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Foto: Matthias Friel

Foundations of Stochastics - Einzelansicht

Veranstaltungsart Vorlesung/Übung Veranstaltungsnummer 18201
SWS 4 Semester WiSe 2020/21
Einrichtung Institut für Mathematik   Sprache englisch
Belegungsfrist 19.10.2020 - 30.11.2020

Belegung über PULS
Gruppe 1:
     jetzt belegen / abmelden
    Tag Zeit Rhythmus Dauer Raum Lehrperson fällt aus am Max. Teilnehmer/-innen
Vorlesung -  bis  wöchentlich am   Jun. Prof. Dr. Lie  
  Bemerkung: online asynchron
Übung -  bis  wöchentlich am   Jun. Prof. Dr. Lie  
  Bemerkung: online asynchron
Kommentar

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.

Literatur

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 .

Bemerkung

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.

Voraussetzungen

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.
Leistungsnachweis

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.

Lerninhalte

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.
Zielgruppe

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


Strukturbaum
Keine Einordnung ins Vorlesungsverzeichnis vorhanden. Veranstaltung ist aus dem Semester WiSe 2020/21 , Aktuelles Semester: WiSe 2021/22