Mathematics And Computing

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Mathematics in Computing

Gerard O’Regan
Mathematics in Computing Book PDF

Author : Gerard O’Regan
Publisher : Springer Nature
Page : 468 pages
File Size : 44,5 Mb
Release : 2020-01-10
Category : Computers
ISBN : 9783030342098

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Mathematics in Computing by Gerard O’Regan Pdf

This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.

Mathematics for Computer Science

Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Mathematics for Computer Science Book PDF

Author : Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher : Unknown
Page : 988 pages
File Size : 53,9 Mb
Release : 2017-03-08
Category : Business & Economics
ISBN : 9888407066

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Mathematics for Computer Science by Eric Lehman,F. Thomson Leighton,Albert R. Meyer Pdf

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.

Mathematics for Future Computing and Communications

Liao Heng,Bill McColl
Mathematics for Future Computing and Communications Book PDF

Author : Liao Heng,Bill McColl
Publisher : Cambridge University Press
Page : 399 pages
File Size : 48,8 Mb
Release : 2021-12-16
Category : Computers
ISBN : 9781316513583

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Mathematics for Future Computing and Communications by Liao Heng,Bill McColl Pdf

A panorama of new ideas in mathematics that are driving innovation in computing and communications.

Building Bridges

Martin Grötschel,Gyula O.H. Katona
Building Bridges Book PDF

Author : Martin Grötschel,Gyula O.H. Katona
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 46,9 Mb
Release : 2010-05-28
Category : Mathematics
ISBN : 9783540852216

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Building Bridges by Martin Grötschel,Gyula O.H. Katona Pdf

Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is László Lovász, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovász’s 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers.

Discrete Mathematics and Computing

Malik Magdon-Ismail
Discrete Mathematics and Computing Book PDF

Author : Malik Magdon-Ismail
Publisher : Unknown
Page : 128 pages
File Size : 47,9 Mb
Release : 2019-12-14
Category : Electronic
ISBN : 0578567873

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Discrete Mathematics and Computing by Malik Magdon-Ismail Pdf

This text is a semester course in the basic mathematical and theoretical foundations of computer science. Students who make heavy use of computing should learn these foundations well, setting a base for a follow-on course in algorithms. A solid theoretical and algorithmic foundation in computer science sets the stage for developing good programs, programs that work, always and efficiently.Each chapter is a lecture that has been taught as such. Part I starts with basic logic, proofs and discrete mathematics, including: induction, recursion, summation, asymptotics and number theory. We then continue with graphs, counting and combinatorics, and wrap up the coverage of discrete mathematics with discrete probability. Part II presents the blockbuster application of discrete mathematics: the digital computer and a theory of computing. The goal is to understand what a computer can and cannot do. We start small, with automata, and end big with Turing Machines.Our approach is Socratic. The reader is encouraged to participate actively in the learning process by doing the quizzes and exercises that are liberally sprinkled through the text. The pace and level is appropriate for readers with one year of training in programming and calculus (college sophomores).

Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators

Alexei Volkov,Viktor Freiman
Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators Book PDF

Author : Alexei Volkov,Viktor Freiman
Publisher : Springer
Page : 471 pages
File Size : 50,7 Mb
Release : 2019-01-11
Category : Education
ISBN : 9783319733968

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Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators by Alexei Volkov,Viktor Freiman Pdf

This volume traces back the history of interaction between the “computational” or “algorithmic” aspects of elementary mathematics and mathematics education throughout ages. More specifically, the examples of mathematical practices analyzed by the historians of mathematics and mathematics education who authored the chapters in the present collection show that the development (and, in some cases, decline) of counting devices and related computational practices needs to be considered within a particular context to which they arguably belonged, namely, the context of mathematics instruction; in their contributions the authors also explore the role that the instruments played in formation of didactical approaches in various mathematical traditions, stretching from Ancient Mesopotamia to the 20th century Europe and North America.

Mathematics and Computation

Avi Wigderson
Mathematics and Computation Book PDF

Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 41,5 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130

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Mathematics and Computation by Avi Wigderson Pdf

An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Mathematics of Quantum Computing

Wolfgang Scherer
Mathematics of Quantum Computing Book PDF

Author : Wolfgang Scherer
Publisher : Springer Nature
Page : 764 pages
File Size : 40,9 Mb
Release : 2019-11-13
Category : Computers
ISBN : 9783030123581

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Mathematics of Quantum Computing by Wolfgang Scherer Pdf

This textbook presents the elementary aspects of quantum computing in a mathematical form. It is intended as core or supplementary reading for physicists, mathematicians, and computer scientists taking a first course on quantum computing. It starts by introducing the basic mathematics required for quantum mechanics, and then goes on to present, in detail, the notions of quantum mechanics, entanglement, quantum gates, and quantum algorithms, of which Shor's factorisation and Grover's search algorithm are discussed extensively. In addition, the algorithms for the Abelian Hidden Subgroup and Discrete Logarithm problems are presented and the latter is used to show how the Bitcoin digital signature may be compromised. It also addresses the problem of error correction as well as giving a detailed exposition of adiabatic quantum computing. The book contains around 140 exercises for the student, covering all of the topics treated, together with an appendix of solutions.

Sets, Logic and Maths for Computing

David Makinson
Sets Logic and Maths for Computing Book PDF

Author : David Makinson
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 55,5 Mb
Release : 2012-02-27
Category : Computers
ISBN : 9781447125006

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Sets, Logic and Maths for Computing by David Makinson Pdf

This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.

Mathematics for Electrical Engineering and Computing

Mary P Attenborough
Mathematics for Electrical Engineering and Computing Book PDF

Author : Mary P Attenborough
Publisher : Elsevier
Page : 576 pages
File Size : 42,8 Mb
Release : 2003-06-30
Category : Mathematics
ISBN : 9780080473406

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Mathematics for Electrical Engineering and Computing by Mary P Attenborough Pdf

Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous systems - particularly vital for Digital Signal Processing (DSP). In addition, as most modern engineers are required to study software, material suitable for Software Engineering - set theory, predicate and prepositional calculus, language and graph theory - is fully integrated into the book. Excessive technical detail and language are avoided, recognising that the real requirement for practising engineers is the need to understand the applications of mathematics in everyday engineering contexts. Emphasis is given to an appreciation of the fundamental concepts behind the mathematics, for problem solving and undertaking critical analysis of results, whether using a calculator or a computer. The text is backed up by numerous exercises and worked examples throughout, firmly rooted in engineering practice, ensuring that all mathematical theory introduced is directly relevant to real-world engineering. The book includes introductions to advanced topics such as Fourier analysis, vector calculus and random processes, also making this a suitable introductory text for second year undergraduates of electrical, electronic and computer engineering, undertaking engineering mathematics courses. Dr Attenborough is a former Senior Lecturer in the School of Electrical, Electronic and Information Engineering at South Bank University. She is currently Technical Director of The Webbery - Internet development company, Co. Donegal, Ireland. Fundamental principles of mathematics introduced and applied in engineering practice, reinforced through over 300 examples directly relevant to real-world engineering

Understand Mathematics, Understand Computing

Arnold L. Rosenberg,Denis Trystram
Understand Mathematics Understand Computing Book PDF

Author : Arnold L. Rosenberg,Denis Trystram
Publisher : Springer Nature
Page : 550 pages
File Size : 49,5 Mb
Release : 2020-12-05
Category : Computers
ISBN : 9783030583767

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Understand Mathematics, Understand Computing by Arnold L. Rosenberg,Denis Trystram Pdf

In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians. By means of lessons and exercises on “doing” mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.

Concrete Mathematics

Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Concrete Mathematics Book PDF

Author : Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Publisher : Addison-Wesley Professional
Page : 811 pages
File Size : 47,6 Mb
Release : 1994-02-28
Category : Computers
ISBN : 9780134389981

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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.

Numerical Mathematics and Computing

Elliott Ward Cheney,David Ronald Kincaid
Numerical Mathematics and Computing Book PDF

Author : Elliott Ward Cheney,David Ronald Kincaid
Publisher : Thomson Brooks/Cole
Page : 678 pages
File Size : 43,6 Mb
Release : 2013
Category : Numerical analysis
ISBN : 1133491812

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Numerical Mathematics and Computing by Elliott Ward Cheney,David Ronald Kincaid Pdf

Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. NUMERICAL MATHEMATICS AND COMPUTING, 7E, International Edition also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors.

Applied Mathematics and Scientific Computing

B. Rushi Kumar,R. Sivaraj,B. S. R. V. Prasad,M. Nalliah,A. Subramanyam Reddy
Applied Mathematics and Scientific Computing Book PDF

Author : B. Rushi Kumar,R. Sivaraj,B. S. R. V. Prasad,M. Nalliah,A. Subramanyam Reddy
Publisher : Springer
Page : 632 pages
File Size : 53,9 Mb
Release : 2019-02-01
Category : Mathematics
ISBN : 9783030011239

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Applied Mathematics and Scientific Computing by B. Rushi Kumar,R. Sivaraj,B. S. R. V. Prasad,M. Nalliah,A. Subramanyam Reddy Pdf

This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences (ICAMS), held at the Vellore Institute of Technology in December 2017. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.

An Introduction to Modern Mathematical Computing

Jonathan M. Borwein,Matthew P. Skerritt
An Introduction to Modern Mathematical Computing Book PDF

Author : Jonathan M. Borwein,Matthew P. Skerritt
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 52,8 Mb
Release : 2012-08-07
Category : Mathematics
ISBN : 9781461442530

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An Introduction to Modern Mathematical Computing by Jonathan M. Borwein,Matthew P. Skerritt Pdf

Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three “M’s” Maple, Mathematica and Matlab. We intend to persuade that Mathematica and other similar tools are worth knowing, assuming only that one wishes to be a mathematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an "experimental mathematician" while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.