Probabilistic Techniques - NTIN022
Title in English: Pravděpodobnostní techniky
Guaranteed by: Computer Science Institute of Charles University (32-IUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017 to 2019
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Additional information: http://iuuk.mff.cuni.cz/~samal/vyuka/pm/
Guarantor: doc. Mgr. Robert Šámal, Ph.D.
doc. RNDr. Martin Tancer, Ph.D.
Class: Informatika Mgr. - Diskrétní modely a algoritmy
M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Informatics > Discrete Mathematics, Theoretical Computer Science
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Annotation -
Last update: (04.05.2015)
Probabilistic techniques are a major tool of discrete mathematics, they are also frequently used in design and analysis of algorithms and other areas of computer science. The lecture introduces basic notions, methods, and estimates and illustrates them on examples from computer science and discrete mathematics.
Aim of the course -
Last update: (04.05.2015)

Student who takes the class will learn to actively use a modern

probabilistic techniques in discrete mathematics and computer science,

including the probabilistic method.

Course completion requirements -
Last update: doc. RNDr. Martin Tancer, Ph.D. (05.10.2018)

For getting the credit from tutorials, the students are required to get at least 50 points from homework. The total number of available points will be at least 180. There is no provision for repeated attempts for the credit. Credit from tutorials is a necessary condition for an attempt to pass an exam.

Literature -
Last update: (04.05.2015)
  • M. Mitzenmacher, E. Upfal: Probability and Computing: Randomized Algorithms and Probabilistic Analysis, Cambridge Univ. Press, 2005.
  • N. Alon, J. Spencer: The Probabilistic Method, 3rd edition, J. Wiley and Sons, 2008.
  • J. Matousek, J. Vondrak: The probabilistic method, lecture notes, KAM MFF UK, electronic version will be available on the web-site of the lecture, printed version in the library of MFF UK.
  • J. Spencer: Ten lectures on the probabilistic method, 2nd edition, SIAM, 1994.

Requirements to the exam -
Last update: doc. RNDr. Martin Tancer, Ph.D. (05.10.2018)

The exam will be oral based on the contents of the lectures. Extra points gained by students by solving problems for tutorials will be considered in favor of the students.

Syllabus -
Last update: (04.05.2015)

Basic notions and methods

  • events, expected value and its linearity
  • conditional probability, Bayes' rule

Basic inequalities and estimates

  • Markov's a Chebyshev's inequality
  • Chernoff-type estimates

Probabilistic method

  • basic method and alteration method
  • Lovász local lemma

Advanced techniques

  • balls and bins model, basic estimates and applications
  • Markov chains, stationary distribution
  • basic continuous distributions as limits of discrete ones, properties and applications