Applications Of Continuous Mathematics To Computer Science
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Applications Of Continuous Mathematics To Computer Science
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Author : Hung T. Nguyen
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-10-31
Applications Of Continuous Mathematics To Computer Science written by Hung T. Nguyen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-31 with Mathematics categories.
This volume is intended to be used as a textbook for a special topic course in computer science. It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision. The work incorporates many new research ideas, and focuses on the role of continuous mathematics. Audience: This book will be valuable to graduate students interested in theoretical computer topics, algorithms, expert systems, neural networks, and software engineering.
Discrete Mathematics Using A Computer
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Author : Cordelia Hall
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Discrete Mathematics Using A Computer written by Cordelia Hall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Mathematics For Computer Science
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Author : Eric Lehman
language : en
Publisher:
Release Date : 2017-06-05
Mathematics For Computer Science written by Eric Lehman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-05 with categories.
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. The color images and text in this book have been converted to grayscale.
Discrete Mathematics For Computer Science
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Author : John Schlipf
language : en
Publisher:
Release Date : 2020-09-22
Discrete Mathematics For Computer Science written by John Schlipf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-22 with categories.
Discrete Mathematics for Computer Science by Gary Haggard , John Schlipf , Sue Whitesides A major aim of this book is to help you develop mathematical maturity-elusive as thisobjective may be. We interpret this as preparing you to understand how to do proofs ofresults about discrete structures that represent concepts you deal with in computer science.A correct proof can be viewed as a set of reasoned steps that persuade another student,the course grader, or the instructor about the truth of the assertion. Writing proofs is hardwork even for the most experienced person, but it is a skill that needs to be developedthrough practice. We can only encourage you to be patient with the process. Keep tryingout your proofs on other students, graders, and instructors to gain the confidence that willhelp you in using proofs as a natural part of your ability to solve problems and understandnew material. The six chapters referred to contain the fundamental topics. Thesechapters are used to guide students in learning how to express mathematically precise ideasin the language of mathematics.The two chapters dealing with graph theory and combinatorics are also core materialfor a discrete structures course, but this material always seems more intuitive to studentsthan the formalism of the first four chapters. Topics from the first four chapters are freelyused in these later chapters. The chapter on discrete probability builds on the chapter oncombinatorics. The chapter on the analysis of algorithms uses notions from the core chap-ters but can be presented at an informal level to motivate the topic without spending a lot oftime with the details of the chapter. Finally, the chapter on recurrence relations primarilyuses the early material on induction and an intuitive understanding of the chapter on theanalysis of algorithms. The material in Chapters 1 through 4 deals with sets, logic, relations, and functions.This material should be mastered by all students. A course can cover this material at differ-ent levels and paces depending on the program and the background of the students whenthey take the course. Chapter 6 introduces graph theory, with an emphasis on examplesthat are encountered in computer science. Undirected graphs, trees, and directed graphsare studied. Chapter 7 deals with counting and combinatorics, with topics ranging from theaddition and multiplication principles to permutations and combinations of distinguishableor indistinguishable sets of elements to combinatorial identities.Enrichment topics such as relational databases, languages and regular sets, uncom-putability, finite probability, and recurrence relations all provide insights regarding howdiscrete structures describe the important notions studied and used in computer science.Obviously, these additional topics cannot be dealt with along with the all the core materialin a one-semester course, but the topics provide attractive alternatives for a variety of pro-grams. This text can also be used as a reference in courses. The many problems provideample opportunity for students to deal with the material presented.
Concrete Mathematics
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Author : Ronald L. Graham
language : en
Publisher: Addison-Wesley Professional
Release Date : 1994-02-28
Concrete Mathematics written by Ronald L. Graham and has been published by Addison-Wesley Professional this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-28 with Computers categories.
This book 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 sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
Mathematics In Computing
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Author : Gerard O’Regan
language : en
Publisher: Springer Nature
Release Date : 2020-01-10
Mathematics In Computing written by Gerard O’Regan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-10 with Computers categories.
This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.
Mathematics And The Natural Sciences The Physical Singularity Of Life
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Author : Giuseppe Longo
language : en
Publisher: World Scientific
Release Date : 2011-03-04
Mathematics And The Natural Sciences The Physical Singularity Of Life written by Giuseppe Longo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-04 with Science categories.
This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work.The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations.Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level./a
Constructing Probability Boxes And Dempster Shafer Structures
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Author : Scott Ferson
language : en
Publisher:
Release Date : 2003
Constructing Probability Boxes And Dempster Shafer Structures written by Scott Ferson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Dempster-Shafer theory categories.
This report summarizes a variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge. The report includes a review of the aggregation methods for handling agreement and conflict when multiple such objects are obtained from different sources.
Linear Algebra And Probability For Computer Science Applications
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Author : Ernest Davis
language : en
Publisher: CRC Press
Release Date : 2012-05-02
Linear Algebra And Probability For Computer Science Applications written by Ernest Davis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-02 with Mathematics categories.
Based on the author's course at NYU, Linear Algebra and Probability for Computer Science Applications gives an introduction to two mathematical fields that are fundamental in many areas of computer science. The course and the text are addressed to students with a very weak mathematical background. Most of the chapters discuss relevant MATLAB functi
Applications Of Optimal Transport To Economics And Related Topics
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Author : Vladik Kreinovich
language : en
Publisher: Springer Nature
Release Date : 2024-11-09
Applications Of Optimal Transport To Economics And Related Topics written by Vladik Kreinovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-09 with Technology & Engineering categories.
Often, when a new successful data processing techniques appears in one of the application areas, it then proves to be useful in many other areas. This was the case of optimal transportation techniques: these techniques were first developed for transportation problems, but now they have been shown to be successful in many statistical applications, including applications to economics. These techniques are the main focus of this book, but this book also contain papers that use other techniques, ranging from more traditional statistical approaches to more recent ones such as stochastic frontier methods, multivariable quantiles, random forest, and deep learning. Applications include all aspects of economics, from production (including agricultural) to trade (including international) and finances, with relation to issues of crime (including computer crime and cyberbullying), demographics, economic freedom, environment, health, and tourism. We hope that this volume will: help practitioners to become better knowledgeable of the state-of-the-art econometric techniques, especially optimal transport techniques, and help researchers to further develop these important research directions. We want to thank all the authors for their contributions and all anonymous referees for their thorough analysis and helpful comments. The publication of this volume was partly supported by the Faculty of Economics of the Chiang Mai University, Thailand. Our thanks to the leadership and staff of the Chiang Mai University for providing crucial support. Our special thanks to Prof. Hung T. Nguyen for his valuable advice and constant support.