Mathematical Computing

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Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Mathematical Computing

Author : David Betounes
Publisher : Springer Science & Business Media
ISBN 13 : 1461300673
Total Pages : 412 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Mathematical Computing by : David Betounes

Download or read book Mathematical Computing written by David Betounes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book teaches introductory computer programming using Maple, offering more mathematically oriented exercises and problems than those found in traditional programming courses, while reinforcing and applying concepts and techniques of calculus. Includes case studies.

Introduction to Computational Mathematics

Author : Xin-She Yang
Publisher : World Scientific Publishing Company
ISBN 13 : 9814635804
Total Pages : 344 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Introduction to Computational Mathematics by : Xin-She Yang

Download or read book Introduction to Computational Mathematics written by Xin-She Yang and published by World Scientific Publishing Company. This book was released on 2014-11-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.

Mathematics in Computing

Author : Gerard O’Regan
Publisher : Springer Nature
ISBN 13 : 3030342093
Total Pages : 468 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Mathematics in Computing by : Gerard O’Regan

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.

Mathematics for Computer Science

Author : Eric Lehman
Publisher :
ISBN 13 : 9789888407064
Total Pages : 988 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Mathematics for Computer Science by : Eric Lehman

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.

Mathematics of Quantum Computing

Author : Wolfgang Scherer
Publisher : Springer Nature
ISBN 13 : 3030123588
Total Pages : 764 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Mathematics of Quantum Computing by : Wolfgang Scherer

Download or read book Mathematics of Quantum Computing written by Wolfgang Scherer and published by Springer Nature. This book was released on 2019-11-13 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computer Methods for Mathematical Computations

Author : George Elmer Forsythe
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computer Methods for Mathematical Computations by : George Elmer Forsythe

Download or read book Computer Methods for Mathematical Computations written by George Elmer Forsythe and published by Prentice Hall. This book was released on 1977 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics for Future Computing and Communications

Author : Liao Heng
Publisher : Cambridge University Press
ISBN 13 : 1316513580
Total Pages : 399 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Mathematics for Future Computing and Communications by : Liao Heng

Download or read book Mathematics for Future Computing and Communications written by Liao Heng and published by Cambridge University Press. This book was released on 2021-12-16 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panorama of new ideas in mathematics that are driving innovation in computing and communications.

Scientific Computing

Author : Michael T. Heath
Publisher : SIAM
ISBN 13 : 1611975573
Total Pages : 567 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Scientific Computing by : Michael T. Heath

Download or read book Scientific Computing written by Michael T. Heath and published by SIAM. This book was released on 2018-11-14 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

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

Author : Alexei Volkov
Publisher : Springer
ISBN 13 : 3319733966
Total Pages : 471 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators by : Alexei Volkov

Download or read book Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators written by Alexei Volkov and published by Springer. This book was released on 2019-01-11 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Analysis

Author : David Kincaid
Publisher : American Mathematical Soc.
ISBN 13 : 0821847880
Total Pages : 810 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Numerical Analysis by : David Kincaid

Download or read book Numerical Analysis written by David Kincaid and published by American Mathematical Soc.. This book was released on 2009 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.

Applied Mathematics and Scientific Computing

Author : B. Rushi Kumar
Publisher : Springer
ISBN 13 : 3030011232
Total Pages : 632 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Applied Mathematics and Scientific Computing by : B. Rushi Kumar

Download or read book Applied Mathematics and Scientific Computing written by B. Rushi Kumar and published by Springer. This book was released on 2019-02-01 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Foundations of Computer Networking

Author : Srinivasan Keshav
Publisher : Pearson Education
ISBN 13 : 0321792106
Total Pages : 496 pages
Book Rating : 4.3/5 (217 download)

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Book Synopsis Mathematical Foundations of Computer Networking by : Srinivasan Keshav

Download or read book Mathematical Foundations of Computer Networking written by Srinivasan Keshav and published by Pearson Education. This book was released on 2012 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical techniques pervade current research in computer networking, yet are not taught to most computer science undergraduates. This self-contained, highly-accessible book bridges the gap, providing the mathematical grounding students and professionals need to successfully design or evaluate networking systems. The only book of its kind, it brings together information previously scattered amongst multiple texts. It first provides crucial background in basic mathematical tools, and then illuminates the specific theories that underlie computer networking. Coverage includes: * Basic probability * Statistics * Linear Algebra * Optimization * Signals, Systems, and Transforms, including Fourier series and transforms, Laplace transforms, DFT, FFT, and Z transforms * Queuing theory * Game Theory * Control theory * Information theory

Mathematical Principles for Scientific Computing and Visualization

Author : Gerald Farin
Publisher : CRC Press
ISBN 13 : 156881321X
Total Pages : 296 pages
Book Rating : 4.5/5 (688 download)

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Book Synopsis Mathematical Principles for Scientific Computing and Visualization by : Gerald Farin

Download or read book Mathematical Principles for Scientific Computing and Visualization written by Gerald Farin and published by CRC Press. This book was released on 2008-10-21 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.

Modelling Computing Systems

Author : Faron Moller
Publisher :
ISBN 13 :
Total Pages : 500 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis Modelling Computing Systems by : Faron Moller

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.

Understand Mathematics, Understand Computing

Author : Arnold L. Rosenberg
Publisher : Springer Nature
ISBN 13 : 3030583767
Total Pages : 550 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Understand Mathematics, Understand Computing by : Arnold L. Rosenberg

Download or read book Understand Mathematics, Understand Computing written by Arnold L. Rosenberg and published by Springer Nature. This book was released on 2020-12-05 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Modern Mathematical Computing

Author : Jonathan M. Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 1461442532
Total Pages : 237 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis An Introduction to Modern Mathematical Computing by : Jonathan M. Borwein

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.