Foundations of Stochastics - Einzelansicht

The aim of this course is to provide an introduction to probability theory and stochastic processes. The course will provide some preparation for the following courses:

1. Statistical data analysis
2. Bayesian inference and data assimilation.

The lectures and exercises for this course will be online and asynchronous.

The language of the course is English.

English: Achim Klenke, "Probability theory: a comprehensive course", Springer (2014)

Deutsch: Achim Klenke, "Wahrscheinlichkeitstheorie", Springer (2013)

Using the university VPN, you can obtain PDF versions of the books from the University library website: https://www.ub.uni-potsdam.de/en/ .

To set up a VPN, go to the following page (German only): https://www.uni-potsdam.de/de/zim/angebote-loesungen/vpn .

To participate in this course, please register on PULS. Registered individuals will be given access to the Moodle page for this course.

If you cannot register on PULS, please send an e-mail to Prof. Lie from your University of Potsdam e-mail account.

A stable internet connection is strongly recommended.

Participants in this course are expected to already know the following concepts:

1. Basic mathematical analysis: inequalities, limits, sequences, series, factorials, etc.
2. Differential and integral calculus: computing derivatives and integrals of scalar- and vector-valued functions, maxima or minima or saddle points of functions, etc.
3. Linear algebra: computing matrix-vector or matrix-matrix products, solving systems of linear equations, computing eigenvalues and eigenvectors, determinants, traces, transposes of matrices, etc.
   

The final grade for this course will be determined by an online written exam of 90 minutes.

In order to obtain permission to take the online written exam, participants must successfully complete at least 70% of the homework assignments.

Important concepts from the following topics will be presented:

1. Set theory, sigma-algebras, probability measures
2. Independence
3. Random variables
4. Conditional probabilities and conditional expectation
5. Moments of random variables
6. Limit theorems
7. Markov chains.

This course is designed primarily for students in the Master of Data Science program.