Spring Semester 2015

Perspectives of Mathematics II

Syllabus

Quick Links:

Class mailing list for announcements and discussion
Homework sheets and handouts

Summary:

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
Email:	m.oliver@jacobs-university.de
Phone:	200-3212
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:

Each student gives 2-5 short presentations.
Each student is reviewer for 2-5 short presentations.
Each student observes all presentations.
There may be lectures with a traditional homework set substituting for a short presentation.
Each student gives one long presentation.
Each student reviews three long presentations.

Short presentations:

A presentation summary of 1-2 pages in LaTeX must be sent to the entire class at least 24h before the presentation. There is a strict 2 page limit, excluding the list of references and possibly figure appendices.
There is a strict 20 Minute time limit.
Short presentations are typically in pairs on closely related topics, students are encouraged to work in pairs and divide the topic into two 20 minute units.
After the two presentations, the reviewers have up to 20 minutes. to ask mathematical/scientific questions on the topic of the presentation, and give a critical assessment of the presentation.
After the reviewer is finished, the class as observer comments on the interaction of presenter and reviewer, and on the fairness of the criticism, there is a short comment sheet to be filled in by everyone.

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:

The long presentation may be done in teams of up to two students with a free selection of topic.
The length should not exceed 60 minutes, so that there is one long presentation with some time for discussion.
The long presentation must be written up in LaTeX (typically no more than 10 pages) and be submitted no later than one week after the presentation.
The written paper is reviewed by three anonymous peers, who write a one page assessment in the style of a review for a scientific journal.

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

Short presentation including summary, homework set: 1
Observer comments (cumulative for entire semester): 1
Reviewer role, written review: 0.5
Long presentation including paper: 2

Reading list:

Least squares, the singular value decomposition, and linear inverse problems

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)