Category: Number Systems

Download e-book for iPad: Number Words and Number Symbols: A Cultural History of by Karl Menninger

By Karl Menninger

''The historian of arithmetic will locate a lot to curiosity him the following . . . whereas the informal reader could be intrigued via the author's greater narrative ability." — Library Journal
This publication is not just a desirable advent to the concept that of quantity and to numbers themselves, hut a multifaceted linguistic and old research of ways numbers have built and developed in lots of various cultures. Drawing on proof from background, literature, philosophy and ethnology, famous German student Karl Menninger. recounts the advance of numbers either as they're spoken (and written as phrases) and as symbolic summary numerals which can he with no trouble manipulated and combined.
Despite the colossal erudition the writer brings to the subject, he continues a mild tone all through, featuring a lot of the knowledge in anecdotal shape. in addition, virtually three hundred illustrations (photographs and drawings) and plenty of comparative language tables serve to reinforce the textual content. the writer starts with a lucid remedy of quantity series and quantity language, together with the formation of quantity phrases in either Indo-European and non-IndoEuropean languages, hidden quantity phrases and the evolution of the quantity series. He then turns to written numerals and computations: finger counting, people symbols for numbers, alphabetical numerals, the "German" Roman numerals, the abacus and extra. the ultimate part matters the advance of our modem decimal approach, with its position notation and 0, in response to the Indian quantity method, and its creation to the West throughout the paintings of the Italian mathematician Fibonacci. the writer concludes with a assessment of spoken numbers and quantity symbols in China and Japan.
"The booklet is mainly stable on early counting and calculating units: primitive tally sticks, the knotted cords of old Peru, the flowery finger symbols as soon as used for numbers, counting forums with movable counters, and naturally the abacus." — Martin Gardner, Book World

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New PDF release: Introduction to Scientific Programming and Simulation Using

By Owen Jones,Robert Maillardet,Andrew Robinson

Learn how one can software Stochastic Models

Highly instructed, the best-selling first variation of Introduction to medical Programming and Simulation utilizing R was lauded as a good, easy-to-read advent with wide examples and routines. This moment version maintains to introduce clinical programming and stochastic modelling in a transparent, functional, and thorough approach. Readers examine programming by way of experimenting with the supplied R code and data.

The book’s 4 components teach:

  • Core wisdom of R and programming concepts

  • How to contemplate arithmetic from a numerical standpoint, together with the applying of those techniques to root discovering, numerical integration, and optimisation

  • Essentials of likelihood, random variables, and expectation required to appreciate simulation

  • Stochastic modelling and simulation, together with random quantity iteration and Monte Carlo integration

In a brand new bankruptcy on platforms of normal differential equations (ODEs), the authors disguise the Euler, midpoint, and fourth-order Runge-Kutta (RK4) schemes for fixing structures of first-order ODEs. They examine the numerical potency of different schemes experimentally and express tips on how to enhance the RK4 scheme through the use of an adaptive step measurement.

Another new bankruptcy makes a speciality of either discrete- and continuous-time Markov chains. It describes transition and cost matrices, category of states, restricting behaviour, Kolmogorov ahead and backward equations, finite soaking up chains, and anticipated hitting occasions. It additionally provides tools for simulating discrete- and continuous-time chains in addition to thoughts for outlining the country area, together with lumping states and supplementary variables.

Building readers’ statistical instinct, Introduction to medical Programming and Simulation utilizing R, moment Edition indicates tips on how to flip algorithms into code. it really is designed when you have the desire to make instruments, not only use them. The code and knowledge can be found for obtain from CRAN.

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George A. Anastassiou,Razvan Mezei's Numerical Analysis Using Sage (Springer Undergraduate Texts PDF

By George A. Anastassiou,Razvan Mezei

This is the 1st numerical research textual content to take advantage of Sage for the implementation of algorithms and will be utilized in a one-semester path for undergraduates in arithmetic, math schooling, laptop science/information know-how, engineering, and actual sciences. the first objective of this article is to simplify knowing of the theories and ideas from a numerical analysis/numerical equipment path through a contemporary programming language like Sage. apart from the presentation of basic theoretical notions of numerical research through the textual content, every one bankruptcy concludes with numerous workouts which are orientated to real-world program. solutions will be confirmed utilizing Sage.

The provided code, written in center parts of Sage, are backward suitable, i.e., simply acceptable to different software program structures corresponding to Mathematica®. Sage is open resource software program and makes use of Python-like syntax. earlier Python programming event isn't really a demand for the reader, although familiarity with any programming language is a plus. additionally, the code should be written utilizing any net browser and is consequently important with Laptops, pills, iPhones, Smartphones, and so on. All Sage code that's awarded within the textual content is overtly to be had on

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Read e-book online Accuracy Verification Methods: Theory and Algorithms: 32 PDF

By Olli Mali,Pekka Neittaanmäki,Sergey Repin

The value of accuracy verification equipment was once understood on the very starting of the advance of numerical research. contemporary many years have noticeable a quick progress of effects with regards to adaptive numerical tools and a posteriori estimates. notwithstanding, during this vital zone there frequently exists a seen hole among mathematicians developing the idea and researchers constructing utilized algorithms which may be utilized in engineering and clinical computations for assured and effective mistakes control.


The objectives of the booklet are to (1) supply a clear clarification of the underlying mathematical thought in a mode available not just to complex numerical analysts but in addition to engineers and scholars; (2) current unique step by step algorithms that persist with from a concept; (3) speak about their merits and downsides, parts of applicability, provide thoughts and examples.

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New PDF release: Domain Decomposition Methods in Science and Engineering

By Ulrich Langer,Marco Discacciati,David E. Keyes,Olof Widlund,Walter Zulehner

Domain decomposition is an energetic, interdisciplinary examine box fascinated by the advance, research, and implementation of coupling and decoupling thoughts in mathematical and computational versions. This quantity includes chosen papers provided on the seventeenth foreign convention on area Decomposition equipment in technological know-how and Engineering. It provides the latest area decomposition strategies and examines their use within the modeling and simulation of advanced problems.

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Download e-book for iPad: Ordinary and Partial Differential Equations: With Special by Ravi P. Agarwal,Donal O'Regan

By Ravi P. Agarwal,Donal O'Regan

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs via 50 class-tested lectures. Mathematical options are defined with readability and rigor, utilizing totally worked-out examples and useful illustrations. routines are provided on the finish of every bankruptcy for perform. The therapy of ODEs is built at the side of PDEs and is aimed regularly in the direction of purposes. The publication covers very important applications-oriented subject matters comparable to recommendations of ODEs in kind of strength sequence, specific services, Bessel features, hypergeometric services, orthogonal features and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, thought of Fourier series.

Undergraduate and graduate scholars in arithmetic, physics and engineering will make the most of this publication. The e-book assumes familiarity with calculus.

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Download e-book for kindle: Modellistica Numerica per Problemi Differenziali (UNITEXT) by Alfio Quarteroni

By Alfio Quarteroni

In questo testo si introducono i concetti di base according to los angeles modellistica numerica di problemi differenziali alle derivate parziali. Si considerano le classiche equazioni lineari ellittiche, paraboliche ed iperboliche, ma anche altre equazioni, quali quelle di diffusione e trasporto, di Navier-Stokes e le leggi di conservazione; si forniscono inoltre numerosi esempi fisici che stanno alla base di tali equazioni. Quindi si analizzano metodi di risoluzione numerica basati su elementi finiti (continui e discontinui), differenze finite, volumi finiti, metodi spettrali (continui e discontinui), nonché strategie di approssimazione più avanzate basate sui metodi di decomposizione di domini o quelli di risoluzione di problemi di controllo ottimale. In particolare vengono discussi gli aspetti algoritmici e di implementazione al calcolatore e si forniscono diversi programmi di semplice utilizzo. Il testo non presuppone una approfondita conoscenza matematica delle equazioni alle derivate parziali: i concetti rigorosamente indispensabili al riguardo sono riportati nell'Appendice. Esso è pertanto adatto agli studenti dei corsi di laurea di indirizzo scientifico (Ingegneria, Matematica, Fisica, Scienze dell'Informazione) e consigliabile a ricercatori del mondo accademico ed extra-accademico che vogliano avvicinarsi a questo interessante ramo della matematica applicata e delle scienze computazionali.

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New PDF release: Algorithms and Programming: Problems and Solutions (Modern

By Alexander Shen

This e-book is essentially meant for a first-year undergraduate direction in programming. it really is based in a problem-solution layout that calls for the scholar to imagine in the course of the programming strategy, hence constructing an knowing of the underlying idea. every one bankruptcy is kind of self reliant. even though the writer assumes a few average familiarity with programming constructs, the publication is definitely readable by means of a scholar taking a uncomplicated introductory direction in laptop technology. scholars and academics will locate this either an exceptional textual content for studying programming and a resource of difficulties for quite a few courses.

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Read e-book online Numerical Methods for Controlled Stochastic Delay Systems PDF

By Harold Kushner

The Markov chain approximation tools are common for the numerical resolution of nonlinear stochastic regulate difficulties in non-stop time. This e-book extends the easy methods to stochastic structures with delays. The publication is the 1st at the topic and may be of significant curiosity to all those that paintings with stochastic hold up equations and whose major curiosity is both within the use of the algorithms or within the arithmetic. an outstanding source for graduate scholars, researchers, and practitioners, the paintings can be utilized as a graduate-level textbook for a distinct issues direction or seminar on numerical equipment in stochastic control.

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