Elementary Mathematics From An Algorithmic Standpoint
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Elementary Mathematics From An Algorithmic Standpoint
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Author : Arthur Engel
language : en
Publisher:
Release Date : 1984
Elementary Mathematics From An Algorithmic Standpoint written by Arthur Engel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Foundations Of Mathematics
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Author : Erwin Engeler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foundations Of Mathematics written by Erwin Engeler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book appeared about ten years ago in Gennan. It started as notes for a course which I gave intermittently at the ETH over a number of years. Following repeated suggestions, this English translation was commissioned by Springer; they were most fortunate in finding translators whose mathemati cal stature, grasp of the language and unselfish dedication to the essentially thankless task of rendering the text comprehensible in a second language, both impresses and shames me. Therefore, my thanks go to Dr. Roberto Minio, now Darmstadt and Professor Charles Thomas, Cambridge. The task of preparing a La'JEX-version of the text was extremely daunting, owing to the complexity and diversity of the symbolisms inherent in the various parts of the book. Here, my warm thanks go to Barbara Aquilino of the Mathematics Department of the ETH, who spent tedious but exacting hours in front of her Olivetti. The present book is not primarily intended to teach logic and axiomat ics as such, nor is it a complete survey of what was once called "elementary mathematics from a higher standpoint". Rather, its goal is to awaken a certain critical attitude in the student and to help give this attitude some solid foun dation. Our mathematics students, having been drilled for years in high-school and college, and having studied the immense edifice of analysis, regrettably come away convinced that they understand the concepts of real numbers, Euclidean space, and algorithm.
Computer Algebra And Symbolic Computation
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Author : Joel S. Cohen
language : en
Publisher: CRC Press
Release Date : 2002-07-19
Computer Algebra And Symbolic Computation written by Joel S. Cohen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-19 with Computers categories.
This book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and
Elementary Numerical Analysis
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Author : S. D. Conte
language : en
Publisher: SIAM
Release Date : 2018-02-27
Elementary Numerical Analysis written by S. D. Conte and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-27 with Science categories.
This book provides a thorough and careful introduction to the theory and practice of scientific computing at an elementary, yet rigorous, level, from theory via examples and algorithms to computer programs. The original FORTRAN programs have been rewritten in MATLAB and now appear in a new appendix and online, offering a modernized version of this classic reference for basic numerical algorithms.
Elementary Mathematics From An Advanced Standpoint
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Author : Felix Klein
language : en
Publisher: Cosimo, Inc.
Release Date : 2007-06-01
Elementary Mathematics From An Advanced Standpoint written by Felix Klein and has been published by Cosimo, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-01 with Mathematics categories.
Discusses calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers; algebra-related subjects such as real equations with real unknowns and equations in the field of complex quantities. Also explores elements of analysis, with discussions of logarithmic and exponential functions, the goniometric functions, and infinitesimal calculus. 1932 edition. 125 figures.
Elementary Numerical Analysis
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Author : Samuel Daniel Conte
language : en
Publisher:
Release Date : 1965
Elementary Numerical Analysis written by Samuel Daniel Conte and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Algorithms categories.
Number systems and errors; The solution of nonlinear equations; Interpolation and approximation; Differentiation and integration; Matrices and systems of linear equations; The solution of differential equations; Boundary-value problems in ordinary differential equations.
Elementary Mathematics From A Higher Standpoint
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Author : Felix Klein
language : en
Publisher: Springer
Release Date : 2016-06-28
Elementary Mathematics From A Higher Standpoint written by Felix Klein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Education categories.
These three volumes constitute the first complete English translation of Felix Klein’s seminal series “Elementarmathematik vom höheren Standpunkte aus”. “Complete” has a twofold meaning here: First, there now exists a translation of volume III into English, while until today the only translation had been into Chinese. Second, the English versions of volume I and II had omitted several, even extended parts of the original, while we now present a complete revised translation into modern English. The volumes, first published between 1902 and 1908, are lecture notes of courses that Klein offered to future mathematics teachers, realizing a new form of teacher training that remained valid and effective until today: Klein leads the students to gain a more comprehensive and methodological point of view on school mathematics. The volumes enable us to understand Klein’s far-reaching conception of elementarisation, of the “elementary from a higher standpoint”, in its implementation for school mathematics. This volume I is devoted to what Klein calls the three big “A’s”: arithmetic, algebra and analysis. They are presented and discussed always together with a dimension of geometric interpretation and visualisation - given his epistemological viewpoint of mathematics being based in space intuition. A particularly revealing example for elementarisation is his chapter on the transcendence of e and p, where he succeeds in giving concise yet well accessible proofs for the transcendence of these two numbers. It is in this volume that Klein makes his famous statement about the double discontinuity between mathematics teaching at schools and at universities – it was his major aim to overcome this discontinuity.
Elementary Functions
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Author : Jean-Michel Muller
language : en
Publisher: Birkhäuser
Release Date : 2016-11-16
Elementary Functions written by Jean-Michel Muller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Computers categories.
This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding, as well as some examples of implementation are explored in Part III. Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. New to this edition are an in-depth overview of the IEEE-754-2008 standard for floating-point arithmetic; a section on using double- and triple-word numbers; a presentation of new tools for designing accurate function software; and a section on the Toom-Cook family of multiplication algorithms. The techniques presented in this book will be of interest to implementers of elementary function libraries or circuits and programmers of numerical applications. Additionally, graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find this a useful reference and resource. PRAISE FOR PREVIOUS EDITIONS “[T]his book seems like an essential reference for the experts (which I'm not). More importantly, this is an interesting book for the curious (which I am). In this case, you'll probably learn many interesting things from this book. If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class." — MAA Reviews (Review of Second Edition) "The rich content of ideas sketched or presented in some detail in this book is supplemented by a list of over three hundred references, most of them of 1980 or more recent. The book also contains some relevant typical programs." — Zentralblatt MATH (Review of Second Edition) “I think that the book will be very valuable to students both in numerical analysis and in computer science. I found [it to be] well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find." — Numerical Algorithms (Review of First Edition)
Numerical Mathematics
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Author : Shlomo Breuer
language : en
Publisher: Cambridge University Press
Release Date : 1993-07-30
Numerical Mathematics written by Shlomo Breuer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07-30 with Mathematics categories.
Numerical Mathematics is a unique book that introduces computational microcomputer laboratories as a vehicle for teaching algorithmic aspects of mathematics. This is achieved through a sequence of laboratory assignments, presupposing no previous knowledge of calculus or linear algebra, where the "chalk- and-talk" lecturer turns into a laboratory istructor. The computational assignments cover iterative processes, area approximations, linear systems, convergence acceleration, interpolative approximations, and construction of computer-library functions. The material is part and parcel of the mathematical foundations that should be acquired by a college student in the microcomputer era.
Prime Numbers And Computer Methods For Factorization
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Author : Hans Riesel
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-23
Prime Numbers And Computer Methods For Factorization written by Hans Riesel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-23 with Mathematics categories.
From the original hard cover edition: In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. Hans Riesel’s highly successful first edition of this book has now been enlarged and updated with the goal of satisfying the needs of researchers, students, practitioners of cryptography, and non-scientific readers with a mathematical inclination. It includes important advances in computational prime number theory and in factorization as well as re-computed and enlarged tables, accompanied by new tables reflecting current research by both the author and his coworkers and by independent researchers. The book treats four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition of primes and the factorization of large numbers. The author provides explicit algorithms and computer programs, and has attempted to discuss as many of the classically important results as possible, as well as the most recent discoveries. The programs include are written in PASCAL to allow readers to translate the programs into the language of their own computers. The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.