Download or read book Mathematics in Computing written by Gerard O’Regan and published by Springer Nature. This book was released on 2020-01-10 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematics and Computation in Music written by Jason Yust and published by Springer. This book was released on 2013-06-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013. The 18 papers presented were carefully reviewed and selected from numerous submissions. They are promoting the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition and other related fields.

Download or read book An Introduction to Modern Mathematical Computing written by Jonathan M. Borwein and published by Springer Science & Business Media. This book was released on 2012-08-07 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Numerical Mathematics and Computing written by Elliott Ward Cheney and published by Thomson Brooks/Cole. This book was released on 2013 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Foundation Mathematics for Computer Science written by John Vince and published by Springer. This book was released on 2015-07-27 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Foundations of Geometric Algebra Computing written by Dietmar Hildenbrand and published by Springer Science & Business Media. This book was released on 2012-12-31 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.

Download or read book Computational and Analytical Mathematics written by David H. Bailey and published by Springer Science & Business Media. This book was released on 2013-09-15 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Jonathan Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980-1999. He has served the Canadian Mathematics Community through his presidency (2000–02) as well as his 15 years of editing the CMS book series. Jonathan Borwein’s vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein’s honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop on ‘Computational and Analytical Mathematics’ held in May 2011 in celebration of Dr. Borwein’s 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches.

Download or read book Modelling Computing Systems written by Faron Moller and published by . This book was released on 2013 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title explores concepts of games and strategies to provide a paradigm for understanding the nature of computation and provides an elementary introduction to the mathematics and modelling of computing systems through exercises and examples, giving readers the opportunities to test their understanding and broaden their knowledge.

Download or read book Computer Aided Assessment of Mathematics written by Chris Sangwin and published by OUP Oxford. This book was released on 2013-05-02 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded and, in articulating precisely the desired criteria, the teacher needs to think very carefully about the goals of the task. Hence CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. One example is how it is natural for busy teachers to set only those questions that can be marked by hand in a straightforward way, even though the constraints of paper-based formats restrict what they do and why. There are other kinds of questions, such as those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. However, such questions have their place and value in provoking thought and learning. This book, aimed at teachers in both schools and universities, explores how, in certain cases, different question types can be automatically assessed. Case studies of existing systems have been included to illustrate this in a concrete and practical way.

Download or read book Mathematics for Computer Science written by Eric Lehman and published by . This book was released on 2017-03-08 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Building Bridges written by Martin Grötschel and published by Springer Science & Business Media. This book was released on 2010-05-28 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematics for Computer Graphics written by John Vince and published by Springer Science & Business Media. This book was released on 2005-11-09 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise and informal introductory book on the mathematical concepts that underpin computer graphics. The author, John Vince, makes the concepts easy to understand, enabling non-experts to come to terms with computer animation work. The book complements the author's other works and is written in the same accessible and easy-to-read style. It is also a useful reference book for programmers working in the field of computer graphics, virtual reality, computer animation, as well as students on digital media courses, and even mathematics courses.

Download or read book The Best Writing on Mathematics 2010 written by Mircea Pitici and published by Princeton University Press. This book was released on 2021-09-14 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year’s most memorable writing on mathematics This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more. In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it's headed.

Download or read book Concrete Mathematics written by Ronald L. Graham and published by Addison-Wesley Professional. This book was released on 1994-02-28 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Relational Mathematics written by Gunther Schmidt and published by Cambridge University Press. This book was released on 2011 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relational mathematics is to operations research and informatics what numerical mathematics is to engineering: it is intended to help modelling, reasoning, and computing. Its applications are therefore diverse, ranging from psychology, linguistics, decision aid, and ranking to machine learning and spatial reasoning. Although many developments have been made in recent years, they have rarely been shared amongst this broad community of researchers. This comprehensive 2010 overview begins with an easy introduction to the topic, assuming a minimum of prerequisites; but it is nevertheless theoretically sound and up to date. It is suitable for applied scientists, explaining all the necessary mathematics from scratch using a multitude of visualised examples, via matrices and graphs. It ends with tangible results on the research level. The author illustrates the theory and demonstrates practical tasks in operations research, social sciences and the humanities.

Download or read book Mathematics for Electrical Engineering and Computing written by Mary P Attenborough and published by Elsevier. This book was released on 2003-06-30 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Mathematics and Climate written by Hans Kaper and published by SIAM. This book was released on 2013-10-18 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics and Climate is a timely textbook aimed at students and researchers in mathematics and statistics who are interested in current issues of climate science, as well as at climate scientists who wish to become familiar with qualitative and quantitative methods of mathematics and statistics. The authors emphasize conceptual models that capture important aspects of Earth's climate system and present the mathematical and statistical techniques that can be applied to their analysis. Topics from climate science include the Earth?s energy balance, temperature distribution, ocean circulation patterns such as El Ni?o?Southern Oscillation, ice caps and glaciation periods, the carbon cycle, and the biological pump. Among the mathematical and statistical techniques presented in the text are dynamical systems and bifurcation theory, Fourier analysis, conservation laws, regression analysis, and extreme value theory. The following features make Mathematics and Climate a valuable teaching resource: issues of current interest in climate science and sustainability are used to introduce the student to the methods of mathematics and statistics; the mathematical sophistication increases as the book progresses and topics can thus be selected according to interest and level of knowledge; each chapter ends with a set of exercises that reinforce or enhance the material presented in the chapter and stimulate critical thinking and communication skills; and the book contains an extensive list of references to the literature, a glossary of terms for the nontechnical reader, and a detailed index.