Mathematical Foundation for Computer Science

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semanti

Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circ

Advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. Self-contained treatm

Logic is, and should be, the core subject area of modern mathemat- ics. The blueprint for twentieth century mathematical thought, thanks to Hilbert and Bourbaki, is the axiomatic development of the su

Category theory has become increasingly important and popular in computer science, and many universities now have introductions to category theory as part of their courses for undergraduate computer scientists. The author is a respected category theorist and has based this textbook on a course given over the last few years at the University of Sydney. The theory is developed in a straightforward way, and is enriched with many examples from computer science. Thus this book meets the needs of undergradute computer scientists, and yet retains a level of mathematical correctness that will broaden its appeal to include students of mathematics new to category theory.

This book provides a solid foundation to a number of important topics in mathematics of interest to science and engineering students. The authors' approach is simple and direct, the emphasis being on the analytical structure and applications of the material. The text is virtually self-contained, assuming only that the student has received a good basic course in ancillary mathematics. Each chapter contains a large number of worked examples, and concludes with problems for solution, with answers given in the back of the book. There is no comparable text that covers this material in such a concise form. This book will be of great value to undergraduates in physics, chemistry, theoretical biology, and in all engineering disciplines, as a source book of advanced mathematical methods, and also to postgraduate students as a revision text.

Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, writ

Designed for the introductory computing and computer science course, the student-friendly Computer Science Illuminated, Eighth Edition provides students with a solid foundation for further study, and offers non-majors a complete introduction to computing. Fully revised and updated, the eighth edition of this best-selling text retains the accessibility and in-depth coverage of previous editions, while incorporating all-new material on cutting-edge issues in computer science. Authored by the award-winning team Nell Dale and John Lewis, the text provides a unique and innovative layered approach, moving through the levels of computing from an organized, language-neutral perspective. Updated to latest AP CS PrinciplesNew section on cryptocurrencyExpanded coverage of blockchain, cybersecurity attacks, and e-commerceCloud Desktop and companion lab exercises are available on Navigate, which include 23 different lab exercises on topics such as programming, databases, networking, and more

This volume provides a practical introduction to the method of maximum likelihood as used in social science research. Ward and Ahlquist focus on applied computation in R and use real social science data from actual, published research. Unique among books at this level, it develops simulation-based tools for model evaluation and selection alongside statistical inference. The book covers standard models for categorical data as well as counts, duration data, and strategies for dealing with data missingness. By working through examples, math, and code, the authors build an understanding about the contexts in which maximum likelihood methods are useful and develop skills in translating mathematical statements into executable computer code. Readers will not only be taught to use likelihood-based tools and generate meaningful interpretations, but they will also acquire a solid foundation for continued study of more advanced statistical techniques.

This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available i

The purpose of the volume is to provide a support for a first course in Mathematics. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in

Computing is an exact science and the systematic study of any aspect necessarily involves the use of mathematical models. Moreover, the rate at which the subject is evolving demands a facility for developing new mathematical systems to keep pace with new computing systems and this requires an appreciation of how mathematics works. An understanding of the underlying mathematical structure facilitates the construction of suitable computer programs to perform computations. Assuming no specific knowledge of mathematics, the authors describe all the basic concepts required and progress from sets (rather than numbers) through a variety of algebraic structures that permit the precise description, specification and subsequent analysis of many problems in computing. The material included provides the essential mathematical foundations for core topics of computer science and extends into the areas of language theory, abstract machine theory and computer geometry. Computer Mathematics will be of

A top-down,layered approach to computer networking. Unique among computernetworking texts, the 8th Edition, Global Edition, of thepopular Computer Networking: A Top Down Approach buildson the authors' long tradition of teaching this complex subject through alayered approach in a "top-down manner." The text works its way from theapplication layer down toward the physical layer, motivating students byexposing them to important concepts early in their study of networking.Focusing on the Internet and the fundamentally important issues of networking,this text provides an excellent foundation for students in computer science andelectrical engineering, without requiring extensive knowledge of programming ormathematics. The 8th Edition, Global Edition, has been updatedto reflect the most important and exciting recent advances in networking,including the importance of software-defined networking (SDN) and the rapidadoption of 4G/5G networks and the mobile applications they enable.Chapter 1:Comp

Domain theory is an established part of theoretical computer science, used in giving semantics to programming languages and logics. In mathematics and logic it has also proved to be useful in the study of algorithms. This book is devoted to providing a unified and self-contained treatment of the subject. The theory is presented in a mathematically precise manner which nevertheless is accessible to mathematicians and computer scientists alike. The authors begin with the basic theory including domain equations, various domain representations and universal domains. They then proceed to more specialized topics such as effective and power domains, models of lambda-calculus and so on. In particular, the connections with ultrametric spaces and the Kleene–Kreisel continuous functionals are made precise. Consequently the text will be useful as an introductory textbook (earlier versions have been class-tested in Uppsala, Gothenburg, Passau, Munich and Swansea), or as a general reference for prof

Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject and formalizing within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy and computer science as an account of how mathematics and artificial intelligence can complement and enrich each other.

Give your first grader a strong computer science foundation with Smart Start: Beginning Coding Stories and Activities. Children will learn important coding concepts with engaging stories and practice activities. Based on the K-12 Computer Science Framework, this dynamic early learning series helps children understand coding concepts to develop a strong foundation in computer science, including computational thinking, problem solving, and critical thinking. Each full-color activity book is organized into eight themed units around one coding concept and includes: - Coding stories that demonstrate what coders do and include an audio read-aloud feature - Concept pages that connect coding concepts to real-world situations - Practice activities that reinforce important coding rules - Review pages for every coding concept practiced - Coding projects with print-based games and puzzles - Mini coding handbook with key terms Computer science concepts and skills help early learners become critical

Give your preschooler a strong computer science foundation with Smart Start: Beginning Coding Stories and Activities. Children will learn important coding concepts with engaging stories and practice activities. Based on the K-12 Computer Science Framework, this dynamic early learning series helps children understand coding concepts to develop a strong foundation in computer science, including computational thinking, problem solving, and critical thinking. Each full-color activity book is organized into eight themed units around one coding concept and includes: - Coding stories that demonstrate what coders do and include an audio read-aloud feature - Concept pages that connect coding concepts to real-world situations - Practice activities that reinforce important coding rules - Review pages for every coding concept practiced - Coding projects with print-based games and puzzles - Mini coding handbook with key terms Computer science concepts and skills help early learners become critical

Give your kindergartner a strong computer science foundation with Smart Start: Beginning Coding Stories and Activities. Children will learn important coding concepts with engaging stories and practice activities. Based on the K-12 Computer Science Framework, this dynamic early learning series helps children understand coding concepts to develop a strong foundation in computer science, including computational thinking, problem solving, and critical thinking. Each full-color activity book is organized into eight themed units around one coding concept and includes: - Coding stories that demonstrate what coders do and include an audio read-aloud feature - Concept pages that connect coding concepts to real-world situations - Practice activities that reinforce important coding rules - Review pages for every coding concept practiced - Coding projects with print-based games and puzzles - Mini coding handbook with key terms Computer science concepts and skills help early learners become critica

This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in mul

Explore the exhilarating world of information technology. This title builds an essential foundation for computing study for children aged 7-9 by exploring the computer devices we use every day and exp

Written for a wide range of mathematical abilities this book emphasizes the conceptual aspects of decision-making rather than mathematical techniques or computer methods. It shows how hard 'OR' incorp

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.

Charles Babbage was a key figure of a great era of British history. Best remembered for his pioneering Difference and Analytical Engines, forerunners of the modern computer, Babbage was also an active reformer of science and society. Among his friends were the Bonapartes, the Duke of Wellington, the Duke of Somerset, Byron's daughter Ada Lovelace and the reforming Earl of Shaftesbury, whose interest Babbage directed to the factories. In this book, Anthony Hyman has selected passages from Babbage's many publications, including his proposals on profit sharing and life peerages and his ideas on such topics as the applications of science, scientific management, taxation and life assurance. Setting each extract in perspective, Hyman has provided the passages with an explanatory editorial commentary. Together with his concern for the systematic application of science, technology and mathematical method to commercial, industrial and economic problems, his work on computing makes Charles Babba

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every cha

This book bridges the fields of finance, mathematical finance and engineering, and is suitable for engineers and computer scientists who are looking to apply engineering principles to financial market

Inferring the precise locations and splicing patterns of genes in DNA is a difficult but important task, with broad applications to biomedicine. The mathematical and statistical techniques that have been applied to this problem are surveyed and organized into a logical framework based on the theory of parsing. Both established approaches and methods at the forefront of current research are discussed. Numerous case studies of existing software systems are provided, in addition to detailed examples that work through the actual implementation of effective gene-predictors using hidden Markov models and other machine-learning techniques. Background material on probability theory, discrete mathematics, computer science, and molecular biology is provided, making the book accessible to students and researchers from across the life and computational sciences. This book is ideal for use in a first course in bioinformatics at graduate or advanced undergraduate level, and for anyone wanting to kee

Discrete mathematics is fundamental to computer science, and this text covers its ideas and mathematical language. Features counting and listing, functions, decision trees and recursion, and basic con

Computing developed as a branch of mathematics, only to drift away from this home as computer science diverged towards more general topics such as the theory of how a computer works. Recently the emphasis has become more mathematical and the new disciplines of software engineering and information technology have emerged. This book is designed to form the basis of a one year course in discrete mathematics for first year computer scientists or software engineers. The material presented covers much of undergraduate algebra with a particular bias towards the computing applications. Topics covered include mathematical logic, set theory, finite and infinite relations and mappings, graphs, graphical algorithms and axiom systems. It concludes with implementations of many of the algorithms in Modula-2 to illustrate how the mathematics may be turned into concrete calculations. Numerous examples and exercises are included with selected solutions to the problems appearing in the appendix. Discrete

Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or econo

The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus

Formal semantics - the scientific study of meaning in natural language - is one of the most fundamental and long-established areas of linguistics. This Handbook offers a comprehensive, yet compact guide to the field, bringing together research from a wide range of world-leading experts. Chapters include coverage of the historical context and foundation of contemporary formal semantics, a survey of the variety of formal/logical approaches to linguistic meaning and an overview of the major areas of research within current semantic theory, broadly conceived. The Handbook also explores the interfaces between semantics and neighbouring disciplines, including research in cognition and computation. This work will be essential reading for students and researchers working in linguistics, philosophy, psychology and computer science.

Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and production, graph connectivity has made tremendous algorithmic progress under the influence of the theory of complexity and algorithms in modern computer science. The book contains various definitions of connectivity, including edge-connectivity and vertex-connectivity, and their ramifications, as well as related topics such as flows and cuts. The authors thoroughly discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices. Covering both basic definitions and advanced topics, this book can be used as a textbook in graduate courses in mathematical sciences, such as discrete mathematics, combinatorics, and operations research, and as a reference book for specialists i

This is an introduction to the dynamics of fluids at small scales, the physical and mathematical underpinnings of Brownian motion, and the application of these subjects to the dynamics and flow of complex fluids such as colloidal suspensions and polymer solutions. It brings together continuum mechanics, statistical mechanics, polymer and colloid science, and various branches of applied mathematics, in a self-contained and integrated treatment that provides a foundation for understanding complex fluids, with a strong emphasis on fluid dynamics. Students and researchers will find that this book is extensively cross-referenced to illustrate connections between different aspects of the field. Its focus on fundamental principles and theoretical approaches provides the necessary groundwork for research in the dynamics of flowing complex fluids.

Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.