Donald Knuth Fletcher Jones Professor of Computer Science, Emeritus Curriculum Vitae Available Online
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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). -
Surviving the TEX Font Encoding Mess Understanding The
Surviving the TEX font encoding mess Understanding the world of TEX fonts and mastering the basics of fontinst Ulrik Vieth Taco Hoekwater · EuroT X ’99 Heidelberg E · FAMOUS QUOTE: English is useful because it is a mess. Since English is a mess, it maps well onto the problem space, which is also a mess, which we call reality. Similary, Perl was designed to be a mess, though in the nicests of all possible ways. | LARRY WALL COROLLARY: TEX fonts are mess, as they are a product of reality. Similary, fontinst is a mess, not necessarily by design, but because it has to cope with the mess we call reality. Contents I Overview of TEX font technology II Installation TEX fonts with fontinst III Overview of math fonts EuroT X ’99 Heidelberg 24. September 1999 3 E · · I Overview of TEX font technology What is a font? What is a virtual font? • Font file formats and conversion utilities • Font attributes and classifications • Font selection schemes • Font naming schemes • Font encodings • What’s in a standard font? What’s in an expert font? • Font installation considerations • Why the need for reencoding? • Which raw font encoding to use? • What’s needed to set up fonts for use with T X? • E EuroT X ’99 Heidelberg 24. September 1999 4 E · · What is a font? in technical terms: • – fonts have many different representations depending on the point of view – TEX typesetter: fonts metrics (TFM) and nothing else – DVI driver: virtual fonts (VF), bitmaps fonts(PK), outline fonts (PFA/PFB or TTF) – PostScript: Type 1 (outlines), Type 3 (anything), Type 42 fonts (embedded TTF) in general terms: • – fonts are collections of glyphs (characters, symbols) of a particular design – fonts are organized into families, series and individual shapes – glyphs may be accessed either by character code or by symbolic names – encoding of glyphs may be fixed or controllable by encoding vectors font information consists of: • – metric information (glyph metrics and global parameters) – some representation of glyph shapes (bitmaps or outlines) EuroT X ’99 Heidelberg 24. -
Tug2007-Slides-2X2.Pdf
Dedication ÅEÌ Professor Donald Knuth (Stanford) Extending TEX and Professor William Kahan (Berkeley) ÅEÌAFÇÆÌ with Floating-Point Arithmetic AF Nelson H. F. Beebe ÇÆÌ X and Department of Mathematics University of Utah E T Salt Lake City, UT 84112-0090 USA TEX Users Group Conference 2007 talk. – p. 1/30 TEX Users Group Conference 2007 talk. – p. 2/30 ÅEÌAFÇÆÌ Arithmetic in TEX and Arithmetic in ÅEÌAFÇÆÌ ÅEÌ ÅEÌ Binary integer arithmetic with 32 bits (T X \count ÅEÌAFÇÆÌ restricts input numbers to 12 integer bits: ≥ E registers) % mf expr Fixed-point arithmetic with sign bit, overflow bit, 14 gimme an expr: 4095 >> 4095 ≥ gimme an expr: 4096 integer bits, and 16 fractional bits (T X \dimen, E ! Enormous number has been reduced. \muskip, and \skip registers) AF >> 4095.99998 AF Overflow detected on division and multiplication but not gimme an expr: infinity >> 4095.99998 on addition (flaw (NHFB), feature (DEK)) gimme an expr: epsilon >> 0.00002 gimme an expr: 1/epsilon Gyrations sometimes needed in ÅEÌAFÇÆÌ to work ÇÆÌ ! Arithmetic overflow. ÇÆÌ Xwith and fixed-point numbers X and >> 32767.99998 Uh, oh.E A little while ago one of the quantities gimmeE an expr: 1/3 >> 0.33333 that I was computing got too large, so I’m afraid gimme an expr: 3*(1/3) >> 0.99998 T T your answers will be somewhat askew. You’ll gimme an expr: 1.2 • 2.3 >> •1.1 probably have to adopt different tactics next gimme an expr: 1.2 • 2.4 >> •1.2 time. But I shall try to carry on anyway. -
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. -
Leading the Way in Scientific Computing. Addison-Wesley. I When Looking for the Best in Scientific Computing, You've Come to Rely on Addison-Wesley
Leading the way in scientific computing. Addison-Wesley. I When looking for the best in scientific computing, you've come to rely on Addison-Wesley. I Take a moment to see how we've made our list even stronger. The LATEX Companion sional programming languages. This book is the definitive user's Michael Goossens, Frank Mittelbach, and Alexander Samarin guide and reference manual for the CWEB system. This book is packed with information needed to use LATEX even 1994 (0-201 -57569-8) approx. 240 pp. Softcover more productively. It is a true companion to Leslie Lamport's users guide as well as a valuable complement to any LATEX introduction. Concrete Mathematics. Second Edition Describes the new LATEX standard. Ronald L. Graham, Donald E. Knuth, and Oren Patashnick 1994 (0-201 -54 199-8) 400 pp. Softcover With improvements to almost every page, the second edition of this classic text and reference introduces the mathematics that LATEX: A Document Preparation System, Second Edition supports advanced computer programming. Leslie Lamport 1994 (0-201 -55802-5) 672 pp. Hardcover The authoritative user's guide and reference manual has been revised to document features now available in the new standard Applied Mathematics@: Getting Started, Getting It Done software release-LATEX~E.The new edition features additional styles William T. Shaw and Jason Tigg and functions, improved font handling, and much more. This book shows how Mathematics@ can be used to solve problems in 1994 (0-201-52983-1) 256 pp. Softcover the applied sciences. Provides a wealth of practical tips and techniques. 1 994 (0-201 -542 1 7-X) 320 pp. -
Solving Sudoku with Dancing Links
Solving Sudoku with Dancing Links Rob Beezer [email protected] Department of Mathematics and Computer Science University of Puget Sound Tacoma, Washington USA Stellenbosch University October 8, 2010 Available at http://buzzard.pugetsound.edu/talks.html Example: Combinatorial Enumeration Create all permutations of the set f0; 1; 2; 3g Simple example to demonstrate key ideas Creation, cardinality, existence? There are more efficient methods for this example Rob Beezer (U Puget Sound) Solving Sudoku with Dancing Links Stellenbosch U October 2010 2 / 37 Brute Force Backtracking BLACK = Forward BLUE = Solution RED = Backtrack root 0 1 2 0 1 3 3 0 2 1 0 2 3 3 0 3 1 0 3 1 0 2 0 0 1 2 2 0 1 3 0 2 1 3 0 2 3 0 3 1 3 0 3 3 1 0 2 1 0 0 0 1 2 0 1 0 2 1 0 2 0 3 1 0 3 1 0 2 0 0 1 2 3 0 0 2 0 0 3 0 1 0 2 2 0 1 0 1 2 0 2 0 2 2 0 3 0 3 2 root 1 0 2 0 1 0 0 1 0 2 0 0 2 0 3 0 0 3 2 0 1 1 0 2 3 0 1 0 1 3 0 2 0 2 3 0 3 0 3 2 1 0 1 0 2 . 0 1 1 0 1 3 0 0 2 1 0 2 3 0 0 3 1 0 3 2 1 1 0 0 . -
Typeset MMIX Programs with TEX Udo Wermuth Abstract a TEX Macro
TUGboat, Volume 35 (2014), No. 3 297 Typeset MMIX programs with TEX Example: In section 9 the lines \See also sec- tion 10." and \This code is used in section 24." are given. Udo Wermuth No such line appears in section 10 as it only ex- tends the replacement code of section 9. (Note that Abstract section 10 has in its headline the number 9.) In section 24 the reference to section 9 stands for all of ATEX macro package is presented as a literate pro- the eight code lines stated in sections 9 and 10. gram. It can be included in programs written in the If a section is not used in any other section then languages MMIX or MMIXAL without affecting the it is a root and during the extraction of the code a assembler. Such an instrumented file can be pro- file is created that has the name of the root. This file cessed by TEX to get nicely formatted output. Only collects all the code in the sequence of the referenced a new first line and a new last line must be entered. sections from the code part. The collection process And for each end-of-line comment a flag is set to for all root sections is called tangle. A second pro- indicate that the comment is written in TEX. cess is called weave. It outputs the documentation and the code parts as a TEX document. How to read the following program Example: The following program has only one The text that starts in the next chapter is a literate root that is defined in section 4 with the headline program [2, 1] written in a style similar to noweb [7]. -
Math Symbol Tables
APPENDIX A I Math symbol tables A.I Hebrew letters Type: Print: Type: Print: \aleph ~ \beth :J \daleth l \gimel J All symbols but \aleph need the amssymb package. 346 Appendix A A.2 Greek characters Type: Print: Type: Print: Type: Print: \alpha a \beta f3 \gamma 'Y \digamma F \delta b \epsilon E \varepsilon E \zeta ( \eta 'f/ \theta () \vartheta {) \iota ~ \kappa ,.. \varkappa x \lambda ,\ \mu /-l \nu v \xi ~ \pi 7r \varpi tv \rho p \varrho (} \sigma (J \varsigma <; \tau T \upsilon v \phi ¢ \varphi 'P \chi X \psi 'ljJ \omega w \digamma and \ varkappa require the amssymb package. Type: Print: Type: Print: \Gamma r \varGamma r \Delta L\ \varDelta L.\ \Theta e \varTheta e \Lambda A \varLambda A \Xi ~ \varXi ~ \Pi II \varPi II \Sigma 2: \varSigma E \Upsilon T \varUpsilon Y \Phi <I> \varPhi t[> \Psi III \varPsi 1ft \Omega n \varOmega D All symbols whose name begins with var need the amsmath package. Math symbol tables 347 A.3 Y1EX binary relations Type: Print: Type: Print: \in E \ni \leq < \geq >'" \11 « \gg \prec \succ \preceq \succeq \sim \cong \simeq \approx \equiv \doteq \subset c \supset \subseteq c \supseteq \sqsubseteq c \sqsupseteq \smile \frown \perp 1- \models F \mid I \parallel II \vdash f- \dashv -1 \propto <X \asymp \bowtie [Xl \sqsubset \sqsupset \Join The latter three symbols need the latexsym package. 348 Appendix A A.4 AMS binary relations Type: Print: Type: Print: \leqs1ant :::::; \geqs1ant ): \eqs1ant1ess :< \eqs1antgtr :::> \lesssim < \gtrsim > '" '" < > \lessapprox ~ \gtrapprox \approxeq ~ \lessdot <:: \gtrdot Y \111 «< \ggg »> \lessgtr S \gtr1ess Z < >- \lesseqgtr > \gtreq1ess < > < \gtreqq1ess \lesseqqgtr > < ~ \doteqdot --;- \eqcirc = .2.. -
Zapfcoll Minikatalog.Indd
Largest compilation of typefaces from the designers Gudrun and Hermann Zapf. Most of the fonts include the Euro symbol. Licensed for 5 CPUs. 143 high quality typefaces in PS and/or TT format for Mac and PC. Colombine™ a Alcuin™ a Optima™ a Marconi™ a Zapf Chancery® a Aldus™ a Carmina™ a Palatino™ a Edison™ a Zapf International® a AMS Euler™ a Marcon™ a Medici Script™ a Shakespeare™ a Zapf International® a Melior™ a Aldus™ a Melior™ a a Melior™ Noris™ a Optima™ a Vario™ a Aldus™ a Aurelia™ a Zapf International® a Carmina™ a Shakespeare™ a Palatino™ a Aurelia™ a Melior™ a Zapf book® a Kompakt™ a Alcuin™ a Carmina™ a Sistina™ a Vario™ a Zapf Renaissance Antiqua® a Optima™ a AMS Euler™ a Colombine™ a Alcuin™ a Optima™ a Marconi™ a Shakespeare™ a Zapf Chancery® Aldus™ a Carmina™ a Palatino™ a Edison™ a Zapf international® a AMS Euler™ a Marconi™ a Medici Script™ a Shakespeare™ a Zapf international® a Aldus™ a Melior™ a Zapf Chancery® a Kompakt™ a Noris™ a Zapf International® a Car na™ a Zapf book® a Palatino™ a Optima™ Alcuin™ a Carmina™ a Sistina™ a Melior™ a Zapf Renaissance Antiqua® a Medici Script™ a Aldus™ a AMS Euler™ a Colombine™ a Vario™ a Alcuin™ a Marconi™ a Marconi™ a Carmina™ a Melior™ a Edison™ a Shakespeare™ a Zapf book® aZapf international® a Optima™ a Zapf International® a Carmina™ a Zapf Chancery® Noris™ a Optima™ a Zapf international® a Carmina™ a Sistina™ a Shakespeare™ a Palatino™ a a Kompakt™ a Aurelia™ a Melior™ a Zapf Renaissance Antiqua® Antiqua® a Optima™ a AMS Euler™ a Introduction Gudrun & Hermann Zapf Collection The Gudrun and Hermann Zapf Collection is a special edition for Macintosh and PC and the largest compilation of typefaces from the designers Gudrun and Hermann Zapf. -
Posterboard Presentation
Dancing Links and Sudoku A Java Sudoku Solver By: Jonathan Chu Adviser: Mr. Feinberg Algorithm by: Dr. Donald Knuth Sudoku Sudoku is a logic puzzle. On a 9x9 grid with 3x3 regions, the digits 1-9 must be placed in each cell such that every row, column, and region contains only one instance of the digit. Placing the numbers is simply an exercise of logic and patience. Here is an example of a puzzle and its solution: Images from web Nikoli Sudoku is exactly a subset of a more general set of problems called Exact Cover, which is described on the left. Dr. Donald Knuth’s Dancing Links Algorithm solves an Exact Cover situation. The Exact Cover problem can be extended to a variety of applications that need to fill constraints. Sudoku is one such special case of the Exact Cover problem. I created a Java program that implements Dancing Links to solve Sudoku puzzles. Exact Cover Exact Cover describes problems in h A B C D E F G which a mtrix of 0’s and 1’s are given. Is there a set of rows that contain exactly one 1 in each column? The matrix below is an example given by Dr. Knuth in his paper. Rows 1, 4, and 5 are a solution set. 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 We can represent the matrix with toriodal doubly-linked lists as shown above. -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
An Interview with Donald Knuth 33
Bijlage M An Interview with Donald Knuth 33 An Interview with Donald Knuth DDJ chats with one of the world's leading computer scientists Jack Woehr Dr. Dobb's Journal∗ [email protected] April 1996 For over 25 years, Donald E. Knuth has generally been honorable term, but to some people a computer program- considered one of the world's leading computer scientists. mer is somebody who just follows instructions without un- Although he's authored more than 150 publications, it is derstanding what he's doing, one who just knows how to Knuth's three-volume The Art of Computer Programming get through the idiosyncrasies of some language. which has become a staple on every programmer's book- To me, a computer scientist is somebody who has a way shelf. In 1974, Knuth was the recipient of computer sci- of thinking, which resonates with computer programming. ence's most prestigious prize, the Turing Award. He also The way a computer scientist views knowledge in general received the National Medal of Science in 1979. is different from the way a mathematician views knowl- In addition to his work developing fundamental algorithms edge, which is different from the way a physicist views for computer programming, Knuth was a pioneer in com- knowledge, which is different from the way a chemist, puter typesetting with his TEX, METAFONT, and WEB ap- lawyer, or poet views knowledge. plications. He has written on topics as singular as ancient There's about one person in every ®fty who has this pecu- Babylonian algorithms and has penned a novel.