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Instructors: Dr. Sven Möller
Event type:
Information session
Displayed in timetable as:
M-VK
Hours per week:
2,14
Language of instruction:
English
Min. | Max. participants:
10 | -
Comments/contents:
Schedule
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Room: Geomatikum H6
Time: 10.-14.10.2022, 9:00-17:00
Teacher: Dr. Sven Möller (www.moeller-sven.de)
Daily schedule (Mo-Fr)
* 9:00-10:30 Lecture 1
* Break + Questions
* 11:00-12:30 Lecture 2
* Lunch break
* 14:00-15:30 Lecture 3
* 15:30-17:00 Group Exercises
(Friday: only 2 lectures, exact schedule yet to be determined*)
* On Friday, there will be an orientation meeting for mathematical master's students (organised by members of the academic office and the study counselors). During the meeting they would like to explain the registration process in STiNE and give short overviews of the individual course programmes as well as the upcoming semester. Students who have completed their bachelor’s studies in Hamburg are also invited to join this meeting.
Course Summary
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This course is a one-week preparatory course (Vorkurs) for the mathematical master's programmes at the University of Hamburg (Mathematics, Wirtschaftsmathematik, Technomathematik/Industrial Mathematics, Mathematical Physics).
The main goal is to solidify the basic mathematical knowledge expected as prerequisites throughout the master's programmes.
[this course aims especially at new (international) master's students, who have not completed their bachelor’s in hamburg. you will get prepared for the mathematical master's courses in hamburg. of course, graduates from hamburg are also most welcome!]
The course is designed for all four mathematical master's programmes, but many examples and exercises will be related to problems in theoretical physics. (However, no background in physics is required.)
The course will be taught in English.
Literature
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(for further reading)
Books:
* Paul R. Halmos: Finite Dimensional Vector Spaces, Springer, 1987.
* Ilka Agricola, Thomas Friedrich: Vector Analysis, Vieweg, 2010.
* Jürgen Fuchs, Christoph Schweigert: Symmetries, Lie Algebras and Representations, Cambridge University Press, 2003
Lecture Notes:
* Christoph Schweigert: Mathematik für Physiker I-IV (https://www.math.uni-hamburg.de/home/schweigert/skripten.html)
* Winston Fairbairn, Catherine Meusburger: Concepts and Methods of Mathematical Physics (https://www.math.uni-hamburg.de/master/mphys/material/skript_w.pdf)
Contents (preliminary)
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I) Linear Algebra
1) Vector Spaces, Base Change, Tensors, Alternating Forms
2) Scalar Product, Orthonormal Basis, Identification with Dual, Self-Adjoint, Orthogonal and Unitary Maps
3) Eigenvalues, Jordan Decomposition, Diagonalisation
II) Analysis
1) Manifolds
2) Differential Form Calculus
3) Integration on Manifolds
III) Function Spaces
1) Topological Vectorspaces, Hilbert spaces
2) Spectrum of Operators
3) Spectrum of Differential Operators
IV) Symmetries*
1) Basics in Categories and Groups
2) Matrix Lie Groups
3) Lie Algebras
4) Noether's theorem
5) Tensoring Representations
* if time permits
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