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The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes
Portland State University PDXScholar Mathematics and Statistics Faculty Fariborz Maseeh Department of Mathematics Publications and Presentations and Statistics 3-2018 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes Xu Hu Sun University of Macau Christine Chambris Université de Cergy-Pontoise Judy Sayers Stockholm University Man Keung Siu University of Hong Kong Jason Cooper Weizmann Institute of Science SeeFollow next this page and for additional additional works authors at: https:/ /pdxscholar.library.pdx.edu/mth_fac Part of the Science and Mathematics Education Commons Let us know how access to this document benefits ou.y Citation Details Sun X.H. et al. (2018) The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes. In: Bartolini Bussi M., Sun X. (eds) Building the Foundation: Whole Numbers in the Primary Grades. New ICMI Study Series. Springer, Cham This Book Chapter is brought to you for free and open access. It has been accepted for inclusion in Mathematics and Statistics Faculty Publications and Presentations by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. Authors Xu Hu Sun, Christine Chambris, Judy Sayers, Man Keung Siu, Jason Cooper, Jean-Luc Dorier, Sarah Inés González de Lora Sued, Eva Thanheiser, Nadia Azrou, Lynn McGarvey, Catherine Houdement, and Lisser Rye Ejersbo This book chapter is available at PDXScholar: https://pdxscholar.library.pdx.edu/mth_fac/253 Chapter 5 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes Xu Hua Sun , Christine Chambris Judy Sayers, Man Keung Siu, Jason Cooper , Jean-Luc Dorier , Sarah Inés González de Lora Sued , Eva Thanheiser , Nadia Azrou , Lynn McGarvey , Catherine Houdement , and Lisser Rye Ejersbo 5.1 Introduction Mathematics learning and teaching are deeply embedded in history, language and culture (e.g. -
Datatype Defining Rewrite Systems for Naturals and Integers
UvA-DARE (Digital Academic Repository) Datatype defining rewrite systems for naturals and integers Bergstra, J.A.; Ponse, A. DOI 10.23638/LMCS-17(1:17)2021 Publication date 2021 Document Version Final published version Published in Logical Methods in Computer Science License CC BY Link to publication Citation for published version (APA): Bergstra, J. A., & Ponse, A. (2021). Datatype defining rewrite systems for naturals and integers. Logical Methods in Computer Science, 17(1), [17]. https://doi.org/10.23638/LMCS- 17(1:17)2021 General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:30 Sep 2021 Logical Methods in Computer Science Volume 17, Issue 1, 2021, pp. 17:1–17:31 Submitted Jan. 15, 2020 https://lmcs.episciences.org/ Published Feb. -
Experimental Methods and Instrumentation for Chemical Engineers Experimental Methods and Instrumentation for Chemical Engineers
Experimental Methods and Instrumentation for Chemical Engineers Experimental Methods and Instrumentation for Chemical Engineers Gregory S. Patience AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Elsevier 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands First edition 2013 Copyright © 2013 Elsevier B.V. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments -
TUTORIAL BÁSICO DE GIMP 2.2 Por Günther Natusch
TUTORIAL BÁSICO DE GIMP 2.2 Por Günther Natusch Desenvolvido para o Projeto Aprendi NESTA-UFRGS/Petrobrás Cultural Introdução: O programa gráfico GIMP - The GNU Image Manipulation Program - foi desenvolvido para plataforma livre LINUX, mas é também compatível com plataforma Windows. Sendo um software livre, é gratuito para qualquer usuário, basta baixar o arquivo executável no site oficial GIMP ( www.gimp.org ). IMPORTANTE: Existem versões para as plataformas LINUX, Windows e Mac disponíveis no site oficial do GIMP, mas atenção para fazer o download da versão compatível com o seu sistema operacional. Também verifique o idioma da versão que está baixando, além, evidentemente, de usar sites seguros para fazer download para a sua máquina. FATOS: O projeto foi criado no ano de 1995 por Spencer Kimball e Peter Mattis quando o desenvolveram como um projeto para a faculdade. O mascote oficial do projeto chama-se Wilber e foi criado dois anos depois do desenvolvimento do programa, no dia 25 de setembro de 1997 por Tuomas Kuosmanen. GIMP e outros softwares de manipulação de imagem: Embora a comparação não seja “justa”, o GIMP é geralmente comparado ao programa Adobe Photoshop, conhecido manipulador e criador de imagem digital. De uma forma mais direta, ao se conhecer os dois programas se encontrará similaridades, mas também diferenças; especialmente em termos de efeitos e caminhos para acessar funções. Ainda existem diversos outros programas de manipulação e criação de imagem digital, e especialmente uma grande variedade de programas-livres (freeware), tais como o Pixia e Tux Paint (este mais voltado para o público infantil), e outros bem mais complexos para criação de imagens em 3D, a exemplo do Blender e do Daz Studio. -
R-Photo User's Manual
User's Manual © R-Tools Technology Inc 2020. All rights reserved. www.r-tt.com © R-tools Technology Inc 2020. All rights reserved. No part of this User's Manual may be copied, altered, or transferred to, any other media without written, explicit consent from R-tools Technology Inc.. All brand or product names appearing herein are trademarks or registered trademarks of their respective holders. R-tools Technology Inc. has developed this User's Manual to the best of its knowledge, but does not guarantee that the program will fulfill all the desires of the user. No warranty is made in regard to specifications or features. R-tools Technology Inc. retains the right to make alterations to the content of this Manual without the obligation to inform third parties. Contents I Table of Contents I Start 1 II Quick Start Guide in 3 Steps 1 1 Step 1. Di.s..k.. .S..e..l.e..c..t.i.o..n.. .............................................................................................................. 1 2 Step 2. Fi.l.e..s.. .M..a..r..k.i.n..g.. ................................................................................................................ 4 3 Step 3. Re..c..o..v..e..r.y.. ...................................................................................................................... 6 III Features 9 1 File Sorti.n..g.. .............................................................................................................................. 9 2 File Sea.r.c..h.. ............................................................................................................................ -
Questionário De Caracterização Da Amostra (A)
LimeSurvey - Questionário de Caracterização da Amostra (A) http://www.fmh.utl.pt/inqueritos/admin/admin.php?action=showprintab... Questionário de Caracterização da Amostra (A) Este questionário versa um conjunto de temáticas relativas à utilização da ferramenta folha de cálculo pelos funcionários da instituição. Realce-se que não há respostas certas ou erradas relativamente a qualquer dos itens, pretendendo-se apenas a sua opinião pessoal e sincera, pelo que é de toda a conveniência que responda com o máximo de rigor e honestidade. Apesar de não ser anónimo, este questionário é de natureza confidencial . Pelo que o seu nome não será referido em nenhum momento ao longo de todo o trabalho. Este questionário versa um conjunto de temáticas relativas à utilização da ferramenta folha de cálculo pelos funcionários da instituição. Realce-se que não há respostas certas ou erradas relativamente a qualquer dos itens, pretendendo-se apenas a sua opinião pessoal e sincera, pelo que é de toda a conveniência que responda com o máximo de rigor e honestidade. Apesar de não ser anónimo, este questionário é de natureza confidencial . Pelo que o seu nome não será referido em nenhum momento ao longo de todo o trabalho. Existem 43 perguntas neste inquérito Identificação Este grupo de questões é referente à identificação do respondente. Importa recordar que este questionário apesar de não ser anónimo, o seu nome não será mencionado no trabalho, pelo que está garantida a sua confidencialidade. 1 Escreva o seu primeiro nome e o apelido. * Por favor, escreva aqui a(s) sua(s) resposta(s): Nome Apelido Escreva o seu primeiro e último nome por favor. -
R-Linux User's Manual
User's Manual R-Linux © R-Tools Technology Inc 2019. All rights reserved. www.r-tt.com © R-tools Technology Inc 2019. All rights reserved. No part of this User's Manual may be copied, altered, or transferred to, any other media without written, explicit consent from R-tools Technology Inc.. All brand or product names appearing herein are trademarks or registered trademarks of their respective holders. R-tools Technology Inc. has developed this User's Manual to the best of its knowledge, but does not guarantee that the program will fulfill all the desires of the user. No warranty is made in regard to specifications or features. R-tools Technology Inc. retains the right to make alterations to the content of this Manual without the obligation to inform third parties. Contents I Table of Contents I Introduction to R-Linux 1 1 R-Studi.o.. .F..e..a..t.u..r.e..s.. ................................................................................................................. 2 2 R-Linux.. .S..y..s.t.e..m... .R...e..q..u..i.r.e..m...e..n..t.s. .............................................................................................. 4 3 Contac.t. .I.n..f.o..r.m...a..t.i.o..n.. .a..n..d.. .T..e..c..h..n..i.c.a..l. .S...u..p..p..o..r.t. ......................................................................... 4 4 R-Linux.. .M...a..i.n.. .P..a..n..e..l. .............................................................................................................. 5 5 R-Linu..x.. .S..e..t.t.i.n..g..s. .................................................................................................................. 10 II Data Recovery Using R-Linux 16 1 Basic .F..i.l.e.. .R..e..c..o..v..e..r.y.. ............................................................................................................ 17 Searching for. -
Grafika Rastrowa I Wektorowa
GRAFIKA RASTROWA I WEKTOROWA Grafikę komputerową, w dużym uproszczeniu, można podzielić na dwa rodzaje: 1) grafikę rastrową, zwaną też bitmapową, pikselową, punktową 2) grafikę wektorową zwaną obiektową. Grafika rastrowa – obraz budowany jest z prostokątnej siatki punktów (pikseli). Skalowanie rysunków bitmapowych powoduje najczęściej utratę jakości. Grafika ta ma największe zastosowanie w fotografice cyfrowej. Popularne formaty to: BMP, JPG, TIFF, PNG GIF, PCX, PNG, RAW Znane edytory graficzne: Paint, Photoshop, Gimp. Grafika wektorowa – stosuje obiekty graficzne zwane prymitywami takie jak: punkty, linie, krzywe opisane parametrami matematycznymi. Podstawową zaletą tej grafiki jest bezstratna zmian rozmiarów obrazów bez zniekształceń. Popularne formaty to: SVG, CDR, EPS, WMF - cilparty Znane edytory graficzne: Corel Draw, Sodipodi, Inscape, Adobe Ilustrator, 3DS LISTA PROGRAMÓW DO GRAFIKI BITMAPOWEJ Darmowe: CinePaint , DigiKam , GIMP , GimPhoto , GIMPshop , GNU Paint , GrafX2 , GraphicsMagick , ImageJ , ImageMagick , KolourPaint , Krita , LiveQuartz , MyPaint , Pencil , Pinta , Pixen , Rawstudio , RawTherapee , Seashore , Shotwell , Tile Studio , Tux Paint , UFRaw , XPaint , ArtRage Starter Edition , Artweaver , Brush Strokes Image Editor , Chasys Draw IES , FastStone Image Viewer , Fatpaint , Fotografix , IrfanView , Paint.NET , Picasa , Picnik , Pixia , Project Dogwaffle , TwistedBrush Open Studio , Xnview Płatne: Ability Photopaint, ACD Canvas, Adobe Fireworks, Adobe Photoshop, Adobe Photoshop Lightroom, Adobe Photoshop Elements, -
Parallel Branch-And-Bound Revisited for Solving Permutation Combinatorial Optimization Problems on Multi-Core Processors and Coprocessors Rudi Leroy
Parallel Branch-and-Bound revisited for solving permutation combinatorial optimization problems on multi-core processors and coprocessors Rudi Leroy To cite this version: Rudi Leroy. Parallel Branch-and-Bound revisited for solving permutation combinatorial optimization problems on multi-core processors and coprocessors. Distributed, Parallel, and Cluster Computing [cs.DC]. Université Lille 1, 2015. English. tel-01248563 HAL Id: tel-01248563 https://hal.inria.fr/tel-01248563 Submitted on 27 Dec 2015 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. Ecole Doctorale Sciences Pour l’Ingénieur Université Lille 1 Nord-de-France Centre de Recherche en Informatique, Signal et Automatique de Lille (UMR CNRS 9189) Centre de Recherche INRIA Lille Nord Europe Maison de la Simulation Thèse présentée pour obtenir le grade de docteur Discipline : Informatique Parallel Branch-and-Bound revisited for solving permutation combinatorial optimization problems on multi-core processors and coprocessors. Défendue par : Rudi Leroy Novembre 2012 - Novembre 2015 Devant le jury -
Tied to the Representation of Numbers
1 www.onlineeducation.bharatsevaksamaj.net www.bssskillmission.in INTRODUCTION TO COMPUTER SCIENCE Topic Objective: At the end of this topic the student will be able to understand: Concrete devices Numbers Early computation Navigation and astronomy Weather prediction Symbolic computations Definition/Overview: History of Computing: The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or without the aid of tables. The timeline of computing presents a summary list of major developments in computing by date. Key Points: 1. Concrete devices Computing is intimatelyWWW.BSSVE.IN tied to the representation of numbers. But long before abstractions like number arose, there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as : one-to-one correspondence, a rule to count how many items, say on a tally stick, eventually abstracted into number; comparison to a standard, a method for assuming reproducibility in a measurement, for example, the number of coins; the 3-4-5 right triangle was a device for assuring a right angle, using ropes with 12 evenly spaced knots, for example. 2. Numbers www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in 2 www.onlineeducation.bharatsevaksamaj.net www.bssskillmission.in Eventually, the concept of numbers became concrete and familiar enough for counting to arise, at times with sing-song mnemonics to teach sequences to others. All the known languages have words for at least "one" and "two", and even some animals like the blackbird can distinguish a surprising number of items. -
A NUMERAL SYSTEM BASICS of NUMBER SYSTEMS Lecture 5 EVERYTHING IS a NUMBER in a DIGITAL DEVICE!
A NUMERAL SYSTEM BASICS OF NUMBER SYSTEMS Lecture 5 EVERYTHING IS A NUMBER IN A DIGITAL DEVICE! •How to code a text in digital view? a picture? a video? a sound? something else? •To remember: we can code any kind of information into a digital view! It’s only a question about algorithm and our ideas! Do you agree? A. GRIGOREV | UKHTA STATE TECHNICAL UNIVERSITY 2 A NUMBER •A computer can understand positional number system where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number. •A value of each digit in a number can be determined using The digit The position of the digit in the number The base of the number system (where base is defined as the total number of digits available in the number system). A. GRIGOREV | UKHTA STATE TECHNICAL UNIVERSITY 3 A NUMERAL SYSTEM •A numeral system (or system of numeration) is a writing system for expressing numbers; that is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. A. GRIGOREV | UKHTA STATE TECHNICAL UNIVERSITY 4 UNARY NUMERAL SYSTEM (JUST STICKS) A. GRIGOREV | UKHTA STATE TECHNICAL UNIVERSITY 5 POSITIONAL NOTATION PLACE-VALUE NOTATION A. GRIGOREV | UKHTA STATE TECHNICAL UNIVERSITY 6 RADIX •In mathematical numeral systems the base or radix is usually the number of unique digits, including zero, that a positional numeral system uses to represent numbers. •For example, for the decimal system the radix is 10, because it uses the 10 digits from 0 through 9. -
Proposal to Encode Tally Marks Source: Dr
L2/15-328 Title: Proposal to encode tally marks Source: Dr. Ken Lunde (Adobe) & Daisuke MIURA Status: Individual contribution Action: For consideration by the UTC Date: 2015-11-30 Abstract Tally marks, which form a unary numeral system, have been used for thousands of years as a method of counting or keeping score through the use of stroke clusters. Tally marks also predate modern digits, and in some cases, served as their basis for some scripts. Most tally mark systems represent five digits, which correspond to the number of digits on a single human hand, but there is one system in this proposal that can represent ten digits. This proposal introduces four “tally mark” systems, and provides evidence that suggests that they require a “plain text” representa- tion, and should thus be encoded. Introduction Wikipedia’s very brief Tally marks article describes four tally mark systems, which serve as the basis for this proposal. The most common tally mark system, which is widely used in Europe, North America, and elsewhere, uses one to four parallel vertical strokes to represent the digits one through four, respectively, along with a horizontal or diagonal stroke that crosses over the four previous vertical strokes—completing the tally cluster—to represent the digit five. This tally mark sys- tem is sometimes referred to as the Barred-Gate Tally Mark System, because the four vertical strokes represent a gate, and the fifth stroke represents a bar that closes the gate.In this pro- posal, this system uses character names that begin with TALLY DIGIT. Another tally mark system, which is used in some French- and Spanish-speaking regions and particularly in South America, uses four strokes to form a box or square, with the number of successive strokes representing the digits one through four, respectively, along with a 45-de- gree diagonal stroke—completing the tally cluster—to represent the digit five.