This course consists of two seperate components:
- Mathematical Colloquium (throughout the year)
- One of the two projects on
- Robotics: Computational affine geometry
- History: from ellipses to elliptic curves
The two project will alternate every two years. In the year 2018-2019 the project on History of mathematics is planned, in the year 2019-2020 the project on Robotics.
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Mathematical Colloquium
The mathematics department organizes six mathematical colloquia throughout the year: four quarterly colloquia, the Monna lecture and the Kan memorial lecture.
The master students of Mathematical Sciences are invited to join these lectures. It is mandatory to attend four of these six lectures during your master Mathematical Sciences.
Each student has to upload a short summary (around 200 words, half a A4) of the lecture that he/she has attended on Blackboard.
The lectures will be announced via Blackboard or via the news letter (Wisper).
Computational Affine Geometry
Material
Learning Goals
- Knowledge of the notion of affine varieties in terms of ideals, monomial orderings, division algorithm for multivariate polynomials, Dickson's Lemma, Gröbner basis, Hilbert's basis theorem, Buchberger's criterion
- Modelling a robotic arm, and knowledge of the terms forward/inverse kinematic problem, kinematic singularity, configuration space
- Numerical methods for solving systems of non-linear equations including Newton-like methods and fixed-point iterations
- Implement various methods in computer algebra system SAGE
History: from ellipses to elliptic curves
The topic we present is the 18th and 19th century history leading up to elliptic
curves. The subject is accessible from bachelor level, shows how central topics of the
20th century are rooted in the 19th (and earlier), and may increase the student’s awareness that
mathematics is a developing and man-made discipline.
Format
We will paint a broad general picture in the lectures, provide recommended reading (primary or secondary sources) and let the students work out
the details themselves. After one week they hand in a “textbook-style” paper of the previous lecture. There is ample room to follow your own interests. Work can be done individually or in pairs.
Learning Goals
Students give proof that they:
- understand the original motivations and contexts to create elliptic curves and related concepts;
- see the similarities and dissimilarities between contemporary mathematics and mathematics of earlier times;
- experience mathematics as a dynamically developing discipline made by real people;
- are able to write a coherent and intelligible text discussing mathematics in a historic context.
Evaluation matrix:
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report robotica
100% |
report history of mathematics
100% |
colloquia lectures 0% |
| orient him/herself in contemporary research in fundamental/applied mathematics |
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x |
| has knowledge of the notion of affine varieties in terms of ideals, monomial orderings, division algorithm for multivariate polynomials, Dickson's Lemma, Gröbner basis, Hilbert's basis theorem, Buchberger's criterion |
x |
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| is able to model a robotic arm, and has knowledge of the terms forward/inverse kinematic problem, kinematic singularity, configuration space |
x |
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| is able to apply numerical methods for solving systems of non-linear equations including Newton-like methods and fixed-point iterations |
x |
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| is able to implement various methods in computer algebra system SAGE |
x |
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| understands the original motivations and contexts to create elliptic curves and related concepts |
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x |
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