Maple T.A. in Mathematical Education of Engineers in Austria

F. Breitenecker, A. Körner, S. Winkler Vienna University of Technology

Institute for Analysis and Scientific Computing

Felix Breitenecker

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Vienna University of Technology

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Vienna University of Technology

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Vienna University of Technology

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Vienna University of Technology

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• Since 1814

• 4.500 staff

• 28.000 students

• 5.400 students for 2014

Vienna University of Technology: • > 3.400 staff for research • 8 faculties Faculty of Mathematics and Geoinformation: • > 300 staff Institute for Analysis and Scientific Computing • 60 staff Research Group Mathematical Modelling and

Simulation • 3 staff

Vienna UT, Institute ASC, RG MMS

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Problem 1

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Knowledge Test

Problem 2

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Problem 3

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Skills

Understanding

• Refresher Course Mathematics

• Blended Learning

• Continuity in first semesters

Solution Approach

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• Computer Algebra System Maple • Maple T.A.: Testing and Assessment via Web • Usage in USA, partly in Europe • Examples: standardised Databank • Alternative Platforms: Moodle Math.EL System RWTH Aachen Extension of MMT (Mathematics, Modelling and Tools)

Why Maple T.A.?

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Result 1

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Knowledge Test Final Test

Results 2

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Result 3

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Skills

Understanding

Skills

Understanding

• Maple T.A. used since 2006/2008

• 2 part-time staff: Administration and Content Adviser

• 3 part-time Tutors: Example Development • Around 820 examples:

• Refresher course level: 120 • Basic mathematical level: 200+230 • Advanced mathematical level: 270

Facts

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Evolution using Maple T.A.

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• Refresher Course Mathematics

• Mathematics 1 for electrical engineers • Mathematics 2 for electrical engineers

• Examination going online

• Mathematics 3 for electrical engineers

Moodle Usage • Administraion of lectures

• Offering lecture materials • Administration e-exams

• Administration of Homeworks (Kreuzerlliste) • Uploading the homework examples • On Monday they have the say which

example they prepared • Administration of exercises

• Group administraion • Creation of marks

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MTA connection • Since winter 2013 connection to

MTA (Tool of Moodle) • Former times 3 accounts necessary • Example pools linked in TUWEL • Tests are linked in TUWEL • Test results stored in TUWEL • Results directly useable in assessment

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Course Structure

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First Use of Maple T.A.

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First Use of Maple T.A.

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• Create a common mathematical level • Short course duration • Big amount of students • Using of e-learning • Focus on practice • Coordination with regular lectures

Refresher Course – Structure

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Anonymous Test AKMATH First Turnus AKMATH Second Turnus Final Exmaination

AKMATH – Course Structure • 6-8 modules focusing on different topics • one module contains:

o 2 h classical lecture o 2 h classical exercises combined with Maple T.A. , guided self education o→∞ practising on MTA

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AKMATH Content

• Basics and Introduction • Number Ranges • Basics of Equations • Linear equation systems

• Elementary functions and equations • Vector calculus

• Geometry in plane • Geometry in space • Vector products • Matrix calculations (for some field of studies)

• Complex numbers • Differential Calculus • Integral Calculus

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AKMATH – Teilnehmer

2014 ET MB TPH BI INF VG DIV total

total 212 546 295 268 275 35 282 1913

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0 100 200 300 400 500 600

AKMATH ET

AKMATH MB

AKMATH TPH

AKMATH BI

AKMATH RP

AKMATH

AKMATH INF

2014

2013

2012

2011

2010

2009

AKMATH Lecture

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AKMATH Exercice & Practice

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Refresher Course: The Start

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Refresher Course: Advanced Examples

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Advanced Use of Maple T.A.

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Basic Mathematical Courses

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• Classic lectures 3-4 times a week • Homework

o 8-10 examples per week, 60% necessary o Presentation of the prepared examples

• Examples in MTA o 1-3 assignements per week o 10-20 examples

• 3 Tests o Spread through semester o Pass 2 of 3 tests o Bonus points for pretests

Content Mathematics 1

• Real Numbers • Sequences and Series • Complex Numbers • Elementary functions • Rational functions • Continuity of real functions • Differential Calculus • Integral Calculus

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ò

Content Mathematics 2

• Linear Algebra • Vector spaces • Orthogonality • Matrix calculus • Eigenvalues, Eigenvactors

• Multivariate Functions • Pre-calculus • Derivatives, Taylorpolynom, etc.

• Differential Equations • Ordinary differential equations • Initial Value Problem

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Advanced Mathematical Courses

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• Classic lectures 4 times a week • Homework

o 8-10 examples per two weeks, 60% necessary o Presentation of the prepared examples

• Examples in MTA o 1-3 assignements per topic o 10-20 examples

• 3 Tests o Spread through semester o Pass 2 of 3 tests

Content Mathematics 3

• Vector Analysis: • grad, rot, div • Intgration

• Integral Transformation: • Laplace-Transform • Fourier Transform

• Statistics: descriptive • Numerical Mathematics

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òò

Examples Mathematics 1

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Examples Mathematics 1

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Content Mathematics 1

• Real Numbers • Sequences and Series • Complex Numbers • Elementary functions • Rational functions • Continuity of real functions • Differential Calculus • Integral Calculus

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Maple T.A. - Grading

• Grade[Expr], Grade[ExprDiff]

• Grade[Set]

• Grade[ParFrac]

• Grade[Vec]

• Grade[Mat]

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Maple T.A. - Creating

• Random[FromSet]

• Random[VecInts]

• Random[MatInts] • rows, cols • zerocount, rank

• Random[MatsIntsDef]

• Random[MatRatsEig]

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Examples Mathematics 2

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Examples Mathematics 3

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Numerical Examples Mathematics 3

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MMT Mathematics, Modelling and Tools

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MMT Server structure

User Adam Ries(e)

Standard Matlab

Octave

Weitere Moodle 06.10.2014 47

MMT: Example

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E-Exams

Examination for electrical engineers: written exams (2h)

New regulations: written & oral exams written exams: e-test or ordinary

oral exam

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E-Exams

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Any Questions?

Maple T.A. in Mathematical Education of Engineers in Austria

A. Körner, S. Winkler, F. Breitenecker Vienna University of Technology

Institute for Analysis and Scientific Computing