• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Economics, Finance, Mathematics, Theoretical Physics
• Course convener
• Dr Jan Rozendaal
• Mode of delivery In Person
• Co-taught Course
• Offered in First Semester 2020
Probability Theory with Applications (MATH6109)

The course introduces probability theory, including probability spaces, random variables, conditional probability and independence, limit theorems, and Markov chains, with an introduction to Brownian motion. The course will provide students with a solid theoretical foundation for probability theory, as well as describing some practical applications of probability in information theory and option pricing.

The course will provide a sound foundation to progress to MATH6115 Stochastic Analysis with Financial Applications, as well as other post-graduate courses emphasizing the theory of mathematical finance and stochastic analysis.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Understand and use fundamental concepts of probability theory, both in the abstract setting of probability spaces, sigma algebras, and probability measures, and as applied to concrete problems
2. Demonstrate accurate and efficient use of probability theory techniques, including limiting processes
3. Solve problems using probabilistic methods and ideas
4. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from probability theory
5. Ability to use their deep knowledge and understanding of probability theory to formulate responses to complex concrete and abstract problems
6. Ability to communicate their understanding and skills in probability theory with colleagues and non-experts and apply their knowledge in an occupational situation.

## Indicative Assessment

1. Assignments (30) [LO 1,2,3,4,5,6]
2. Participation in lectures and workshops (quizzes, presentations, group work) (5) [LO 1,2,3]
3. Mid-semester exam (25) [LO 1,2,3,4,5,6]
4. Final Exam (40) [LO 1,2,3,4,5,6]

In response to COVID-19: Please note that Semester 2 Class Summary information (available under the classes tab) is as up to date as possible. Changes to Class Summaries not captured by this publication will be available to enrolled students via Wattle.

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

Three lectures per week and regular workshops.

Not applicable

## Requisite and Incompatibility

You are not able to enrol in this course if you have completed MATH3029.

You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.

## Prescribed Texts

Stochastics: Introduction to Probability and Statistics by Hans-Otto Georgii, de Gruyter, 2nd edition.
Course notes will also be provided to students.

## Assumed Knowledge

Calculus, linear algebra and basic real analysis. Some knowledge of measure theory would be helpful, but it is not essential to take this course.

## Fees

Tuition fees are for the academic year indicated at the top of the page.

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
2
Unit value:
6 units

If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees.  Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500

## Course fees

Domestic fee paying students
Year Fee
2020 \$4050
International fee paying students
Year Fee
2020 \$5760
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
3571 24 Feb 2020 02 Mar 2020 08 May 2020 05 Jun 2020 In Person View