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Abstract
This course provides a gentle introduction to the Probabilistic Method, with an emphasis on methodology. We will try to illustrate the main ideas by showing the application of probabilistic reasoning to various combinatorial problems.
Content
The topics covered in the class will include (but are not limited to): linearity of expectation, the second moment method, the local lemma, correlation inequalities, martingales, large deviation inequalities, Janson and Talagrand inequalities and pseudo-randomness.
Resources
Literature
- The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008. - Random Graphs, by B. Bollobás, 2nd Edition, Cambridge University Press, 2001. - Random Graphs, by S. Janson, T. Luczak and A. Rucinski, Wiley, 2000. - Graph Coloring and the Probabilistic Method, by M. Molloy and B. Reed, Springer, 2002.
Learning Materials (Links)
- Main link
- Website of the course (Moodle)
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Every two years
Examination
- Type
- session examination
- Mode
- written 180 minutes
- Aids
- Students are allowed to bring ONLY a printed copy of the lecture notes with no extra writing (highlighting and blank post-its are allowed).
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Probabilistic Methods in Combinatorics
Does not take place this semester.
|
No time listed | 2 h weekly |
| exercise |
Probabilistic Methods in Combinatorics
Does not take place this semester.
|
No time listed | 1 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Track: Signal Processing and Machine Learning (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
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Specialisation Courses (These specialisation courses are particularly recommended for the area of "Signal Processing and Machine Learning", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialisation courses during the MSc EEIT.)
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Major Courses (A total of 42 CP must be achieved during the Master Programme. The individual study plan is subject to the tutor's approval.)
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