Mathematical Foundation for Computer Science

In this text for advanced undergraduate and graduate students in areas such as communications, computer science, economics, and public health, Kapadia (biostatistics, University of Texas School of Pub

This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations. Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician's bookshelf.

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

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

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

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.

The Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB®, this book supports readers in applying appropriate analytical or computational methods to solving real research questi

Networks are everywhere, from the internet, to social networks, and the genetic networks that determine our biological existence. Illustrated throughout in full colour, this pioneering textbook, spanning a wide range of topics from physics to computer science, engineering, economics and the social sciences, introduces network science to an interdisciplinary audience. From the origins of the six degrees of separation to explaining why networks are robust to random failures, the author explores how viruses like Ebola and H1N1 spread, and why it is that our friends have more friends than we do. Using numerous real-world examples, this innovatively designed text includes clear delineation between undergraduate and graduate level material. The mathematical formulas and derivations are included within Advanced Topics sections, enabling use at a range of levels. Extensive online resources, including films and software for network analysis, make this a multifaceted companion for anyone with an

This new book brings together innovative research, new concepts, and novel developments in the application of informatics tools for applied chemistry and computer science. It presents a modern approac

Through just a handful of papers, Ettore Majorana left an indelible mark in the fields of physics, mathematics, computer science and even economics before his mysterious disappearance in 1938. It is only now that the importance of Majorana's work is being realised: Majorana fermions are intensely studied today, and his work on neutrino physics has provided possible explanations for the existence of dark matter. In this unique volume, Salvatore Esposito explores not only Majorana's known papers but, even more interestingly, unveils his unpublished works as well. These include powerful methods and results, ranging from the atomic two-centre problem, the Thomas–Fermi model and ferromagnetism to quasi-stationary states, n-component relativistic wave equations and quantum scalar electrodynamics. Featuring biographical notes and contributions from leading experts Evgeny Akhmedov and Nobel Laureate Frank Wilczek, this fascinating book will captivate graduate students and researchers intereste

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.

Written for undergraduate and graduate students in math, applied math, computer science, and engineering, this book stresses the connections between the theoretical nature of mathematical objects and

This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understand

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

Discover the fundamental principles of biomedical measurement design and performance evaluation with this hands-on guide. Whether you develop measurement instruments or use them in novel ways, this practical text will prepare you to be an effective generator and consumer of biomedical data. Designed for both classroom instruction and self-study, it explains how information is encoded into recorded data and can be extracted and displayed in an accessible manner. Describes and integrates experimental design, performance assessment, classification, and system modelling. Combines mathematical concepts with computational models, providing the tools needed to answer advanced biomedical questions. Includes MATLAB® scripts throughout to help readers model all types of biomedical systems, and contains numerous homework problems, with a solutions manual available online. This is an essential text for advanced undergraduate and graduate students in bioengineering, electrical and computer engineer

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

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

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

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

"In 1998, the National Science Foundation (NSF) launched a program of Grants for Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE). These grants were designed for ins

Researchers (most of them from Brazil) in mathematics, computer science, and a range of biological and agricultural sciences survey mathematical and computational methods used in agriculture research.

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

1. Principles of structured programming and software engineering are consistently emphasized to provide a solid foundation for future courses2. Figures and tables are used liberally to help students v

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

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

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

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

The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book, first published in 2005, offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These algorithms can be applied to biological problems such as aligning genomes, finding genes and constructing phylogenies. The first part of this book consists of four chapters on the themes of Statistics, Computation, Algebra and Biology, offering speedy, self-contained introductions to the emerging field of algebraic statistics and its applications to genomics. In the second part, the four themes are combined and developed to tackle real problems in computational genomics. As the first book in the exciting and dynamic area, it wi

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

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular attention given to enforcement of incompressibility. Advanced discretizations, implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual app

Csiszár and Körner's book is widely regarded as a classic in the field of information theory, providing deep insights and expert treatment of the key theoretical issues. It includes in-depth coverage of the mathematics of reliable information transmission, both in two-terminal and multi-terminal network scenarios. Updated and considerably expanded, this new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics. The presentations of all core subjects are self contained, even the advanced topics, which helps readers to understand the important connections between seemingly different problems. Finally, 320 end-of-chapter problems, together with helpful hints for solving them, allow readers to develop a full command of the mathematical techniques. It is an ideal resource for graduate students and researchers in electrical and electronic engineering, computer science

A comprehensive account of both basic and advanced material in phylogeny estimation, focusing on computational and statistical issues. No background in biology or computer science is assumed, and there is minimal use of mathematical formulas, meaning that students from many disciplines, including biology, computer science, statistics, and applied mathematics, will find the text accessible. The mathematical and statistical foundations of phylogeny estimation are presented rigorously, following which more advanced material is covered. This includes substantial chapters on multi-locus phylogeny estimation, supertree methods, multiple sequence alignment techniques, and designing methods for large-scale phylogeny estimation. The author provides key analytical techniques to prove theoretical properties about methods, as well as addressing performance in practice for methods for estimating trees. Research problems requiring novel computational methods are also presented, so that graduate stud

Information theory lies at the heart of modern technology, underpinning all communications, networking, and data storage systems. This book sets out, for the first time, a complete overview of both classical and quantum information theory. Throughout, the reader is introduced to key results without becoming lost in mathematical details. Opening chapters present the basic concepts and various applications of Shannon's entropy, moving on to the core features of quantum information and quantum computing. Topics such as coding, compression, error-correction, cryptography and channel capacity are covered from classical and quantum viewpoints. Employing an informal yet scientifically accurate approach, Desurvire provides the reader with the knowledge to understand quantum gates and circuits. Highly illustrated, with numerous practical examples and end-of-chapter exercises, this text is ideal for graduate students and researchers in electrical engineering and computer science, and practitione

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

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

Forty-three international academics, researchers, and computer science professionals contribute 15 chapters demonstrating how mathematical models and computer software can be developed and applied for

Ding (University of Illinois) combines ideas from cognitive science, mathematical modeling, and computer simulation to establish a theoretical framework for addressing homeland security issues related

This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of q