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Utilizing MATHEMATICA Software to Improve Students' Problem Solving
International Journal of Education and Research Vol. 7 No. 11 November 2019 Utilizing MATHEMATICA Software to Improve Students’ Problem Solving Skills of Derivative and its Applications Hiyam, Bataineh , Jordan University of Science and Technology, Jordan Ali Zoubi, Yarmouk University, Jordan Abdalla Khataybeh, Yarmouk University, Jordan Abstract Traditional methods of teaching calculus (1) at most Jordanian universities are usually used. This paper attempts to introduce an innovative approach for teaching Calculus (1) using Computerized Algebra Systems (CAS). This paper examined utilizing Mathematica as a supporting tool for the teaching learning process of Calculus (1), especially for derivative and its applications. The research created computerized educational materials using Mathematica, which was used as an approach for teaching a (25) students as experimental group and another (25) students were taught traditionally as control group. The understandings of both samples were tested using problem solving test of 6 questions. The results revealed the experimental group outscored the control group significantly on the problem solving test. The use of Mathematica not just improved students’ abilities to interpret graphs and make connection between the graph of a function and its derivative, but also motivate students’ thinking in different ways to come up with innovative solutions for unusual and non routine problems involving the derivative and its applications. This research suggests that CAS tools should be integrated to teaching calculus (1) courses. Keywords: Mathematica, Problem solving, Derivative, Derivative’s applivations. INTRODUCTION The major technological advancements assisted decision makers and educators to pay greater attention on making the learner as the focus of the learning-teaching process. The use of computer algebra systems (CAS) in teaching mathematics has proved to be more effective compared to traditional teaching methods (Irving & Bell, 2004; Dhimar & Petal, 2013; Abdul Majid, huneiti, Al- Nafa & Balachander, 2012). -
The Yacas Book of Algorithms
The Yacas Book of Algorithms by the Yacas team 1 Yacas version: 1.3.6 generated on November 25, 2014 This book is a detailed description of the algorithms used in the Yacas system for exact symbolic and arbitrary-precision numerical computations. Very few of these algorithms are new, and most are well-known. The goal of this book is to become a compendium of all relevant issues of design and implementation of these algorithms. 1This text is part of the Yacas software package. Copyright 2000{2002. Principal documentation authors: Ayal Zwi Pinkus, Serge Winitzki, Jitse Niesen. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts and no Back-Cover Texts. A copy of the license is included in the section entitled \GNU Free Documentation License". Contents 1 Symbolic algebra algorithms 3 1.1 Sparse representations . 3 1.2 Implementation of multivariate polynomials . 4 1.3 Integration . 5 1.4 Transforms . 6 1.5 Finding real roots of polynomials . 7 2 Number theory algorithms 10 2.1 Euclidean GCD algorithms . 10 2.2 Prime numbers: the Miller-Rabin test and its improvements . 10 2.3 Factorization of integers . 11 2.4 The Jacobi symbol . 12 2.5 Integer partitions . 12 2.6 Miscellaneous functions . 13 2.7 Gaussian integers . 13 3 A simple factorization algorithm for univariate polynomials 15 3.1 Modular arithmetic . 15 3.2 Factoring using modular arithmetic . -
CAS (Computer Algebra System) Mathematica
CAS (Computer Algebra System) Mathematica- UML students can download a copy for free as part of the UML site license; see the course website for details From: Wikipedia 2/9/2014 A computer algebra system (CAS) is a software program that allows [one] to compute with mathematical expressions in a way which is similar to the traditional handwritten computations of the mathematicians and other scientists. The main ones are Axiom, Magma, Maple, Mathematica and Sage (the latter includes several computer algebras systems, such as Macsyma and SymPy). Computer algebra systems began to appear in the 1960s, and evolved out of two quite different sources—the requirements of theoretical physicists and research into artificial intelligence. A prime example for the first development was the pioneering work conducted by the later Nobel Prize laureate in physics Martin Veltman, who designed a program for symbolic mathematics, especially High Energy Physics, called Schoonschip (Dutch for "clean ship") in 1963. Using LISP as the programming basis, Carl Engelman created MATHLAB in 1964 at MITRE within an artificial intelligence research environment. Later MATHLAB was made available to users on PDP-6 and PDP-10 Systems running TOPS-10 or TENEX in universities. Today it can still be used on SIMH-Emulations of the PDP-10. MATHLAB ("mathematical laboratory") should not be confused with MATLAB ("matrix laboratory") which is a system for numerical computation built 15 years later at the University of New Mexico, accidentally named rather similarly. The first popular computer algebra systems were muMATH, Reduce, Derive (based on muMATH), and Macsyma; a popular copyleft version of Macsyma called Maxima is actively being maintained. -
Prise En Main De Carmetal (1/2)
Prise en main de CaRMetal (1/2) Extrait du Les nouvelles technologies pour l'enseignement des mathématiques http://revue.sesamath.net/spip.php?article599 Prise en main de CaRMetal (1/2) - N°39 - mars 2014 - Date de mise en ligne : jeudi 13 février 2014 Les nouvelles technologies pour l'enseignement des mathématiques Copyright © Les nouvelles technologies pour l'enseignement des mathématiques Page 1/13 Prise en main de CaRMetal (1/2) Pourquoi diable ce nom de « CaRMetal » ?... Explication Il faut bien le reconnaître, ce nom évoque plutôt la sidérurgie que la géométrie dynamique, et on peut considérer que c'est une maladresse de communication. Mais ce jugement hâtif mérite d'être nuancé car ce nom, une fois décodé, traduit très finement l'essence du logiciel. Notons d'abord que si c'est la sidérurgie qui vient à l'esprit (on pense naturellement au groupe ArcelorMittal, qui a fait la une des journaux), c'est une association malheureuse... En réalité, c'est à la forge que « Metal » fait allusion, selon une métaphore très répandue chez les développeurs : le code d'un programme est malléable comme l'acier et se travaille selon un processus analogue (on casse et on recolle pour forger). C'est dans cette veine que s'inscrit par exemple le projet SourceForge. Mais ce n'est pas tout. • CaRMetal dérive de C.a.R (Compass and Ruler = Compas et Règle), et en reprend la racine. • Restait à le distinguer par un suffixe, et ce n'était pas chose aisée. Or, à l'origine, ce qui distingue CaRMetal de C.a.R, c'est la façon de concevoir l'interface. -
GNU Texmacs User Manual Joris Van Der Hoeven
GNU TeXmacs User Manual Joris van der Hoeven To cite this version: Joris van der Hoeven. GNU TeXmacs User Manual. 2013. hal-00785535 HAL Id: hal-00785535 https://hal.archives-ouvertes.fr/hal-00785535 Preprint submitted on 6 Feb 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. GNU TEXMACS user manual Joris van der Hoeven & others Table of contents 1. Getting started ...................................... 11 1.1. Conventionsforthismanual . .......... 11 Menuentries ..................................... 11 Keyboardmodifiers ................................. 11 Keyboardshortcuts ................................ 11 Specialkeys ..................................... 11 1.2. Configuring TEXMACS ..................................... 12 1.3. Creating, saving and loading documents . ............ 12 1.4. Printingdocuments .............................. ........ 13 2. Writing simple documents ............................. 15 2.1. Generalities for typing text . ........... 15 2.2. Typingstructuredtext ........................... ......... 15 2.3. Content-basedtags -
Biblioteka PARI/GP W Zastosowaniu Do Systemu Ćwiczeń Laboratoryjnych
Biblioteka PARI/GP w zastosowaniu do systemu ćwiczeń laboratoryjnych Bartosz Dzirba Gabriel Kujawski opiekun: prof. dr hab. Zbigniew Kotulski 1 Plan prezentacji . Ćwiczenie laboratoryjne . Przykład protokołu (TBD) . Systemy algebry . PARI/GP wstęp problemy… biblioteka 2 Ćwiczenie laboratoryjne wstęp . Tematyka: Kolektywne uzgadnianie klucza . Założenia: Praktyczne zapoznanie studenta z protokołami uzgadniania klucza Wykonanie wybranych protokołów Możliwość łatwej rozbudowy Działanie w laboratorium komputerowym . Potrzebne elementy: Aplikacja Biblioteki protokołów System algebry 3 Ćwiczenie laboratoryjne efekt pracy . Aplikacja sieciowa KUK . Zaimplementowane protokoły dwustronne grupowe (różne topologie) . Scenariusze z atakami MitM kontrola klucza . Realne testy dla kilkunastu uczestników . Przykładowy skrypt ćwiczenia 4 Tree-based Burmester Desmedt topologia KEY A1 A2 A3 A4 A5 A6 5 Tree-based Burmester Desmedt runda 1 KEY A DH0, g1, PID 1 DH0, g1, PID A2 A3 A4 A5 A6 6 Tree-based Burmester Desmedt runda 2 KEY A1 DH1, g2, PID DH1, g3, PID A2 A3 DH0, g3, PID DH0, g3, PID DH0, g2, PID A4 A5 A6 7 Tree-based Burmester Desmedt runda 3 KEY A1 KEY, E (S), SID 12 KEY, E13(S), SID KEY A2 A3 KEY DH1, g5, PID DH1, g4, PID DH1, g6, PID A4 A5 A6 8 Tree-based Burmester Desmedt runda 4 KEY A1 KEY A2 A3 KEY KEY, E35(S), SID KEY, E36(S), SID KEY, E24(S), SID KEY A4 KEY A5 KEY A6 9 Systemy algebry wstęp . Potrzeby: obsługa dużych liczb operacje modulo p znajdowanie generatora grupy znajdowanie elementu odwrotnego modulo p znajdowanie liczb pierwszych możliwość wykorzystania w MS VC++ .NET 2008 . Możliwe podejścia: wykorzystanie gotowego systemu napisanie własnej biblioteki 10 Systemy algebry dostępne możliwości Crypto++ Yacas OpenSSL PARI/GP cryptlib Maxima MathCAD Axiom Maple 11 PARI/GP wstęp . -
Ginac 1.8.1 an Open Framework for Symbolic Computation Within the C++ Programming Language 8 August 2021
GiNaC 1.8.1 An open framework for symbolic computation within the C++ programming language 8 August 2021 https://www.ginac.de Copyright c 1999-2021 Johannes Gutenberg University Mainz, Germany Permission is granted to make and distribute verbatim copies of this manual provided the copy- right notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the condi- tions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. i Table of Contents GiNaC :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 1 1 Introduction :::::::::::::::::::::::::::::::::::::::::::::::::::: 2 1.1 License :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 2 2 A Tour of GiNaC::::::::::::::::::::::::::::::::::::::::::::::: 3 2.1 How to use it from within C++ :::::::::::::::::::::::::::::::::::::::::::::::::::: 3 2.2 What it can do for you::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 4 3 Installation:::::::::::::::::::::::::::::::::::::::::::::::::::::: 8 3.1 Prerequisites ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 8 3.2 Configuration :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 8 3.3 Building GiNaC ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 9 3.4 Installing GiNaC::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 9 4 Basic concepts::::::::::::::::::::::::::::::::::::::::::::::::: -
Open Source Resources for Teaching and Research in Mathematics
Open Source Resources for Teaching and Research in Mathematics Dr. Russell Herman Dr. Gabriel Lugo University of North Carolina Wilmington Open Source Resources, ICTCM 2008, San Antonio 1 Outline History Definition General Applications Open Source Mathematics Applications Environments Comments Open Source Resources, ICTCM 2008, San Antonio 2 In the Beginning ... then there were Unix, GNU, and Linux 1969 UNIX was born, Portable OS (PDP-7 to PDP-11) – in new “C” Ken Thompson, Dennis Ritchie, and J.F. Ossanna Mailed OS => Unix hackers Berkeley Unix - BSD (Berkeley Systems Distribution) 1970-80's MIT Hackers Public Domain projects => commercial RMS – Richard M. Stallman EMACS, GNU - GNU's Not Unix, GPL Open Source Resources, ICTCM 2008, San Antonio 3 History Free Software Movement – 1983 RMS - GNU Project – 1983 GNU GPL – GNU General Public License Free Software Foundation (FSF) – 1985 Free = “free speech not free beer” Open Source Software (OSS) – 1998 Netscape released Mozilla source code Open Source Initiative (OSI) – 1998 Eric S. Raymond and Bruce Perens The Cathedral and the Bazaar 1997 - Raymond Open Source Resources, ICTCM 2008, San Antonio 4 The Cathedral and the Bazaar The Cathedral model, source code is available with each software release, code developed between releases is restricted to an exclusive group of software developers. GNU Emacs and GCC are examples. The Bazaar model, code is developed over the Internet in public view Raymond credits Linus Torvalds, Linux leader, as the inventor of this process. http://en.wikipedia.org/wiki/The_Cathedral_and_the_Bazaar Open Source Resources, ICTCM 2008, San Antonio 5 Given Enough Eyeballs ... central thesis is that "given enough eyeballs, all bugs are shallow" the more widely available the source code is for public testing, scrutiny, and experimentation, the more rapidly all forms of bugs will be discovered. -
The Current State of Computer Algebra System on Tablet Devices
The current state of computer algebra system on tablet devices Mitsushi Fujimoto Fukuoka University of Education ∗ 1 Introduction Infty project[1] developed and released some useful software including InftyReader { an OCR system for mathematical documents. InftyEditor is one of the products developed by Infty project, and is a mathematics typesetting tool. The author, a core member of Infty project, built into InftyEditor a computing function for mathematical expressions[2]. In 2003, AsirPad[3], a computer algebra system with a handwriting interface on PDA, was developed using the technology of InftyEditor. AsirPad can communicate with Risa/Asir[4] through OpenXM protocol[5], and calculate mathematical expressions inputted by handwriting. This is an application for Zaurus that is a PDA with 400MHz CPU, 64MB memory, Linux OS, 3.7inch VGA screen and the weight 250g. The mainstream of the current mobile devices is shifting to smartphones or tablet devices and some computer algebra systems for these platforms are developed. In this article we explore the current state of computer algebra system on tablet devices. 2 Mathellan project and tablet devices AsirPad was used to present a lecture on RSA cryptography at a junior high school[6]. Ordinary calculator is not available because encryption and decryption in RSA use division of large numbers. The students learned how to encrypt/decrypt their messages through calculations by AsirPad. They could input mathematical expressions and calculate without any special training. We could get a result for usefulness of PDA and handwriting interface from this lecture. In 2010, we started Mathellan Project, a mobile Math e-Learning project, to go the next step. -
217192991.Pdf
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Saint Petersburg State University САНКТ-ПЕТЕРБУРГСКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ КАФЕДРА ТЕХНОЛОГИИ ПРОГРАММИРОВАНИЯ Широбоков Михаил Владимирович Магистерская диссертация Реализация высокопроизводительных растровых вычислений для Web ГИС Направление 02.04.02 Фундаментальная информатика и информационные технологии Научный руководитель, канд. техн. наук, доцент Блеканов И. С. Санкт-Петербург 2018 Содержание Содержание .......................................................................................................... 2 Введение ............................................................................................................... 5 Постановка задачи ................................................................................................ 7 Обзор литературы ................................................................................................ 8 1. Общая архитектура вычислительного модуля ............................................. 10 2. Обзор существующих решений и пакетов .................................................... 14 2.1. СУБД с возможностью хранения пространственных данных ............. 14 2.1.1. MySQL ........................................................................................ 15 2.1.2. PostGIS........................................................................................ 15 2.1.3. MongoDB .................................................................................... 16 2.1.4. -
Ev3: a Library for Symbolic Computation in C++ Using N-Ary Trees
Ev3: A Library for Symbolic Computation in C++ using n-ary Trees Leo Liberti LIX, Ecole´ Polytechnique, 91128 Palaiseau, France ([email protected]) 3 october 2003 Abstract Ev3 is a callable C++ library for performing symbolic computation (calculation of symbolic derivatives and various expression simplification). The purpose of this library is to furnish a fast means to use symbolic derivatives to third-party scientific software (e.g. nonlinear optimization, solution of nonlinear equations). It is small, easy to interface, even reasonably easy to change; it is written in C++ and the source code is available. One feature that makes Ev3 very efficient in algebraic manipulation is that the data structures are based on n-ary trees. 1 Introduction Computer Algebra Systems (CAS) have helped mathematicians, physicists, engineers and other scientists enormously since their appearance. CASes are extremely useful in performing complex symbolic calcu- lations quickly. They do not generally require particular programming skills, yet they manage to carry out numerical analysis, symbolic manipulation and graph plotting in 2 and 3 dimensions. The range of existing CASes is impressive, both commercially available (e.g. Mathematica, Maple, Matlab, Mathcad, Reduce, Mupad etc.) and as free software (e.g. Maxima, GAP, yacas, Singular, GiNaC etc.); however most of them (with the notable exception of GiNaC, see below) fall short on the external Application Programming Interface (API), i.e. it is difficult, or impossible in many cases, to create a program in a compiled language, say in C/C++ or Fortran, which can use the external CAS facilities. This is a serious hindrance for user applications with programming requirements that go beyond those offered by the CAS proprietary language, or for those applications that need to be coded in a compiled language for efficiency, but would still benefit from the CAS facilities. -
Module C2i2e Quels Logiciels Pour Enseigner ?
Module C2i2e Quels logiciels pour enseigner ? Les logiciels de géométrie dynamique : Casenpoche Casenpoche est un tableur mathématiques pour le collège, intégrable dans des documents multimedia interactifs, en local ou sur Internet, grâce à la technologie Flash (c) Macromedia. Casenpoche intégre les possibilités basiques des tableurs mais ajoute : des calculs numériques comme la manipulation des fractions , ... des calculs littéraux comme la manipulation d'expressions littérales, ... des calculs fonctionnels comme évaluer une expression littérale en affectant une valeur aux variables, ... des représentations graphiques mathématiques comme la représentation correcte de données fonctionnelles (x,f(x)) sans problème de graduation de l'axe des abscisses, ... téléchargeable sur : http://casenpoche.sesamath.net/ David Rolland, formateur à l’IUFM de l’Université de la Polynésie française 1 Module C2i2e Tracenpoche TracenPoche est un logiciel de géométrie dynamique utilisable sur Internet ou en local grâce à la technologie Flash (c) Adobe. C’est un projet de Sésamath, et un module de l’ensemble MathenPoche. TracenPoche est prévu pour être utilisé par tout curieux de la chose géométrique qui, en faisant bouger, voit apparaît des propriétés de la figure. TracenPoche est réalisé par des enseignants de mathématiques et donc plutôt destiné à être utilisé par des élèves et des enseignants dans le cadre d’activités scolaires, avec des documents papiers complémentaires réalisés avec OpenOffice.org. TracenPoche s’adresse aussi aux webmasters avec une interface complète ou une interface simplifiée, ainsi que des plugins pour la publication de figures dynamiques en ligne. Quant aux programmeurs, TracenPoche est libre donc ils peuvent soit le piloter ou l’incorporer comme composant, soit en récupérer le source et le modifier à leur convenance.