Mathematics of Discrete Structures for Computer Science

Using basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Gödel's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises.

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This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overv

This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overv

This introductory treatment of theory, proof techniques, and related concepts is designed for undergraduate courses. Topics include propositional logic, quantifiers, sets, functions, relations, mathem

Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science&nb

For the Introduction to Computer Science course. A broad exploration of computer science–with the depth needed to understand concepts Computer Science: An Overview provides a bottom

Discrete mathematics has been rising in prominence in the past fifty years, both as a tool with practical applications and as a source of new and interesting mathematics. The topics in discrete mathematics have become so well developed that it is easy to forget that common threads connect the different areas, and it is through discovering and using these connections that progress is often made. For over fifty years, Ron Graham has been able to illuminate some of these connections and has helped to bring the field of discrete mathematics to where it is today. To celebrate his contribution, this volume brings together many of the best researchers working in discrete mathematics, including Fan Chung, Erik D. Demaine, Persi Diaconis, Peter Frankl, Alfred W. Hales, Jeffrey C. Lagarias, Allen Knutson, Janos Pach, Carl Pomerance, N. J. A. Sloane, and of course, Ron Graham himself.

Discrete mathematics has been rising in prominence in the past fifty years, both as a tool with practical applications and as a source of new and interesting mathematics. The topics in discrete mathematics have become so well developed that it is easy to forget that common threads connect the different areas, and it is through discovering and using these connections that progress is often made. For over fifty years, Ron Graham has been able to illuminate some of these connections and has helped to bring the field of discrete mathematics to where it is today. To celebrate his contribution, this volume brings together many of the best researchers working in discrete mathematics, including Fan Chung, Erik D. Demaine, Persi Diaconis, Peter Frankl, Alfred W. Hales, Jeffrey C. Lagarias, Allen Knutson, Janos Pach, Carl Pomerance, N. J. A. Sloane, and of course, Ron Graham himself.

The implementation of computers and other networking and storage devices for processing, retrieving and transmitting data is known as information technology. Database administration, information secur

This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the sixth publication in the Lecture Notes in Logic series, collects the proceedings of the conference 'Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Gödel's Legacy', held in Brno, Czech Republic, on the 90th anniversary of Gödel's birth. The broad range of speakers who participated in this event affirms the continuing importance of Gödel's work in logic, physics, and the philosophy and foundations of mathematics and computer science. The papers in this volume range over all these topics and contribute to our present understanding of them.

Today, learning to program and understanding the basics of computation isn't just indispensable for every science and engineering student: it's crucial for everyone who wants to understand the world t

This book is the 1st volume of the “SpringerBriefs in the Mathematics of Materials” and shows the overall introduction to the application of mathematics to materials science. In the anterior par

This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming l

The proceedings consists of 30 papers which have been selected and invited from the submissions to the2nd International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA 20

In this conversational reader, DeVito aims to illuminate the usefulness, universality, and particularity of mathematics for a popular audience by discussing the Search for Extraterrestrial Intelligenc

This book presents four mathematical essays that explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. It details the state of the

Now in a second, expanded edition, this book bridges the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics and introduces a range of geometri

Improving Computer Science Education examines suitable theoretical frameworks for conceptualizing teaching and learning computer science. This highly useful book provides numerous examples of practic

Improving Computer Science Education examines suitable theoretical frameworks for conceptualizing teaching and learning computer science. This highly useful textbook provides numerous examples of prac

Based on the author’s course at NYU, Linear Algebra and Probability for Computer Science Applicationsgives an introduction to two mathematical fields that are fundamental in many areas of comput

Logic and its components (propositional, first-order, non-classical) play a key role in Computer Science and Artificial Intelligence. While a large amount of information exists scattered throughout va

This unique volume presents reviews of research in several important areas of applications of mathematical concepts to science and technology, for example applications of inverse problems and wavelets

Fundamentals of Java?: AP* Computer Science Essentials, Fourth Edition covers all of the AP requirements for Computer Science Exam A.

The revised classic for designing mathematics and science professional development presents an updated planning framework and many professional development strategies and emphasizes continuous progra

The revised classic for designing mathematics and science professional development presents an updated planning framework and many professional development strategies and emphasizes continuous progra

The logic and methodology of design is examined in this book from the perspective of computer science. Computers provide the context for this examination both by discussion of the design process for hardware and software systems and by consideration of the role of computers in design in general. The central question posed by the author is whether or not we can construct a theory of design. This book concentrates upon the relationship between design, mathematics and science and thus its audience must include designers and software designers as well as computer scientists.

This is an entry level text for a wide range of courses in computer science, medicine, health sciences, social sciences, business, engineering and science. Using the phenomenally successful approach o

This book is a completely revised and updated version of this invaluable text which allows science students to extend necessary skills and techniques, with the topics being developed through examples

Essential Mathematics and Statistics for Science, Second Edition is a completely revised and updated version of this invaluable text which allows science students to extend necessary skills and techni

This book covers the main areas of mathematics used in the first years of a typical engineering, science or applied mathematics degree. This is not a textbook. It is a concise guide to what the import

There has been an enormous increase in research activity aimed at elucidating the basis for cortical activity in the brain. Among modern techniques used in this area of scientific endeavour, few have proved as popular as computer simulation. Model neural networks are the subject of intense study, and some remarkable properties have already come to light: these networks are able to discriminate, remember and associate. Professor Cotterill has assembled leading experts in this burgeoning field to produce an exciting review of advances. The volume covers the creation of computer models of neural networks, and their use in the study of neural function, of cognition, memory and vision. The results and future directions explored here will have an important bearing on research into brain function, physiology, psychology, biophysics and artificial intelligence.

Adams is an educational consultant in Canada; Hamm teaches science and math education at San Francisco State U. They offer teachers a wide range of creative ways to build on the social nature of learn

Never let rusty mathematics skills hinder success in your engineering or science courses!Here are just some of the questions answered in this book:How can:·a logarithm be converted from one base to an

This book presents some fundamental concepts behind the basic theories and tools of discrete element methods (DEM), its historical development, and its wide scope of applications in geology, geophysic

Linear logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs. These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and concurrency theory. The volume is rounded-off by two invited contributions on new topics rooted in recent developments of linear logic. The book derives from a summer school that was the climax of the EU Training and Mobility of Researchers project 'Linear Logic in Computer Science'. It is an excellent introduction to some of the most active research topics in the area.