Mathematics of Discrete Structures for Computer Science

The Invocation Model of Process Expression argues that mathematics does not provide the most appropriate conceptual foundations for computer science, but, rather, that these foundations are a primary

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.

This anthology of essays from the inventor of literate programming is a survey of Donald Knuth's papers on computer science. Donald Knuth's influence in computer science ranges from the invention of

This volume details the mathematical background needed for geometric modeling in computer graphics. It begins with material from linear algebra and a discussion of the transformations in affine

Practicing researchers provide an overview of how to investigate education in computer science, including such domains as informatics, computing, information systems, and software engineering, for tho

The ?rst International Summer School on Theoretical Aspects of Computer Science was organized by the Institute for Studies in Theoretical Physics and Mathematics(IPM)inTehran,Iran. ProgramCommittee Co

This book develops a type theory, studies its properties, and explains its uses in computer science. The book focuses in particular on how the study of type theory may offer a powerful and uniform la

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 is designed for a first course in numerical analysis. It differs considerably from other such texts in its choice of topics.

Formal specification is the name given to the use of discrete mathematics in computer science for describing the function of both hardware and software systems. Poor specification often gives rise to

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.

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

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 textbook, covering the basic mathematics taught to first-year students of science and engineering, reflects the growing awareness that ancillary mathematics should not be taught in isolation from its applications. Topics covered include calculus, ordinary and partial differential equations and statistics. Each chapter starts with two or three examples setting the new techniques to be studied in the context of the scientific world; the mathematics is then presented, along with worked examples. Numerical methods are integrated with analytical techniques where appropriate. The resulting textbook provides the teacher with a rich and varied source of applications for classroom use and students with a textbook for self-learning, giving insight into the significance and role of mathematics in science and engineering.

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.

Poems about historical women in STEM fields.You know you want to read about Mary Anning’s seashells by the seashore, Elizabeth Blackwell losing her eye, Bertha Pallan’s side hustle in the circus, Honor Fell bringing a ferret to her sister’s wedding, Annie Jump Cannon cataloguing stars, Mary G. Ross stumping the panellists on What’s My Line, Alice Ball’s cure for leprosy, and Roberta Eike stowing away on a research vessel. Some of these women triumphed spectacularly. Others barely survived. Carefully researched, emotional, and witty, these poems about historical women in science, technology, engineering, mathematics, and medicine will make you laugh out loud and break your heart in just a few lines. Mathematics for Ladies offers a wickedly funny and feminist take on the lives and work of women who resisted their parents, their governments, the rules and conventions of their times, and sometimes situations as simple and infuriating as a lack of a women’s bathroom in a science building o

A comprehensive guide to the AP Computer Science Principles Exam, with detailed content review and 3 full-length practice tests.AP Computer Science Principles Prep, 2023 gives students everything they need for this exam, including thorough subject reviews of all relevant topics, techniques to help them strategically prepare, and plenty of drills and practice questions to hone their skills. This is a brand new book for an exam that is growing in popularity. More than 96,000 students took this test in 2019.

Bringing together contributions on a diverse range of topics, this text explores the relationship between discrete and continuum mechanics as a tool to model new and complex metamaterials. Providing a comprehensive bibliography and historical review of the field, it covers mechanical, acoustic and pantographic metamaterials, discusses Naive Model Theory and Lagrangian discrete models, and their applications, and presents methods for pantographic structures and variational methods for multidisciplinary modeling and computation. The relationship between discrete and continuous models is discussed from both mathematical and engineering viewpoints, making the text ideal for those interested in the foundation of mechanics and computational applications, and innovative viewpoints on the use of discrete systems to model metamaterials are presented for those who want to go deeper into the field. An ideal text for graduate students and researchers interested in continuum approaches to the study

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

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.

This book provides comprehensive details of all Swarm Intelligence based Techniques available till date in a comprehensive manner along with their mathematical proofs. It will act as a foundation for

The quantity, diversity and availability of transport data is increasing rapidly, requiring new skills in the management and interrogation of data and databases. Recent years have seen a new wave of

This book combines elementary theory from computer science with real-world challenges in global geodetic observation, based on examples from the Geodetic Observatory Wettzell, Germany. It starts with

Held in Guilin of China from August 13–14, 2016, the 2016 International Conference on Computer Science and Artificial Intelligence (CSAI2016) provides an excellent international platform for all invit

This book is the first volume of an intensive “Russian-style” two-year graduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras,

This comprehensive text provides a modern and technically precise exposition of the fundamental theory and applications of temporal logics in computer science. Part I presents the basics of discrete transition systems, including constructions and behavioural equivalences. Part II examines the most important temporal logics for transition systems and Part III looks at their expressiveness and complexity. Finally, Part IV describes the main computational methods and decision procedures for model checking and model building - based on tableaux, automata and games - and discusses their relationships. The book contains a wealth of examples and exercises, as well as an extensive annotated bibliography. Thus, the book is not only a solid professional reference for researchers in the field but also a comprehensive graduate textbook that can be used for self-study as well as for teaching courses.

Over the past sixty years, the spectacular growth of the technologies associated with the computer is visible for all to see and experience. Yet, the science underpinning this technology is less visib

Originally published in 1939, this book forms the second part of a two-volume series on the mathematics required for the examinations of the Institute of Actuaries, focusing on finite differences, probability and elementary statistics. Miscellaneous examples are included at the end of the text. This book will be of value to anyone with an interest in actuarial science and mathematics.

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

Student Handbook for Discrete Mathematics with Ducks is a Student Reference, Review, Supplemental Learning, and Example Handbook (SRRSLEH) that mirrors the content of the author’s popular textbookDisc

Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an out