The course Mathematics Colloquium consists of two separate components:
Component 1. Summaries of four (online) seminar/colloquium talks that you attend.
Component 2. Complete the Robotics project or the History of Elliptic Curves project. The two projects alternate every two years. In the year 2020-2021 the project on History of Elliptic Curves will be offered, in the year 2021-2022 the Robotics project. The History of Elliptic Curves project will be organized in the year 2020-2021 in period 4 on Fridays 15.15-17.00 starting 30 April 2021.
Summaries of four (online) seminar/colloquium talks.
You should write summaries of four (online) seminar/colloquium talks that you attend. The summaries have to be at least 200 words. The online seminars that you can attend are the Applied Mathematics seminar and the Dutch Differential Topology and Geometry seminar (organized together with Leiden, UvA, VU). The calendar of the Applied Mathematics seminar can be found here: http://www2.projects.science.uu.nl/css-math/, and the calendar of the Dutch Differential Topology and Geometry seminar here: https://www.few.vu.nl/~trt800/ddtg.html. In case of the Dutch Differential Topology and Geometry seminar you may write a summary of a part of the talk/mini-course. Other seminar/colloquium talks will be announced via the newsletter Wisper. If you want to write a summary of a seminar/colloquium talk that you think is suitable, let Wilfred de Graaf know. Upload your summaries in Blackboard under Assessments called Summary 1, 2, 3, 4. The summaries can be uploaded at any time during your master. Write down clearly in your summary the title of the talk, name of the seminar, name of the speaker and date.
Robotics project.
Material.
Learning goals. After completion of the project, the student is able to:
- 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
- modeling 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 of Elliptic Curves project.
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. After completion of the project, the student is able to:
- 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.
| |
report robotics
100% |
report history of elliptic curves
100% |
seminar/colloquium talks 0% |
| orient him/herself in contemporary research in fundamental/applied mathematics |
|
|
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 |
|
|
| is able to model a robotic arm, and has knowledge of the terms forward/inverse kinematic problem, kinematic singularity, configuration space |
x |
|
|
| is able to apply numerical methods for solving systems of non-linear equations including Newton-like methods and fixed-point iterations |
x |
|
|
| is able to implement various methods in computer algebra system SAGE |
x |
|
|
| understands the original motivations and contexts to create elliptic curves and related concepts |
|
x |
|
|
 |
|