ACM Bytecast Don Knuth - Episode 2 Transcript
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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. -
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 . -
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. -
Covering Systems
Covering Systems by Paul Robert Emanuel Bachelor of Science (Hons.), Bachelor of Commerce Macquarie University 2006 FACULTY OF SCIENCE This thesis is presented for the degree of Doctor of Philosophy Department of Mathematics 2011 This thesis entitled: Covering Systems written by Paul Robert Emanuel has been approved for the Department of Mathematics Dr. Gerry Myerson Prof. Paul Smith Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. Thesis directed by Senior Lecturer Dr. Gerry Myerson and Prof. Paul Smith. Statement of Candidate I certify that the work in this thesis entitled \Covering Systems" has not previously been submitted for a degree nor has it been submitted as part of requirements for a degree to any other university or institution other than Macquarie University. I also certify that the thesis is an original piece of research and it has been written by me. Any help and assistance that I have received in my research work and the prepa- ration of the thesis itself have been appropriately acknowledged. In addition, I certify that all information sources and literature used are indicated in the thesis. Paul Emanuel (40091686) March 2011 Summary Covering systems were introduced by Paul Erd}os[8] in 1950. A covering system is a collection of congruences of the form x ≡ ai(mod mi) whose union is the integers. These can then be specialised to being incongruent (that is, having distinct moduli), or disjoint, in which each integer satisfies exactly one congruence. -
Visual Sudoku Solver
Visual Sudoku Solver Nikolas Pilavakis MInf Project (Part 1) Report Master of Informatics School of Informatics University of Edinburgh 2020 3 Abstract In this report, the design, implementation and testing of a visual Sudoku solver app for android written in Kotlin is discussed. The produced app is capable of recog- nising a Sudoku puzzle using the phone’s camera and finding its solution(s) using a backtracking algorithm. To recognise the puzzle, multiple vision and machine learn- ing techniques were employed, using the OpenCV library. Techniques used include grayscaling, adaptive thresholding, Gaussian blur, contour edge detection and tem- plate matching. Digits are recognised using AutoML, giving promising results. The chosen methods are explained and compared to possible alternatives. Each component of the app is then evaluated separately, with a variety of methods. A very brief user evaluation was also conducted. Finally, the limitations of the implemented app are discussed and future improvements are proposed. 4 Acknowledgements I would like to express my sincere gratitude towards my supervisor, professor Nigel Topham for his continuous guidance and support throughout the academic year. I would also like to thank my family and friends for the constant motivation. Table of Contents 1 Introduction 7 2 Background 9 2.1 Sudoku Background . 9 2.2 Solving the Sudoku . 10 2.3 Sudoku recognition . 12 2.4 Image processing . 13 2.4.1 Grayscale . 13 2.4.2 Thresholding . 13 2.4.3 Gaussian blur . 14 3 Design 17 3.1 Design decisions . 17 3.1.1 Development environment . 17 3.1.2 Programming language . 17 3.1.3 Solving algorithm . -
Types in Logic, Mathematics, and Programming from the Handbook of Proof Theory
CHAPTER X Types in Logic, Mathematics and Programming Robert L. Constable Computer Science Department, Cornell University Ithaca, New York 1~853, USA Contents 1. Introduction ..................................... 684 2. Typed logic ..................................... 692 3. Type theory ..................................... 726 4. Typed programming languages ........................... 754 5. Conclusion ...................................... 766 6. Appendix ...................................... 768 References ........................................ 773 HANDBOOK OF PROOF THEORY Edited by S. R. Buss 1998 Elsevier Science B.V. All rights reserved 684 R. Constable 1. Introduction Proof theory and computer science are jointly engaged in a remarkable enter- prise. Together they provide the practical means to formalize vast amounts of mathematical knowledge. They have created the subject of automated reasoning and a digital computer based proof technology; these enable a diverse community of mathematicians, computer scientists, and educators to build a new artifact a globally distributed digital library of formalized mathematics. I think that this artifact signals the emergence of a new branch of mathematics, perhaps to be called Formal Mathematics. The theorems of this mathematics are completely formal and are processed digitally. They can be displayed as beautifully and legibly as journal quality mathematical text. At the heart of this library are completely formal proofs created with computer assistance. Their correctness is based on the axioms and rules of various foundational theories; this formal accounting of correctness supports the highest known standards of rigor and truth. The need to formally relate results in different foundational theories opens a new topic in proof theory and foundations of mathematics. Formal proofs of interesting theorems in current foundational theories are very large rigid objects. Creating them requires the speed and memory capacities of modern computer hardware and the expressiveness of modern software. -
Concrete Mathematics: Foundation for Computer Science Free Download
CONCRETE MATHEMATICS: FOUNDATION FOR COMPUTER SCIENCE FREE DOWNLOAD Ronald Graham,Oren Patashnik,Donald Ervin Knuth | 672 pages | 10 Mar 1994 | Pearson Education (US) | 9780201558029 | English | Boston, United States Concrete Mathematics: A Foundation for Computer Science, Second Edition Seller Inventory ING Reprinted as chapter 18 of the book Digital Typography. Table of contents Product information. The second edition includes important new material about the revolutionary Gosper-Zeilberger algorithm for mechanical summation. Midpoint between a discrete math text and dedicated algorithms text. Original Title. However, I promise to reply in due time. By continuing, you're agreeing to use of cookies. Dewey Decimal. Concrete Mathematics: Foundation for Computer Science response to the widespread use of the first edition as a reference book, the Concrete Mathematics: Foundation for Computer Science and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Credits for Exercises. Apr 15, Bishu rated it it was amazing. Donald Knuth. Concrete Mathematics: Foundation for Computer Science Reviews. Dust Jacket Condition: New. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the Tex and Metafont systems for computer typesetting, and for his prolific and influential writing. If you like books and love to build cool products, we may be looking for you. This second edition includes important new material about mechanical summation. It is an indispensable text and reference not only Concrete Mathematics: Foundation for Computer Science computer scientists - the authors themselves rely heavily on it! It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! Other Editions Example 4: A convoluted recurrence. -
The Art of Computer Programming, Vol. 4A
THE ART OF COMPUTER PROGRAMMING Missing pages from select printings of Knuth, The Art of Computer Programming, Volume 4A (ISBN-13: 9780201038040 / ISBN-10: 0201038048). Copyright © 2011 Pearson Education, Inc. All rights reserved. DONALD E. KNUTH Stanford University 6 77 ADDISON–WESLEY Missing pages from select printings of Knuth, The Art of Computer Programming, Volume 4A (ISBN-13: 9780201038040 / ISBN-10: 0201038048). Copyright © 2011 Pearson Education, Inc. All rights reserved. Volume 4A / Combinatorial Algorithms, Part 1 THE ART OF COMPUTER PROGRAMMING Boston · Columbus · Indianapolis · New York · San Francisco Amsterdam · Cape Town · Dubai · London · Madrid · Milan Munich · Paris · Montréal · Toronto · Mexico City · São Paulo Delhi · Sydney · Hong Kong · Seoul · Singapore · Taipei · Tokyo Missing pages from select printings of Knuth, The Art of Computer Programming, Volume 4A (ISBN-13: 9780201038040 / ISBN-10: 0201038048). Copyright © 2011 Pearson Education, Inc. All rights reserved. The poem on page 437 is quoted from The Golden Gate by Vikram Seth (New York: Random House, 1986), copyright ⃝c 1986 by Vikram Seth. The author and publisher have taken care in the preparation of this book, but make no expressed or implied warranty of any kind and assume no responsibility for errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of the use of the information or programs contained herein. The publisher offers excellent discounts on this book when ordered in quantity forbulk purposes or special sales, which may include electronic versions and/or custom covers and content particular to your business, training goals, marketing focus, and branding interests. For more information, please contact: U.S. -
Math Never Seen
TUGboat, Volume 31 (2010), No. 2 221 Math never seen ò Quality criteria Johannes Küster What makes a notation superior to another? What makes a symbol successful (in the sense that other mathemati- Abstract cians accept and adopt it)? e following list gives the Why have certain mathematical symbols and notations most important quality criteria. A mathematical symbol gained general acceptance while others fell into oblivion? or notation should be: To answer this question I present quality criteria for • readable, clear and simple mathematical symbols. I show many unknown, little- • needed known or little-used notations, some of which deserve • international (or derived from Latin) much wider use. • mnemonic I also show some new symbols and some ideas for new notations, especially for some well-known concepts • writable which lack a good notation (Stirling numbers, greatest • pronounceable common divisor and least common multiple). • similar and consistent • distinct and unambiguous • adaptable Ô Introduction • available For TEX’s "20th birthday it seems appropriate to present is list is certainly not exhaustive, but these are the most some ne points of mathematical typography and some important points. Not all criteria are equally important, ideas for new symbols and notations. Let’s start with a and some may conict with others, so few symbols really quotation from e METAFONTbook [ , p. ]: fulll all criteria. — Let me explain each point in turn. Above all, a notation should be readable — but what “Now that authors have for the rst time the power constitutes readability? Certainly it comprises clear and to invent new symbols with great ease, and to have simple. -
Performance and Scalability of Sudoku Solvers
Performance and Scalability of Sudoku Solvers Prestanda och Skalbarhet för Sudoku Lösare VIKSTÉN, HENRIK NORRA STATIONSGATAN 99 STOCKHOLM 113 64 073 643 76 29 [email protected] MATTSSON, VIKTOR FURUSUNDSGATAN 10 STOCKHOLM 115 37 073 061 74 90 [email protected] Bachelor’s Thesis at NADA Supervisor: Mosavat, Vahid Examiner: Björkman, Mårten TRITA xxx yyyy-nn Abstract This paper aims to clarify the differences in algorithm de- sign with a goal of solving sudoku. A few algorithms were chosen suitable to the problem, yet different from one an- other. To take an everyday puzzle and utilize common com- puter science algorithms and learn more about them. Get relevant data to see how they perform in situations, how easily they can be modified and used in larger sudokus. Also how their performance scales when the puzzle grows larger. From the results Dancing links was the fastest and scaled best of the algorithms tested, while Brute-force and Simu- lated annealing struggled keeping consistent results. Referat Prestanda och Skalbarhet för Sudoku Lösare Detta dokument syftar till att klargöra skillnaderna i algo- ritmer med målet att lösa sudoku. Välja ett par olika algo- rithmer lämpliga för problemet, men som samtidigt skiljer sig från varandra. Att ta ett dagligt pussel och utnyttja van- ligt förekommande algoritmer inom datavetenskap och lära sig mer om dem. Få relevant data och se hur de presterar i olika situationer, hur lätt de kan modifieras och användas i större Sudokus. Även hur deras prestanda skalar när puss- let blir större. Dancing links var den snabbaste algoritmen och skalade bäst av de som testades. -
The Concrete Mathematics of Microfluidic Mixing, Part I
The Concrete Mathematics of Microfluidic Mixing, Part I∗ UNM TR-CS-2006-09 Jennifer Sager, Maxwell Young, and Darko Stefanovic Department of Computer Science University of New Mexico Albuquerque, NM 87131 May 1, 2006 ∗Supplementary Material to Characterization of Transverse Channel Concentration Profiles Obtainable With a Class of Microfluidic Networks, published in Langmuir, 22(9), 4452–4455 (2006) Abstract We analyze mathematically a previously reported class of passive microfluidic mixing networks. The networks produce nonhomogeneous concentrations in the out- put channel, resulting in diverse concentration profiles. We formally prove that all profiles obtainable with this class of networks can be described as polynomials of degree no higher than the number of input channels less one. We derive explicit for- mulas for the calculation of resultant output concentration profiles and conversely for the calculation of input concentrations needed to obtain set output profiles. 1 Introduction Microfluidic technology presents the opportunity for low-cost fabrication of sophisticated reaction assemblies in which chemical and biochemical reactions, including open-system reactions, can be performed with very small reactant volumes and with high volumetric accuracy. For instance, microfluidic assemblies have found uses in the design of reac- tion chambers for DNA computing [14, 15, 4]. Fluid flow in microfluidic channels is entirely laminar, owing to typical channel cross-sections, flow velocities, and fluid prop- erties. Therefore, when two miscible flows are merged into a common channel, they mix only by diffusion. This means that mixing is generally slower than with turbulent flows and special care must be taken to achieve complete mixing of flows (assuming this is desired).