Teaching Mathematical Modelling National Network
Project
Matti Heiliö, LUTRobert Piché and Seppo
PohjolainenInstitute of Mathematics,
TUT
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National virtual university network
•a pilot project of Finnish Virtual University
•course methods and contents
•IT tools
•student and expert comments
•conclusions, future directions
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The Finnish Virtual University
Started in 2001 by ministry of educationGoals:• improve networking between universities• develop pedagogical skills• support innovative uses of ICT in education• make VU an attractive alternative
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Good choice as a national pilot project
•modelling skills useful to industry & science
•curriculum not established
•experts & students scattered
•emphasis on independent study and communication
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Brings together teachers and students across the country
Participating institutions:Tampere University of
TechnologyHelsinki University of
TechnologyLappeenranta Univ of
TechnologyUniversity of HelsinkiUniversity of JoensuuUniversity of Jyväskylä University of KuopioUniversity of OuluUniversity of TampereCentre for Scientific
Computing
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Course structure
•60-70 students and 9 teachers
•A&O: sign-up, schedule, links, uploads, discussion
•videoconferenced opening lecture
•local tutor & tech support
•streaming video lectures, synchronised slides
•weekly assignments, student comments
•project, videoconference presentation
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Project themes are open-ended
Design the flow control for a fountain in a windy square
Predict the population of Finland in 2100
Does toast tend to fall buttered side down?
Are fingerprints unique?
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Courses cover a range of topics
Introduction to MMmathematics applications the modelling processnumerical software continuum modelsdifferential equations dimensional analysis discrete models fitting data probabilistic models decision analysis
Modelling with PDEsfields, flows and waves FEM for multiphysics tractor cabin acousticsmelting and solidificationsilicon crystal growthimpedance tomography
Modern Data Analysisfuzzy & multivalued logicneural networksgenetic algorithmsdata miningdecision analysis
Statistical ModellingMCMC for process parameter estimationstatistical methods for pattern recognitionmixed models for forest harvester operationmultivariate regression and DOE for process optimization.
Modelling RandomnessBrownian motion in finance and communicationsstochastic diff eqnstime series analysisinverse problemsfiltering
Modelling visual motionHow to reconstruct motion and shape from a video sequence: feature extraction, optical flow and visual velocity field, projecting 3d rigid body motion onto image sequence, statistical calibration.
Methods for Continuum Modellinglinearisation, asymptotics, regularisation, model fitting, model based optimization and control
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Student feedback generally positive
Would you like to take asimilar course again?
Would you recommend this course to a friend?
How many lectures did you watch?
How many hours did you work?
*
Were technical problemsa significant obstacle?
Overall grade?
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Pedagogical experts’ evaluation
Term projects support meaningful learning• contexts are novel & authentic• students are active• collaboration• structure & apply theory• oral presentation & comments
Good technical implementation • A&O learning environment simple to use, good
visual layout, easy navigation, schedule• use of widely supported file types (HTML, PDF)• local tutors & tech support• in video lectures, the lecturers’ train of thought
was supported rhythmically with motion and articulation
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Cooperation of teachers & practitioners in math modelling
•steering committee meets 4-5 times/year
•Finnish students to ECMI Modelling Week
•Study Groups in Tampere ‘02, Helsinki ‘04
•graduate school proposal
•EU project application
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What next?
Courses are now integrated into the standard curriculum at 7 universities
Textbook projectInternational network
alpha.cc.tut.fi/mallinnus/