This subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. The subject coverage divides roughly into thirds: Fundamental concepts of mathematics: definitions, proofs, sets, functions, relations. Discrete structures: graphs, state machines, modular arithmetic, counting. Discrete probability theory. On completion of 6.042, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in Computer Science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering and computer systems.
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.
Algebraic Theory of Automata provides information pertinent to the methods and results of algebraic theory of automata. This book covers a variety of topics, including sets, semigroup, groupoids, isomorphism, semiautomata, proof of Kleene's theorem, and algebraic manipulations. Organized into seven chapters, this book begins with an overview of the fundamental properties of groups and semigroups. This text then examines the notion of semiautomaton, which serves as a basis for a rich and interesting theory. Other chapters consider algebraic notions and methods that are very useful in dealing with semiautomata. This book discusses as well some properties of the notion of covering of semiautomata. The final chapter deals with the theory of Krohn and Rhodes. This book is a valuable resource for graduate students.
The first edition of Caroline Whitbeck's Ethics in Engineering Practice and Research focused on the difficult ethical problems engineers encounter in their practice and in research. In many ways, these problems are like design problems: they are complex, often ill defined; resolving them involves an iterative process of analysis and synthesis; and there can be more than one acceptable solution. In the second edition of this text, Dr Whitbeck goes above and beyond by featuring more real-life problems, stating recent scenarios and laying the foundation of ethical concepts and reasoning. This book offers a real-world, problem-centered approach to engineering ethics, using a rich collection of open-ended case studies to develop skill in recognizing and addressing ethical issues.
Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial * Applications * Further Reading
The Person 1 Boris Abramovich Trakhtenbrot (????? ????????? ???????????) – his Hebrew given name is Boaz ( ) – is universally admired as a founding - ther and long-standing pillar of the discipline of computer science. He is the ?eld's preeminent distinguished researcher and a most illustrious trailblazer and disseminator. He is unmatched in combining farsighted vision, unfaltering c- mitment, masterful command of the ?eld, technical virtuosity, æsthetic expr- sion, eloquent clarity, and creative vigor with humility and devotion to students and colleagues. For over half a century, Trakhtenbrot has been making seminal contributions to virtually all of the central aspects of theoretical computer science, inaugur- ing numerous new areas of investigation. He has displayed an almost prophetic ability to foresee directions that are destined to take center stage, a decade or morebeforeanyoneelsetakesnotice.Hehasneverbeentempted toslowdownor limithisresearchtoareasofendeavorinwhichhehasalreadyearnedrecognition and honor. Rather, he continues to probe the limits and position himself at the vanguard of a rapidly developing ?eld, while remaining, as always, unassuming and open-minded.
This volume gives the proceedings of TACS '91, which focused on theoretical foundations of programming, and theoretical aspects of the design, analysis and implementation of programming languages and systems.