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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Introduction.1 MAT 7003 : Mathematical Foundations (for Software Engineering) J Paul Gibson, A207 paul.gibson@it-sudparis.eu http://www-public.it-sudparis.eu/~gibson/Teaching/MAT7003/ Introduction http://www-public.it-sudparis.eu/~gibson/Teaching/MAT7003/L1-Introduction.pdf

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.2 FROM MODULE DESCRIPTION (http://www.telecom-sudparis.eu/p_en_formations-post-grade_MSc_1179.html?idm=63&) Objectives: Engineering is a bridge between science and mathematics, and the technological needs of mankind. Engineering disciplines are fundamentally mathematical and problem solving based. Traditional engineering disciplines, such as chemical, civil, electrical and mechanical, rely heavily upon continuous rather than discrete mathematical foundations. Software engineering is an emerging discipline that applies mathematical and computer science principles to the development and maintenance of software systems. It relies primarily upon principles of discrete mathematics, especially logic. Skills: Capacity to use mathematical reasoning to derive, understand and debug software systems. With sufficient practice, the underlying mathematical concepts become intrinsic to the thought processes, supporting rather than hindering thinking. Pre-requisites: None

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.3 Some Information About Me …. Now, what about you..? Leila DZAFAROVA Thi Mai NGUYEN Van Luong NGUYEN Christos SOTIRIOU Diem BUI THI http://www-public.it-sudparis.eu/~gibson/

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.4 Web Site On My Local Pages – open access TO DO: Check that you can access this page Please note that - to access internet from C106- you may need to set the proxy server for your web browser to proxy.int-evry.fr and port 81.

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.5 Web Site On TMSP Moodle Pages TO DO: Check that you can access this page

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.6 TO DO: Complete Initial Questionnaire

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.7 Some Information About Problem Based Learning …. TO DO: Find and read some background material on the web about PBL

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.8 RODIN – A tool for formal software development We will use it in most of our mathematical problems Its good that you know how to install it yourself It runs on Eclipse … which runs on "any" OS

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.9 INSTALLING RODIN - http://www.event-b.org/

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.10 http://www.event-b.org/ http://sourceforge.net/projects/rodin- b-sharp/

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.11 http://sourceforge.net/projects/rodin-b-sharp/ http://sourceforge.net/project/showfiles.php?group_id=108850

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.12 NOTE: The style of this dowload page changes regularly so you may need to search around for the files you need: take the most up to date platform (2.6) You do not yet need any of the plug-ins but you will probably need the font specific to the tool

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.13 http://sourceforge.net/project/showfiles.php?group_id=108850&package_id=181714 The windows and linux versions will match your choice of OS

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.14 Rodin - Installation Overview for Windows (Linux and Mac installations should be similar) Latest Java (jre +jdk) from http://www.sun.com – because RODIN is built on Eclipse Platform Unzip rodin-2.6-win32.win32.x86.zip/download (to C:\Program Files, eg) Place the font file in C:\Windows\fonts Start Rodin (C:\Program Files\Rodin\Rodin.exe) and install plugins if instructed at the first Rodin (Eclipse) screen.

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.15

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.16 Help Software Updates Available Software

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.17 B2Latex Atelier B ProB Animator These are useful in later modules

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Intro.18 Typical Use of Rodin – default Eclipse window layout

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Introduction.19 We will start to work with RODIN in a few weeks time, but please install it and play around with it (and the on-line tutorials). For the remainder of today I want you to work together on a mathematical problem. This problem can be solved in a number of different ways, and using a number of techniques/skills. My goal is to observe how you choose to work on the problem and what mathematics you choose to employ. The problem is based on a robot walking around a rectangular grid. Your Task is to specify/define formally the required functionality

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Introduction.20 Robot Walker: step1 0,00,5 5,55,0

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Introduction.21 Robot Walker: step2 0,00,5 5,55,0

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Introduction.22 Robot Walker: step3 0,00,5 5,55,0

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Introduction.23 Robot Walker: step4 0,00,5 5,55,0

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2012: J Paul GibsonT&MSP: Mathematical FoundationsMAT7003/Introduction.24 Robot Walker: step5 – testing each of the previous steps How sure are you that your function is correct? Is it easier to do the maths if the function allows a degree of error? What is the error bound of your function? What mathematics did you (re)use in each step? Would it be easier to program a solution? Why not try? We will return to the robot walker later in the module

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Addition 14 Days (English) Slide Show Menu 1st2ndEnd DAY 11+1=2 1+2=3 1+3=4*1+4=5 1+5=6 1+6=7*1+7=8 1+8=9 1+9=10* DAY 22+2=4 2+3=5 2+4=6*2+5=7 2+6=8 2+7=9*2+8=10.

Addition 14 Days (English) Slide Show Menu 1st2ndEnd DAY 11+1=2 1+2=3 1+3=4*1+4=5 1+5=6 1+6=7*1+7=8 1+8=9 1+9=10* DAY 22+2=4 2+3=5 2+4=6*2+5=7 2+6=8 2+7=9*2+8=10.

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