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An Introduction to Modern Mathematical Computing

Author: Jonathan M. Borwein
Publisher: Springer Science & Business Media
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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 Mathematical Modeling

Author: Edward A. Bender
Publisher: Courier Corporation
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Format Type: PDF, ePub, Docs
Size: 14,75 MB
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Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.


Introduction to Experimental Mathematics

Author: Søren Eilers
Publisher: Cambridge University Press
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Size: 27,39 MB
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Mathematics is not, and never will be, an empirical science, but mathematicians are finding that the use of computers and specialized software allows the generation of mathematical insight in the form of conjectures and examples, which pave the way for theorems and their proofs. In this way, the experimental approach to pure mathematics is revolutionizing the way research mathematicians work. As the first of its kind, this book provides material for a one-semester course in experimental mathematics that will give students the tools and training needed to systematically investigate and develop mathematical theory using computer programs written in Maple. Accessible to readers without prior programming experience, and using examples of concrete mathematical problems to illustrate a wide range of techniques, the book gives a thorough introduction to the field of experimental mathematics, which will prepare students for the challenge posed by open mathematical problems.


Introduction to Computational Mathematics

Author: Xin-She Yang
Publisher: World Scientific
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Size: 30,62 MB
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This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of modern numerical algorithms and scientific computing. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. It covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithms, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, to nonlinear curve-fitting and swarm optimization. Especially suitable for undergraduates and graduates in computational mathematics, numerical algorithms, and scientific computing, it can be used as a textbook and/or reference book.


An Introduction to Formal Languages and Machine Computation

Author: Song Y. Yan
Publisher: World Scientific
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Size: 19,94 MB
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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 Mathematical Taxonomy

Author: Graham Dunn
Publisher: Courier Corporation
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Size: 12,56 MB
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For students of mathematical biology, an introduction to taxonomic characters, measurement of similarity, analysis of principal components, multidimensional scaling, cluster analysis, identification and assignment techniques, and the construction of evolutionary trees.


A Short Introduction to Numerical Analysis

Author: M. V. Wilkes
Publisher: CUP Archive
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Format Type: PDF
Size: 28,87 MB
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This short book sets out the principles of the methods commonly employed in obtaining numerical solutions to mathematical equations and shows how they are applied in solving particular types of equations. Now that computing facilities are available to most universities, scientific and engineering laboratories and design shops, an introduction to numerical method is an essential part of the training of scientists and engineers. A course on the lines of Professor Wilkes's book is given to graduate or undergraduate students of mathematics, the physical sciences and engineering at many universities and the number will increase. By concentrating on the essentials of his subject and giving it a modern slant, Professor Wilkes has written a book that is both concise and that covers the needs of a great many users of digital computers; it will serve also as a sound introduction for those who need to consult more detailed works.


Linear Programming

Author: Howard Karloff
Publisher: Springer Science & Business Media
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Size: 26,49 MB
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To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming.... Style is informal. ...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews This is a textbook intended for advanced undergraduate or graduate students. It contains both theory and computational practice. —Zentralblatt Math


An Introduction to Computational Physics

Author: Tao Pang
Publisher: Cambridge University Press
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Size: 29,51 MB
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This advanced textbook provides an introduction to the basic methods of computational physics, as well as an overview of recent progress in several areas of scientific computing. The author presents many step-by-step examples of practical numerical methods, often with the relevant program listing. The first half of the book deals with basic computational tools and routines, covering differential equations, spectral analysis and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as Monte Carlo simulations, lattice gas methods, molecular dynamics and symbolic computing. The book includes many exercises, and it can be used as a textbook for senior undergraduate or first-year graduate courses on scientific computation. It will also be a useful reference for anyone involved in computational physics or related disciplines.


Numerical Analysis in Modern Scientific Computing

Author: Andreas Hohmann
Publisher: Springer Science & Business Media
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Size: 19,36 MB
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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.