, P.O. Box 616, 6200 MD Maastricht, Netherlands Received May 1998; revised October 1998 Communicated by A.S. Fraenkel Abstract So far the game of Domineering has mainly been investigated by combinatorial-games re- searchers. Yet, it is a genuine two-player zero-sum game with perfect information, of which the general formulation is a topic of AI research. In that domain, many techniques have been developed for two-person games, especially for chess. In this article we show that one such technique, i.e., transposition tables, is ÿt for solving standard Domineering (i.e., on an 8×8 board). The game turns out to be a win for the player ÿrst to move. This result coincides with a result obtained independently by Morita Kazuro. Moreover, the technique of transposition tables is also applied to di erently sized m × n boards, m ranging from 2 to 8, and n from m to 9. The results are given in tabular form. Finally, some conclusions on replacement schemes are drawn. In an appendix an analysis of four tournament games is provided. c 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Domineering; Solving games; Transposition tables; Replacement schemes 1. Introduction Domineering is a two-player zero-sum game with perfect information. -
The Magic Collection of David Baldwin
Public Auction #043 The Magic Collection of David Baldwin Including Apparatus, Books, Ephemera, Posters, Automatons and Mystery Clocks Auction Saturday, October 29, 2016 v 10:00 am Exhibition October 26-28 v 10:00 am - 5:00 pm Inquiries [email protected] Phone: 773-472-1442 Potter & Potter Auctions, Inc. 3759 N. Ravenswood Ave. -Suite 121- Chicago, IL 60613 The Magic Collection of David M. Baldwin An Introduction he magic collection of David M. Baldwin (1928 – 2014) Tis a significant one, reaching back to the glorified era of nineteenth century parlor and stage magic that sees its greatest physical achievements embodied in the instruments of mystery we offer here: clocks, automata, and fine conjuring apparatus. It crosses into that treasured phase of the twentieth century when the influence magic held over Western popular culture reached its zenith, and continues on to the present age, where modern practitioners and craftsmen commemorate and reinvigorate old A thoughtful and kind gentleman, he never spoke unkindly about ideas in new forms. anyone. He was modest, generous, and known by many for his philanthropy in supporting the visual and performing arts, medicine, The bedrock of the collection is composed of material the education, and, of course, magic. Among his contributions to other sources of provenance of which will be well known to any conjuring organizations, he was a major benefactor to The Magic Circle, collector or historian of the art: the show, personal artifacts and and was awarded an Honorary Life Member of the Inner Magic Circle. props gathered and used by Maurice F. Raymond (“The Great Raymond”); the library and collection of Walter B. -
By Glenn A. Emelko
A NEW ALGORITHM FOR EFFICIENT SOFTWARE IMPLEMENTATION OF REED-SOLOMON ENCODERS FOR WIRELESS SENSOR NETWORKS by Glenn A. Emelko Submitted to the Office of Graduate Studies at Case Western Reserve University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in ELECTRICAL ENGINEERING Department of Electrical Engineering and Computer Science Case Western Reserve University Glennan 321, 10900 Euclid Ave. Cleveland, Ohio 44106 May 2009 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of _Glenn A. Emelko____________________________________ candidate for the _Doctor of Philosophy_ degree *. (signed)_Francis L. Merat______________________________ (chair of the committee) _Wyatt S. Newman______________________________ _H. Andy Podgurski_____________________________ _William L. Schultz______________________________ _David A. Singer________________________________ ________________________________________________ (date) _March 2, 2009__________ * We also certify that written approval has been obtained for any proprietary material contained therein. i Dedication For my loving wife Liz, and for my children Tom and Leigh Anne. I thank you for giving me love and support and for believing in me every step along my journey. ii Table of Contents Dedication........................................................................................................................... ii List of Figures......................................................................................................................4 -
Mathematical Circus & 'Martin Gardner
MARTIN GARDNE MATHEMATICAL ;MATH EMATICAL ASSOCIATION J OF AMERICA MATHEMATICAL CIRCUS & 'MARTIN GARDNER THE MATHEMATICAL ASSOCIATION OF AMERICA Washington, DC 1992 MATHEMATICAL More Puzzles, Games, Paradoxes, and Other Mathematical Entertainments from Scientific American with a Preface by Donald Knuth, A Postscript, from the Author, and a new Bibliography by Mr. Gardner, Thoughts from Readers, and 105 Drawings and Published in the United States of America by The Mathematical Association of America Copyright O 1968,1969,1970,1971,1979,1981,1992by Martin Gardner. All riglhts reserved under International and Pan-American Copyright Conventions. An MAA Spectrum book This book was updated and revised from the 1981 edition published by Vantage Books, New York. Most of this book originally appeared in slightly different form in Scientific American. Library of Congress Catalog Card Number 92-060996 ISBN 0-88385-506-2 Manufactured in the United States of America For Donald E. Knuth, extraordinary mathematician, computer scientist, writer, musician, humorist, recreational math buff, and much more SPECTRUM SERIES Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Committee on Publications ANDREW STERRETT, JR.,Chairman Spectrum Editorial Board ROGER HORN, Chairman SABRA ANDERSON BART BRADEN UNDERWOOD DUDLEY HUGH M. EDGAR JEANNE LADUKE LESTER H. LANGE MARY PARKER MPP.a (@ SPECTRUM Also by Martin Gardner from The Mathematical Association of America 1529 Eighteenth Street, N.W. Washington, D. C. 20036 (202) 387- 5200 Riddles of the Sphinx and Other Mathematical Puzzle Tales Mathematical Carnival Mathematical Magic Show Contents Preface xi .. Introduction Xlll 1. Optical Illusions 3 Answers on page 14 2. Matches 16 Answers on page 27 3. -
English 271.2: Literature for Young Children Fall 2013 Professor Jan Susina Class Meeting: Tuesday & Thursday 11:00-12:15 P.M
English 271.2: Literature for Young Children Fall 2013 Professor Jan Susina Class Meeting: Tuesday & Thursday 11:00-12:15 p.m. Class Room: Stevenson 347-B Office: Stevenson 402 Office Hours: Tuesday & Thursday 12:30-1:30 p.m. Office Phone: 438-3739 Email: [email protected] . Web site: http://ghostofthetalkingcricket.squarespace.com Tentative Syllabus: Aug. 20 Introduction and Overview to the Course Aug. 22 French Fairy Tales in M.C. Waldrep’s Favorite Fairy Tales: Perrault’s “Cinderella, or the Little Class Slipper,” “Little Red Riding-Hood,” “Toads and Diamonds,” “The Master Cat; or, Puss in Boots.” Madame De Villeneuve’s “Beauty and the Beast,” & Perrault’s “Sleeping Beauty in the Wood” (website) Aug. 27 German Folk Tales in M.C. Waldrep’s Favorite Fairy Tales: Grimm’s” Snowdrop [Snow White],” “Rapunzel,” “Rumplestiltkin,” “The Goose-Girl,” Grimm’s “Little Red-Cap” & “Hansel and Gretel” (website) Aug. 29 Hans Christian Andersen's Literary Fairy Tales in M.C. Waldrep’ Favorite Fairy Tales: “ How to Tell a True Princess (The Princess and the Pea),” “The Nightingale,” “The Ugly Ducking,” “The Story of the Emperor’s New Clothes,” & in Hans Christian Andersen’s The Little Mermaid and Other Fairy Tales “The Little Mermaid” “The Swineherd,” “The Steadfast Tin Soldier,” “The Little Match Girl” Deadline for Sign-up for Children’s Film for Film Paper Sept. 3 English Folk Tales in M.C, Waldrep’s Favorite Fairy Tales: “Jack and the Beanstalk,” “The Ratcatcher [Pied Piper of Hamelin],” & “Three Little Pigs” Sept. 5 American Fairy Tales: Walt Disney’s film adaptation of fairy tales: “Steamboat Willie” “The Three Little Pigs” “Snow White and the Seven “Dwarfs,” “Cinderella” & “The Little Mermaid” Sept. -
Catalogo 2021 Orecchio Acerbo Editore
orecchio acerbo editore catalogo 2021 albi illustrati Noi umaNi uN lupo alla fiNEstra duE piccoli orsi NEW NEW NEW di Dieter Böge di Katerina Gorelik di Ylla illustrazioni Bernd Mölck-Tassel dai 3 anni in su | € 14.00 dai 3 anni in su | € 15.00 dai 5 anni in su | € 19.50 pp. 60 | cm. 23 x 28 pp. 40 | cm. 22 x 28 pp. 160 | cm. 17 x 21 ISBN 9788832070767 | Novembre 2021 ISBN 9788832070736 | Novembre 2021 ISBN 9788832070675 | Novembre 2021 ridErE E sorridErE Gli altri aNimali | GraNdi avvENturE GraNdi tEmi | raccoNtarE il prEsENtE Un quartiere che sembra molto tranquillo. Due piccoli orsi, fratello e sorella, si stanno Alcuni di noi possono fare cose incredibili, Abitato quasi solo da animali: c’è la signora affacciando per la prima volta dalla loro tana, parliamo oltre seimila lingue diverse e non Porcella, ottima cuoca, il dottor Topo, che spesso all’arrivo della primavera. La loro mamma sta per sempre ci capiamo, ma insieme possiamo riuscire visita a casa, il signor Pinguino, che sguazza nella andare in cerca di buon miele selvatico in imprese che nessun’altra creatura è in grado vasca e il signor Volpe che prepara la sua colazione e li ammonisce a non allontanarsi perché di affrontare. Possiamo essere crudeli o gentili, preferita. In quelle villette però ci abitano anche il mondo è ancora troppo grande per loro. Quelle curiosi o noiosi, felici o arrabbiati; c’è chi fa di un drago, una strega brava nel preparare pozioni raccomandazioni però vengono presto dimenticate tutto per trovare una casa o chi vive scoprendo e pure un lupo pieno di denti spesso passa di lì. -
IJR-1, Mathematics for All ... Syed Samsul Alam
January 31, 2015 [IISRR-International Journal of Research ] MATHEMATICS FOR ALL AND FOREVER Prof. Syed Samsul Alam Former Vice-Chancellor Alaih University, Kolkata, India; Former Professor & Head, Department of Mathematics, IIT Kharagpur; Ch. Md Koya chair Professor, Mahatma Gandhi University, Kottayam, Kerala , Dr. S. N. Alam Assistant Professor, Department of Metallurgical and Materials Engineering, National Institute of Technology Rourkela, Rourkela, India This article briefly summarizes the journey of mathematics. The subject is expanding at a fast rate Abstract and it sometimes makes it essential to look back into the history of this marvelous subject. The pillars of this subject and their contributions have been briefly studied here. Since early civilization, mathematics has helped mankind solve very complicated problems. Mathematics has been a common language which has united mankind. Mathematics has been the heart of our education system right from the school level. Creating interest in this subject and making it friendlier to students’ right from early ages is essential. Understanding the subject as well as its history are both equally important. This article briefly discusses the ancient, the medieval, and the present age of mathematics and some notable mathematicians who belonged to these periods. Mathematics is the abstract study of different areas that include, but not limited to, numbers, 1.Introduction quantity, space, structure, and change. In other words, it is the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. Mathematicians seek out patterns and formulate new conjectures. They resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity. -
An Interview with Visualization Pioneer Ben Shneiderman
6/23/2020 The purpose of visualization is insight, not pictures: An interview with visualization pioneer Ben Shneiderman The purpose of visualization is insight, not pictures: An interview with visualization pioneer Ben Shneiderman Jessica Hullman Follow Mar 12, 2019 · 13 min read Few people in visualization research have had careers as long and as impactful as Ben Shneiderman. We caught up with Ben over email in between his travels to get his take on visualization research, what’s worked in his career, and his advice for practitioners and researchers. Enjoy! Multiple Views: One of the main purposes of this blog is to explain to people what visualization research is to practitioners and, possibly, laypeople. How would you answer the question “what is visualization research”? Ben S: First let me define information visualization and its goals, then I can describe visualization research. Information visualization is a powerful interactive strategy for exploring data, especially when combined with statistical methods. Analysts in every field can use interactive information visualization tools for: more effective detection of faulty data, missing data, unusual distributions, and anomalies deeper and more thorough data analyses that produce profounder insights, and richer understandings that enable researchers to ask bolder questions. Like a telescope or microscope that increases your perceptual abilities, information visualization amplifies your cognitive abilities to understand complex processes so as to support better decisions. In our best -
Treemap Art Project
EVERY ALGORITHM HAS ART IN IT Treemap Art Project By Ben Shneiderman Visit Exhibitions @ www.cpnas.org 2 tree-structured data as a set of nested rectangles) which has had a rippling impact on systems of data visualization since they were rst conceived in the 1990s. True innovation, by denition, never rests on accepted practices but continues to investigate by nding new In his book, “Visual Complexity: Mapping Patterns of perspectives. In this spirit, Shneiderman has created a series Information”, Manuel Lima coins the term networkism which of prints that turn our perception of treemaps on its head – an he denes as “a small but growing artistic trend, characterized eort that resonates with Lima’s idea of networkism. In the by the portrayal of gurative graph structures- illustrations of exhibition, Every AlgoRim has ART in it: Treemap Art network topologies revealing convoluted patterns of nodes and Project, Shneiderman strips his treemaps of the text labels to links.” Explaining networkism further, Lima reminds us that allow the viewer to consider their aesthetic properties thus the domains of art and science are highly intertwined and that laying bare the fundamental property that makes data complexity science is a new source of inspiration for artists and visualization eective. at is to say that the human mind designers as well as scientists and engineers. He states that processes information dierently when it is organized visually. this movement is equally motivated by the unveiling of new In so doing Shneiderman seems to daringly cross disciplinary is exhibit is a project of the knowledge domains as it is by the desire for the representation boundaries to wear the hat of the artist – something that has Cultural Programs of the National Academy of Sciences of complex systems.