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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course MATM30F valid from Autumn 2018

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General
Aim
  • The aim of the course is to give mathematical knowledge that facilitates successful studies in probability, stochastic processes and stochastic differential equations. These subjects are becoming more and more important in many applications, such as meteorology, finance and social planning.
Contents
  • The course deepens and extends basic knowledge in probability theory. A central part of the course is existence and uniqueness theorems about measures defined on sigma-algebras, integration theory, conditional expectation and weak convergence in metric spaces.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be able to explain the measure theoretic approach to probabilities and random variables;

    be able to explain the construction of the Lebesgue-integral and the fundamental convergence theorem for this integral;

    be able to explain how the concepts conditional expectation and weak convergence can be formalized through measure theory.
Competences and Skills
  • For a passing grade the doctoral student must
  • be able to use the fundamental theorems in integration theory to solve problems;

    be able to choose an appropriate solution strategy for a problem within the course's range, and thereafter work out a detailed solution.
Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Exercises
Examination Formats
  • Oral exam
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • Linear algebra, calculus in one and several variables, and basic courses in Fourier analysis and mathematical statistics.
Selection Criteria
Literature
  • Probability. Springer Science & Business Media, 1996. ISBN 9780387945491.
Further Information
Course code
  • MATM30F
Administrative Information
  • 2018-11-15
  • Professor Thomas Johansson

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