Concrete Mathematics

A Foundation for Computer Science
Author: Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik
Publisher: Addison-Wesley Professional
ISBN: 9780201558029
Category: Computers
Page: 657
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This book, updated and improved, introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills--the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. It is an indispensable text and reference, not only for computer scientists but for all technical professionals in virtually every discipline.

Fundamentals of Discrete Math for Computer Science

A Problem-Solving Primer
Author: Tom Jenkyns,Ben Stephenson
Publisher: Springer
ISBN: 3319701517
Category: Computers
Page: 512
View: 2026

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This clearly written textbook presents an accessible introduction to discrete mathematics for computer science students, offering the reader an enjoyable and stimulating path to improve their programming competence. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Its motivational and interactive style provokes a conversation with the reader through a questioning commentary, and supplies detailed walkthroughs of several algorithms. This updated and enhanced new edition also includes new material on directed graphs, and on drawing and coloring graphs, in addition to more than 100 new exercises (with solutions to selected exercises). Topics and features: assumes no prior mathematical knowledge, and discusses concepts in programming as and when they are needed; designed for both classroom use and self-study, presenting modular and self-contained chapters that follow ACM curriculum recommendations; describes mathematical processes in an algorithmic manner, often supported by a walkthrough demonstrating how the algorithm performs the desired task; includes an extensive set of exercises throughout the text, together with numerous examples, and shaded boxes highlighting key concepts; selects examples that demonstrate a practical use for the concept in question. Students embarking on the start of their studies of computer science will find this book to be an easy-to-understand and fun-to-read primer, ideal for use in a mathematics course taken concurrently with their first programming course.

Mathematics for the Analysis of Algorithms


Author: Daniel H. Greene,Donald E. Knuth
Publisher: Springer Science & Business Media
ISBN: 0817647295
Category: Computers
Page: 132
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This monograph collects some fundamental mathematical techniques that are required for the analysis of algorithms. It builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions. The authors cover recurrence relations, operator methods, and asymptotic analysis in a format that is concise enough for easy reference yet detailed enough for those with little background with the material.

Combinatorics for Computer Science


Author: Stanley Gill Williamson
Publisher: Courier Corporation
ISBN: 9780486420769
Category: Mathematics
Page: 479
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Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.

A Short Course in Discrete Mathematics


Author: Edward A. Bender,S. Gill Williamson
Publisher: Courier Corporation
ISBN: 0486439461
Category: Mathematics
Page: 240
View: 9824

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What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index.

Companion to Concrete Mathematics


Author: Z. A. Melzak
Publisher: Courier Corporation
ISBN: 0486457818
Category: Mathematics
Page: 683
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A two-volume treatment in a single binding, this supplementary text stresses intuitive appeal and ingenuity. It employs physical analogies, encourages problem formulation, and supplies problem-solving methods. 1973 and 1976 editions.

Discrete Mathematics


Author: Martin Aigner
Publisher: American Mathematical Soc.
ISBN: 9780821886151
Category: Mathematics
Page: 388
View: 530

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The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints andsolutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student ofmathematics and computer science as well as to teachers of these topics. --Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of theMAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.

Foundation Mathematics for Computer Science

A Visual Approach
Author: John Vince
Publisher: Springer
ISBN: 3319214373
Category: Computers
Page: 334
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John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts. Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

The MMIX Supplement

Supplement to The Art of Computer Programming Volumes 1, 2, 3 by Donald E. Knuth
Author: Martin Ruckert
Publisher: Addison-Wesley Professional
ISBN: 013399287X
Category: Computers
Page: 224
View: 7780

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The MMIX Supplement: Supplement to The Art of Computer Programming Volumes 1, 2, 3 by Donald E. Knuth “I encourage serious programmers everywhere to sharpen their skills by devouring this book.” –Donald E. Knuth In the first edition of Volume 1 of The Art of Computer Programming, Donald E. Knuth introduced the MIX computer and its machine language: a teaching tool that powerfully illuminated the inner workings of the algorithms he documents. Later, with the publication of his Fascicle 1, Knuth introduced MMIX: a modern, 64-bit RISC replacement to the now-obsolete MIX. Now, with Knuth’s guidance and approval, Martin Ruckert has rewritten all MIX example programs from Knuth’s Volumes 1-3 for MMIX, thus completing this MMIX update to the original classic. Building on contributions from the international MMIXmasters volunteer group, Ruckert fully addresses MMIX basic concepts, information structures, random numbers, arithmetic, sorting, and searching. In the preparation of this supplement, about 15,000 lines of MMIX code were written and checked for correctness; over a thousand test cases were written and executed to ensure the code is of the highest possible quality. The MMIX Supplement should be read side by side with The Art of Computer Programming, Volumes 1-3, and Knuth’s Fascicle 1, which introduces the MMIX computer, its design, and its machine language. Throughout, this supplement contains convenient page references to corresponding coverage in the original volumes. To further simplify the transition to MMIX, Ruckert stayed as close as possible to the original–preserving programming style, analysis techniques, and even wording, while highlighting differences where appropriate. The resulting text will serve as a bridge to the future, helping readers apply Knuth’s insights in modern environments, until his revised, “ultimate” edition of The Art of Computer Programming is available. From Donald E. Knuth’s Foreword: “I am thrilled to see the present book by Martin Ruckert: It is jam-packed with goodies from which an extraordinary amount can be learned. Martin has not merely transcribed my early programs for MIX and recast them in a modern idiom. He has penetrated to their essence and rendered them anew with elegance and good taste. His carefully checked code represents a significant contribution to the art of pedagogy as well as to the art of programming.” Dr. Martin Ruckert maintains the MMIX home page at mmix.cs.hm.edu. He is professor of mathematics and computer science at Munich University of Applied Sciences in Munich, Germany.

Discrete Mathematics Using a Computer


Author: Cordelia Hall,John O'Donnell
Publisher: Springer Science & Business Media
ISBN: 1447136578
Category: Mathematics
Page: 339
View: 8919

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Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools such as proof checkers. These connections are emphasised throughout the book. Software tools (see Appendix A) enable the computer to serve as a calculator, but instead of just doing arithmetic and trigonometric functions, it will be used to calculate with sets, relations, functions, predicates and inferences. There are also special software tools, for example a proof checker for logical proofs using natural deduction.

TEX and METAFONT

New Directions in Typesetting
Author: Donald Ervin Knuth
Publisher: N.A
ISBN: N.A
Category: Computerized typesetting
Page: 105
View: 351

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Things a Computer Scientist Rarely Talks about


Author: Donald Ervin Knuth
Publisher: Stanford Univ Center for the Study
ISBN: 9781575863269
Category: Computers
Page: 269
View: 9561

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How does a computer scientist understand infinity? What can probability theory teach us about free will? Can mathematical notions be used to enhance one's personal understanding of the Bible? Perhaps no one is more qualified to address these questions than Donald E. Knuth, whose massive contributions to computing have led others to nickname him "The Father of Computer Science"—and whose religious faith led him to understand a fascinating analysis of the Bible called the 3:16 project. In this series of six spirited, informal lectures, Knuth explores the relationships between his vocation and his faith, revealing the unique perspective that his work with computing has lent to his understanding of God. His starting point is the 3:16 project, an application of mathematical "random sampling" to the books of the Bible. The first lectures tell the story of the project's conception and execution, exploring its many dimensions of language translation, aesthetics, and theological history. Along the way, Knuth explains the many insights he gained from such interdisciplinary work. These theological musings culminate in a surprising final lecture tackling the ideas of infinity, free will, and some of the other big questions that lie at the juncture of theology and computation. Things a Computer Scientist Rarely Talks About, with its charming and user-friendly format—each lecture ends with a question and answer exchange, and the book itself contains more than 100 illustrations—is a readable and intriguing approach to a crucial topic, certain to edify both those who are serious and curious about their faiths and those who look at the science of computation and wonder what it might teach them about their spiritual world. Includes "Creativity, Spirituality, and Computer Science," a panel discussion featuring Harry Lewis, Guy L. Steele, Jr., Manuela Veloso, Donald E. Knuth, and Mitch Kapor.

Mathematics for Computer Science


Author: Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher: N.A
ISBN: 9789888407064
Category:
Page: 979
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This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Discrete Mathematics

Elementary and Beyond
Author: László Lovász,József Pelikán,Katalin Vesztergombi
Publisher: Springer Science & Business Media
ISBN: 0387217770
Category: Mathematics
Page: 284
View: 6441

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Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

Essential Mathematics for Games and Interactive Applications

A Programmer's Guide, Second Edition
Author: James M. Van Verth,Lars M. Bishop
Publisher: CRC Press
ISBN: 0123742978
Category: Art
Page: 704
View: 6652

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Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction.

Mathematical Logic

Foundations for Information Science
Author: Wei Li
Publisher: Springer
ISBN: 3034808623
Category: Mathematics
Page: 301
View: 7975

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Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.

Purely Functional Data Structures


Author: Chris Okasaki
Publisher: Cambridge University Press
ISBN: 9780521663502
Category: Computers
Page: 220
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This book describes data structures and data structure design techniques for functional languages.