STK-MAT3710 – 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 know the measure-theoretic definitions of probability, independence, random variable, stochastic process, and conditional expectation
- you know different ways to describe the distribution of a random variable
- you know 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.
Admission to the course
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for?in Studentweb.
Special admission requirements
In addition to fulfilling theHigher Education Entrance Qualification, applicants have to meet the following special admission requirements:
- Mathematics R1 (or Mathematics S1 and S2) + R2
And in addition one of these:
- Physics (1+2)
- Chemistry (1+2)
- Biology (1+2)
- Information technology (1+2)
- Geosciences (1+2)
- Technology and theories of research (1+2)
The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies(in Norwegian).
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-MAT4710 – Probability Theory.
Teaching
4 hours lectures/exercises each 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.
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 examination support material is allowed.
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.