Coursebooks 2017-2018

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Probability theory

MATH-432

Lecturer(s) :

Mountford Thomas

Language:

English

Summary

The course provides a rigourous measure theory based introduction to probability. We treat the various forms of convergence for random variables up to convergence in distribution.

Content

- general probability spaces, random variables and measurable functions, measures and probabilities

- expectation for a random variable and reminder of integration theory

- independence and the Borel-Cantelli lemmas

- strong and weak laws of large numbers

- central limit theorem

Learning Prerequisites

Recommended courses

First cycle, Advanced analysis A (measure theory)

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Ex cathedra lecture and exercises in the classroom

Assessment methods

Exam written

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours No
Assistants No
Forum No

Resources

Bibliography

R. Durrett. Probability: theory and examples.

Ressources en bibliothèque
Websites

Prerequisite for

Probabilities, Stochastic process

In the programs

  • Applied Mathematics, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Probability theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Probability theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Probability theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Probability theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 1
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Probability theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 3
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • Subject examined
      Probability theory
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14 MAA112MAA112
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

legend

  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German