An Introduction To Modern Mathematical Computing

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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 : 224 pages
File Size : 51,8 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.

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
Page : 216 pages
File Size : 42,8 Mb
Release : 2011-08-25
Category : Mathematics
ISBN : 1461401232

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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 Maple and other like 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.

Mathematics and Computation

Avi Wigderson
Mathematics and Computation Book PDF

Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 41,7 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

Introduction to Computational Mathematics

Xin-She Yang
Introduction to Computational Mathematics Book PDF

Author : Xin-She Yang
Publisher : World Scientific Publishing Company
Page : 344 pages
File Size : 40,5 Mb
Release : 2014-11-26
Category : Mathematics
ISBN : 9789814635806

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Introduction to Computational Mathematics by Xin-She Yang Pdf

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.

Mathematical Computing

David Betounes,Mylan Redfern
Mathematical Computing Book PDF

Author : David Betounes,Mylan Redfern
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 50,6 Mb
Release : 2001-12-07
Category : Computers
ISBN : 0387953310

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Mathematical Computing by David Betounes,Mylan Redfern Pdf

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.

An Introduction to Mathematical Modeling

Edward A. Bender
An Introduction to Mathematical Modeling Book PDF

Author : Edward A. Bender
Publisher : Courier Corporation
Page : 273 pages
File Size : 54,6 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486137124

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An Introduction to Mathematical Modeling by Edward A. Bender Pdf

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.

An Introduction to Formal Languages and Machine Computation

Song Y. Yan
An Introduction to Formal Languages and Machine Computation Book PDF

Author : Song Y. Yan
Publisher : World Scientific
Page : 424 pages
File Size : 55,6 Mb
Release : 1998
Category : Computers
ISBN : 9810234228

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An Introduction to Formal Languages and Machine Computation by Song Y. Yan Pdf

This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.

An Introduction to Scientific, Symbolic, and Graphical Computation

Eugene Fiume
An Introduction to Scientific Symbolic and Graphical Computation Book PDF

Author : Eugene Fiume
Publisher : CRC Press
Page : 322 pages
File Size : 41,8 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9781439864463

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An Introduction to Scientific, Symbolic, and Graphical Computation by Eugene Fiume Pdf

This down-to-earth introduction to computation makes use of the broad array of techniques available in the modern computing environment. A self-contained guide for engineers and other users of computational methods, it has been successfully adopted as a text in teaching the next generation of mathematicians and computer graphics majors.

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 : 47,9 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.

Numerical Analysis in Modern Scientific Computing

Peter Deuflhard,Andreas Hohmann
Numerical Analysis in Modern Scientific Computing Book PDF

Author : Peter Deuflhard,Andreas Hohmann
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780387215846

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Numerical Analysis in Modern Scientific Computing by Peter Deuflhard,Andreas Hohmann Pdf

This book introduces the main topics of modern numerical analysis: sequence of linear equations, error analysis, least squares, nonlinear systems, symmetric eigenvalue problems, three-term recursions, interpolation and approximation, large systems and numerical integrations. The presentation draws on geometrical intuition wherever appropriate and is supported by a large number of illustrations, exercises, and examples.

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 : 44,6 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.

A Course in Mathematical Biology

Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes M?ller,Birgitt Sch?nfisch
A Course in Mathematical Biology Book PDF

Author : Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes M?ller,Birgitt Sch?nfisch
Publisher : SIAM
Page : 307 pages
File Size : 55,6 Mb
Release : 2006-07-01
Category : Mathematics
ISBN : 9780898718256

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A Course in Mathematical Biology by Gerda de Vries,Thomas Hillen,Mark Lewis,Johannes M?ller,Birgitt Sch?nfisch Pdf

This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.

Mathematical Analysis and the Mathematics of Computation

Werner Römisch,Thomas Zeugmann
Mathematical Analysis and the Mathematics of Computation Book PDF

Author : Werner Römisch,Thomas Zeugmann
Publisher : Springer
Page : 703 pages
File Size : 40,6 Mb
Release : 2016-10-04
Category : Computers
ISBN : 9783319427553

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Mathematical Analysis and the Mathematics of Computation by Werner Römisch,Thomas Zeugmann Pdf

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.

Introduction to Experimental Mathematics

Søren Eilers,Rune Johansen
Introduction to Experimental Mathematics Book PDF

Author : Søren Eilers,Rune Johansen
Publisher : Cambridge University Press
Page : 321 pages
File Size : 55,7 Mb
Release : 2017-06
Category : Computers
ISBN : 9781107156135

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Introduction to Experimental Mathematics by Søren Eilers,Rune Johansen Pdf

This text introduces students to an experimental approach to mathematics, using Maple to systematically investigate and develop mathematical theory.

Mathematics in Computing

Gerard O’Regan
Mathematics in Computing Book PDF

Author : Gerard O’Regan
Publisher : Springer Nature
Page : 468 pages
File Size : 45,7 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.