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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.


Introduction to Experimental Mathematics

Author: Søren Eilers
Publisher: Cambridge University Press
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Size: 20,65 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.


An Introduction to Mathematical Modeling

Author: Edward A. Bender
Publisher: Courier Corporation
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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 Computational Mathematics

Author: Xin-She Yang
Publisher: World Scientific
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Size: 13,55 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.


Computational Statistics

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Publisher: Springer Science & Business Media
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Computational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics. This book describes computationally intensive statistical methods in a unified presentation, emphasizing techniques, such as the PDF decomposition, that arise in a wide range of methods.


Introduction to Theoretical Computer Science

Author: Xiwen Ma
Publisher: World Scientific
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The contents of this book are self-sufficient in the sense that no preliminary knowledge other than elementary set theory is needed and there are no complicated mathematical theorems in the book. A must for those entering the field.


An Introduction to Computational Physics

Author: Tao Pang
Publisher: Cambridge University Press
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Size: 10,38 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.


Mathematics and Its Teaching in the Southern Americas

Author: Héctor Rosario
Publisher: World Scientific
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This anthology presents a comprehensive review of mathematics and its teaching in the following nations in South America, Central America, and the Caribbean: Argentina, Bolivia, Brazil, Chile, Colombia, Costa Rica, Cuba, Guyana, Haiti, Honduras, México, Panamá, Paraguay, Perú, Puerto Rico, Trinidad and Tobago, and Venezuela. The last summary of mathematics education encompassing countries from the Southern Americas appeared in 1966. Progress in the field during five decades has remained unexamined until now. Contents:ARGENTINA: A Review of Mathematics Education through Mathematical Problems at the Secondary Level (Betina Duarte)BOLIVIA: An Approach to Mathematics Education in the Plurinational State (A Pari)BRAZIL: History and Trends in Mathematics Education (Beatriz S D'Ambrosio, Juliana Martins, and Viviane de Oliveira Santos)CHILE: The Context and Pedagogy of Mathematics Teaching and Learning (Eliana D Rojas and Fidel Oteiza)COLOMBIA: The Role of Mathematics in the Making of a Nation (Hernando J Echeverri and Angela M Restrepo)COSTA RICA: History and Perspectives on Mathematics and Mathematics Education (Ángel Ruiz)CUBA: Mathematics and Its Teaching (Otilio B Mederos Anoceto, Miguel A Jiménez Pozo, and José M Sigarreta)GUYANA: The Mathematical Growth of an Emerging Nation (Mahendra Singh and Lenox Allicock)HAITI: History of Mathematics Education (Jean W Richard)HONDURAS: Origins, Development, and Challenges in the Teaching of Mathematics (Marvin Roberto Mendoza Valencia)MÉXICO: The History and Development of a Nation and Its Influence on the Development of Mathematics and Mathematics Education (Eduardo Mancera and Alicia Ávila)PANAMÁ: Towards the First World through Mathematics (Euclides Samaniego, Nicolás A Samaniego, and Benigna Fernández)PARAGUAY: A Review of the History of Mathematics and Mathematics Education (Gabriela Gómez Pasquali)PERÚ: A Look at the History of Mathematics and Mathematics Education (César Carranza Saravia and Uldarico Malaspina Jurado)PUERTO RICO: The Forging of a National Identity in Mathematics Education (Héctor Rosario, Daniel McGee, Jorge M López, Ana H Quintero, and Omar A Hernández)TRINIDAD and TOBAGO: Mathematics Education in the Twin Island Republic (Shereen Alima Khan and Vimala Judy Kamalodeen)VENEZUELA: Signs for the Historical Reconstruction of Its Mathematics Education (Fredy Enrique González) Readership: Graduates and professionals in mathematics education; education planners. Key Features:Featured introduction by Professor Ubiratàn D'Ambrosio of Brazil — the most prestigious of Latin American mathematics educatorsInsights into the impact of political changes of mathematics education in Cuba, Venezuela, Brazil etc.Historical references, not available elsewhere, are covered in this bookKeywords:Mathematics;Mathematics Teaching;South America;Central America;Caribbean;Mathematics Curriculum;History of Mathematics;Mathematics Education;Pedagogy in Mathematics


Introduction to Dynamic Programming

Author: Leon Cooper
Publisher: Elsevier
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Introduction to Dynamic Programming provides information pertinent to the fundamental aspects of dynamic programming. This book considers problems that can be quantitatively formulated and deals with mathematical models of situations or phenomena that exists in the real world. Organized into 10 chapters, this book begins with an overview of the fundamental components of any mathematical optimization model. This text then presents the details of the application of dynamic programming to variational problems. Other chapters consider the application of dynamic programming to inventory theory, Markov processes, chemical engineering, optimal control theory, calculus of variations, and economics. This book discusses as well the approach to problem solving that is typical of dynamic programming. The final chapter deals with a number of actual applications of dynamic programming to practical problems. This book is a valuable resource for .graduate level students of mathematics, economics, statistics, business, operations research, industrial engineering, or other engineering fields.


A Concise Handbook of Mathematics Physics and Engineering Sciences

Author: Andrei D. Polyanin
Publisher: CRC Press
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A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand. The first part of the book contains chapters on arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, functions of complex variables, integral transforms, ordinary and partial differential equations, special functions, and probability theory. The second part discusses molecular physics and thermodynamics, electricity and magnetism, oscillations and waves, optics, special relativity, quantum mechanics, atomic and nuclear physics, and elementary particles. The third part covers dimensional analysis and similarity, mechanics of point masses and rigid bodies, strength of materials, hydrodynamics, mass and heat transfer, electrical engineering, and methods for constructing empirical and engineering formulas. The main text offers a concise, coherent survey of the most important definitions, formulas, equations, methods, theorems, and laws. Numerous examples throughout and references at the end of each chapter provide readers with a better understanding of the topics and methods. Additional issues of interest can be found in the remarks. For ease of reading, the supplement at the back of the book provides several long mathematical tables, including indefinite and definite integrals, direct and inverse integral transforms, and exact solutions of differential equations.