STK-MAT4710 – Probability Theory
Course description
Course content
The course gives an introduction to probability theory in a measure theoretic setting. Among the topics discussed are: Probability measures, σ-algebras, conditional expectations, convergence of random variables, the law of large numbers, characteristic functions, the central limit theorem, filtrations, martingales in discrete time.
Learning outcome
After having completed the course
- you have good knowledge of the measure theoretic definitions of probability, independence, random variable, stochastic process, and conditional expectation
- you master different ways to describe the distribution of a random variable
- you have thorough knowledge of methods for treating and describing limits of sequences of random variables
- you are familiar with how filtrations and conditional expectations are used to represent information, and can work with discrete time martingales
- master LaTeX as an electronic tool for writing mathematics.
Admission to the course
Students admitted at UiO must?apply for courses?in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.
Nordic citizens and applicants residing in the Nordic countries may?apply to take this course as a single course student.
If you are not already enrolled as a student at UiO, please see our information about?admission requirements and procedures for international applicants.
Recommended previous knowledge
- MAT1100 – Calculus
- MAT1110 – Calculus and Linear Algebra
- MAT1120 – Linear Algebra
- STK1100 – Probability and Statistical Modelling
Overlapping courses
- 10 credits overlap with STK-MAT3710 – Probability Theory.
Teaching
4 hours lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Examination
Final written exam, which counts 100 % towards the final grade.
This course has 1 mandatory assignment that must be approved before you can sit the final exam. The assignment must be written with a typesetting software for mathematics, e.g. LaTeX.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses:STK-MAT4710 – Probability Theory
Examination support material
No support materials permitted.
Language of examination
Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.