Spring Semester 2015

Perspectives of Mathematics II


Quick Links:

The aim of this course is to train presentation and writing skills, and to foster critical thinking and discussion. At the same time, we venture into areas of mathematics not usually explored in the standard undergraduate curriculum. This semester, we will focus on topics which relate in some way to the interaction of mathematics, models, and data.

Contact Information:
Instructor:Marcel Oliver
Office hours:  Tu, Th 10:00 in Research I, 107

Time and Place:
Lectures:  Mo 11:15, We 14:15 in East Hall 4

Course requirements:

Short presentations: Update: For the time being, we will schedule only one presentation per class meeting, so you may go up to 40 minutes presentation time.

Long presentations:

Grading policy: Partial grades will be averaged with the following weights.

Reading list:

Tentative Class Schedule

Mon, 2. Feb. 2015: Introduction
Wed, 4. Feb. 2015: Differentiation on normed vector spaces
Mon, 9. Feb. 2015: Kechung (Coco) Mao: Generalized least square and least norm solutions
Wed, 11. Feb. 2015: Denis Korolev: The singular value decomposition
Mon, 16. Feb. 2015: Tianlin Liu: Variational characterization of the singular value decompositon
Wed, 18. Feb. 2015: Hanyu (Maggie) Wu: Matrix Norms
Mon, 23. Feb. 2015: Ekber Shahkeremov: Introduction to ill-posed linear problems
Wed, 25. Feb. 2015:  No class due to Career Fair
Mon, 2. Mar. 2015: Emanuel Stiuler: Error analysis for ill-posed linear problems, Morozov principle
Wed, 4. Mar. 2015: Marius Dumitrel: Practical demonstration of a deconvolution example
Mon, 9. Mar. 2015: Review of probability theory
Wed, 11. Mar. 2015: Emanuel Stiuler: Introduction to maximum likelihood estimation
Mon, 16. Mar. 2015:  Denis Korolev: Maximum likelihood estimation of the normal distribution and the connection to least squares
Wed, 18. Mar. 2015: Kechung (Coco) Mao: Introduction to the Kalman filter
Mon, 23. Mar. 2015: Tianlin Liu: Derivation of the Kalman gain as a least variance estimator
Wed, 25. Mar. 2015: Marius Dumitrel: Computational demonstration of the Kalman filter
Wed, 8. Apr. 2015: Ekber Shahkeremov: Maximum likelihood revisited: efficiency and asymptotic normality
Mon, 13. Apr. 2015: Ekber Shahkeremov and Marius Dumitrel: Introduction to compressed sensing (Bryan and Leise, Section 1)
Wed, 15. Apr. 2015: Kechung (Coco) Mao and Denis Korolev: Uniqueness of k-sparse solutions (Bryan and Leise, Section 2 and statement of results from Section 3)
Mon, 20. Apr. 2015: No class
Wed, 22. Apr. 2015: Tianlin Liu: Finding k-sparse solutions by l1-minimization (Bryan and Leise, Section 4); Emanuel Stiuler: Applications of compressed sensing
Mon, 27. Apr. 2015: Emanuel Stiuler: The Sylvester-Gallai theorem
Wed, 29. Apr. 2015: Ekber Shahkeremov: Prime numbers and cryptography
Mon, 4. May 2015: Kechung (Coco) Mao: Dinitz Problem I
Wed, 6. May 2015: Tianlin Liu: Dinitz Problem II
Mon, 11. May 2015: Marius Dumitrel: Markov chains
Wed, 13. May 2015: Denis Korolev: The Picard-Lindelöf theorem

Last modified: 2015/05/20
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/spring2015/math292/index.html
Marcel Oliver (m.oliver@jacobs-university.de)