Maria Infusino - Teaching

Winter semester 2016/17

Proseminar on Linear Algebra
with Lothar Sebastian Krapp

Thursday 11:45-13:15 (Room D406)

The aim of this cycle of seminars is to develop in more detail some topics that were introduced in the course "Lineare Algebra II'' from the SoSe 2016. The talks could deal with operators on inner product spaces, applications of the spectral theorem, bilinear forms, and direct methods for linear systems and their applications. Further suggestions are welcome. Each talk will provide a review of the results from the literature about one of these topics and illustrate them with examples and applications. Every student should also produce a short handout about the material developed in her/his own talk.

Target group
This seminar is primarily aimed at third-semester Bachelor in Mathematics (Haupt- oder Nebenfach) students, but is also suitable for students of Lehramt and Bachelor of Education.

Preliminary meeting
A preliminary discussion for the assignment of the topics will take place on Thursday July 14th from 11.45 to 13.15 in Room M630 .

Personal Tutorial
A personal tutorial will be offered to each of you on the Wednesday of the week before your talk (13:30-14:30, F408) to assist you in the preparation of your talk, abstract and handout. In case you need more assistance, further personal tutorials can be arranged by appointment.

Weekly deadlines

Monday: submission of the final title and abstract by noon
Thursday: seminar handout at the beginning of the talk (max 10 pages) and seminar talk (75 minutes + 15 minutes for questions).
One week after you receive the feedback on your handout, you should submit the final version of the handout

Final grade You will receive a final grade which will include the evaluation of both your presentation and your handout.

Language
The language of the seminar can be either German or English.

References

G. Allaire, S. M. Kaber, Numerical linear algebra, Texts in Applied Mathematics, 55. Springer, New York, 2008.
W. Ford, Numerical linear algebra with applications, Elsevier/Academic Press, Amsterdam, 2015.
L. Fox, Introduction to numerical linear algebra, Monographs on Numerical Analysis Clarendon Press, Oxford, 1964.
P. R. Halmos, Finite-dimensional vector spaces, Reprinting of the 1958 second edition. Undergraduate Texts in Mathematics. Springer-Verlag, New York-Heidelberg, 1974.
K. Hoffman, R. Kunze, Linear Algebra, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1971.
F. Lorenz, Lineare algebra, vol. I and II, Spektrum Akademischer Verlag, 2008.
L. Perko, Differential equations and dynamical systems, Texts in Applied Mathematics 7, 3rd ed., Springer, New York, 2001.
M. Reed, B. Simon, Methods of modern mathematical physics, Academic Press, Inc., Harcourt Brace Jovanovich, Publishers, New York, 1980.

For further information, see also the announcement of this cycle of seminars and the list of possible topics.

Schedule

October, 27th : Forms on inner product spaces (1-a) (Maria Infusino). Abstract Handout
November, 3rd : Basiswissen über Bilinearformen mit Betrachtung symmetrischer Bilinearformen (3-a,b) (Zhelun Chen). Abstract Handout
November, 10th : Why are Lie groups useful in theoretical physics and soccer? (5) (Jeremy Näscher). Abstract
November, 17th : Positiv (semi-)definite sesquilineare Formen (1-b,c) (Sarah-Tanja Hess). Abstract Handout
November, 24th : Gruppenerhaltende Bilinearformen - Teil I (3-d) (Moritz Schick). Abstract
December, 1st : Gruppenerhaltende Bilinearformen - Teil II (3-d) (Moritz Schick). Abstract
December, 8th : Self-adjoint extensions of symmetric operators (5) (Simon Wozny). Abstract Handout
December, 15th : Skew-symmetric bilinear forms (3-c) (Ramona Schmidt). Abstract
January, 12th : Spectral resolution and functions of diagonalisable normal operators (2-a) (Lothar Sebastian Krapp). Abstract Handout
January, 19th : Sesquilinearformen und Projektionen von Vektorräumen (1-d) (Daniel Sartison). Abstract
January, 26th : Householder-Algorithmus (4-b) (Arlinda Omaj). Abstract
February, 2nd : Tensoren und Relativität (5): (Johannes Fahrner). Abstract Handout
February, 9th : Simultaneous diagonalization of normal operators (2-c) (Florian Griebling). Abstract
February, 16th : Primärzerlegung für normale Operatoren (2-d) (Ramona Schmidt). Abstract

Using LaTeX

useful suggestions for the preparation your handout can be found in this short overview about mathematical typography in LaTeX
if this handout is your work in LaTeX, then you might find useful this sample LaTeX document

ANNOUNCEMENTS
Please, send us via email ASAP and at latest by:

July 31st: Confirmation of participation and Preferred date for your talk.
October 1st: Final choice of the topic of your talk.
October 15th: Final deadline for confirming the topic of your talk.
We will meet personally each of you to discuss the final mark for the proseminar, which includes the evaluation of your talk, handout and participation, and give you some more feedback.
The first meeting will be on February 17th in F408 with the following schedule:
- Moritz Schick 10:30
- Johannes Fahrner 10:50
- Jeremy Näscher 11:10
- Sarah-Tanja Hess 11:30
- Simon Wozny 11:50
- Zhelun Chen 12:10
The second meeting will be on March 15th in F408 with the following schedule:
- Ramona Schmidt 10:30
- Daniel Sartison 10:50
- Arlinda Omaj 11:10
- Florian Griebling 11:30
If you have problems with the schedule above, then please contact us ASAP.

Last update: 06.05.2017