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Mathematical Foundations of Computer Science by Peter A. Fejer,Dan A. Simovici Pdf
Mathematical Foundations of Computer Science, Volume I is the first of two volumes presenting topics from mathematics (mostly discrete mathematics) which have proven relevant and useful to computer science. This volume treats basic topics, mostly of a set-theoretical nature (sets, functions and relations, partially ordered sets, induction, enumerability, and diagonalization) and illustrates the usefulness of mathematical ideas by presenting applications to computer science. Readers will find useful applications in algorithms, databases, semantics of programming languages, formal languages, theory of computation, and program verification. The material is treated in a straightforward, systematic, and rigorous manner. The volume is organized by mathematical area, making the material easily accessible to the upper-undergraduate students in mathematics as well as in computer science and each chapter contains a large number of exercises. The volume can be used as a textbook, but it will also be useful to researchers and professionals who want a thorough presentation of the mathematical tools they need in a single source. In addition, the book can be used effectively as supplementary reading material in computer science courses, particularly those courses which involve the semantics of programming languages, formal languages and automata, and logic programming.
Mathematical Foundations for Computing by G. P. McKeown,V. J. Rayward-Smith Pdf
This text gives a description of the fundamental mathematical concepts used by computer scientists, while also emphasizing the need for careful justification. It provides proofs of all the major results, and all the algorithms presented are developed carefully and their performance analyzed. Throughout, the aim is to provide a well-balanced treatment of both the discrete and continuous mathematics that should be studied by the serious student of computer science. The book should therefore be most suited to those undergraduate programmes that put the emphasis on such areas as programming language semantics, program correctness, and algorithm analysis and design.
Mathematical Foundation of Computer Science by Y. N. Singh Pdf
The Interesting Feature Of This Book Is Its Organization And Structure. That Consists Of Systematizing Of The Definitions, Methods, And Results That Something Resembling A Theory. Simplicity, Clarity, And Precision Of Mathematical Language Makes Theoretical Topics More Appealing To The Readers Who Are Of Mathematical Or Non-Mathematical Background. For Quick References And Immediate Attentions3⁄4Concepts And Definitions, Methods And Theorems, And Key Notes Are Presented Through Highlighted Points From Beginning To End. Whenever, Necessary And Probable A Visual Approach Of Presentation Is Used. The Amalgamation Of Text And Figures Make Mathematical Rigors Easier To Understand. Each Chapter Begins With The Detailed Contents, Which Are Discussed Inside The Chapter And Conclude With A Summary Of The Material Covered In The Chapter. Summary Provides A Brief Overview Of All The Topics Covered In The Chapter. To Demonstrate The Principles Better, The Applicability Of The Concepts Discussed In Each Topic Are Illustrated By Several Examples Followed By The Practice Sets Or Exercises.
Mathematical Foundations of Computer Networking by Srinivasan Keshav Pdf
“To design future networks that are worthy of society’s trust, we must put the ‘discipline’ of computer networking on a much stronger foundation. This book rises above the considerable minutiae of today’s networking technologies to emphasize the long-standing mathematical underpinnings of the field.” –Professor Jennifer Rexford, Department of Computer Science, Princeton University “This book is exactly the one I have been waiting for the last couple of years. Recently, I decided most students were already very familiar with the way the net works but were not being taught the fundamentals–the math. This book contains the knowledge for people who will create and understand future communications systems." –Professor Jon Crowcroft, The Computer Laboratory, University of Cambridge The Essential Mathematical Principles Required to Design, Implement, or Evaluate Advanced Computer Networks Students, researchers, and professionals in computer networking require a firm conceptual understanding of its foundations. Mathematical Foundations of Computer Networking provides an intuitive yet rigorous introduction to these essential mathematical principles and techniques. Assuming a basic grasp of calculus, this book offers sufficient detail to serve as the only reference many readers will need. Each concept is described in four ways: intuitively; using appropriate mathematical notation; with a numerical example carefully chosen for its relevance to networking; and with a numerical exercise for the reader. The first part of the text presents basic concepts, and the second part introduces four theories in a progression that has been designed to gradually deepen readers’ understanding. Within each part, chapters are as self-contained as possible. The first part covers probability; statistics; linear algebra; optimization; and signals, systems, and transforms. Topics range from Bayesian networks to hypothesis testing, and eigenvalue computation to Fourier transforms. These preliminary chapters establish a basis for the four theories covered in the second part of the book: queueing theory, game theory, control theory, and information theory. The second part also demonstrates how mathematical concepts can be applied to issues such as contention for limited resources, and the optimization of network responsiveness, stability, and throughput.
Mathematical Foundations of Computer Science by G. Shanker Rao Pdf
Mathematical Foundations of Computer Science explains the fundamental concepts in mathematics. It can be used by the students in computer science as an introduction to the underlying ideas of mathematics for computer science. It explains topics like mathematical logic, predicates, relations, functions, combinatorics, algebraic structures and graph theory. It would be useful for the students of B.Tech, BCA, & MCA. Key Features: " Comprehensive discussion on logic, function, algebraic systems, recurrence relations and graph theory " Wide variety of exercises at all levels " Several worked out examples
Theoretical and Mathematical Foundations of Computer Science by Qihai Zhou Pdf
This book constitutes the refereed post-proceedings of the Second International Conference on Theoretical and Mathematical Foundations of Computer Science, ICTMF 2011, held in Singapore in May 2011. The conference was held together with the Second International Conference on High Performance Networking, Computing, and Communication systems, ICHCC 2011, which proceedings are published in CCIS 163. The 84 revised selected papers presented were carefully reviewed and selected for inclusion in the book. The topics covered range from computational science, engineering and technology to digital signal processing, and computational biology to game theory, and other related topices.
Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems by Masanori Ohya,I. Volovich Pdf
This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.
Foundation Mathematics for Computer Science by John Vince Pdf
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.
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE, Second Edition by BATHUL, SHAHNAZ Pdf
This book, in its Second Edition, provides the basic concepts and applications of discrete mathematics and graph theory. The book is aimed at undergraduate students of computer science and engineering, and information technology. It is also suitable for undergraduate and postgraduate students of computer science, mathematics and computer applications. The book exposes the students to fundamental knowledge in: - Mathematical logic, tautology and normal forms - Elementary set theory, functions and their relations - Algebraic structure, binary operation, group theory and homomorphism - Theory of permutations and combinations, binomial and multinomial theorems - Recurrence relations and methods of solving them - Graph theory, spanning tree, Eulerian and Hamiltonian circuits and isomorphism Key Features Includes a large number of worked-out problems for sound understanding of the concepts. Offers chapter-end exercises to test students’ comprehension of theory. Gives a quiz section at the end of each chapter to help students prepare for the competitive examinations. Incorporates short questions asked in universities’ examinations.
Concrete Mathematics by Ronald L. Graham,Donald E. Knuth,Oren Patashnik Pdf
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.
A comprehensive introduction to mathematical structures essential for Rough Set Theory. The book enables the reader to systematically study all topics of rough set theory. After a detailed introduction in Part 1 along with an extensive bibliography of current research papers. Part 2 presents a self-contained study that brings together all the relevant information from respective areas of mathematics and logics. Part 3 provides an overall picture of theoretical developments in rough set theory, covering logical, algebraic, and topological methods. Topics covered include: algebraic theory of approximation spaces, logical and set-theoretical approaches to indiscernibility and functional dependence, topological spaces of rough sets. The final part gives a unique view on mutual relations between fuzzy and rough set theories (rough fuzzy and fuzzy rough sets). Over 300 excercises allow the reader to master the topics considered. The book can be used as a textbook and as a reference work.
Mathematical Foundations of Computer Science 2014 by Ersébet Csuhaj-Varjú,Martin Dietzfelbinger,Zoltán Ésik Pdf
This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.
General Systems Theory: Mathematical Foundations by Anonim Pdf
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
