- Class Number 3059
- Term Code 3230
- Class Info
- Unit Value 6 units
- Mode of Delivery In Person
- Dr Sean Harris
- Dr Sean Harris
- Class Dates
- Class Start Date 21/02/2022
- Class End Date 27/05/2022
- Census Date 31/03/2022
- Last Date to Enrol 28/02/2022
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.
Upon successful completion, students will have the knowledge and skills to:
- 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
- Demonstrate accurate and efficient use of probability theory techniques, including limiting processes
- Solve problems using probabilistic methods and ideas
- Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from probability theory
- Ability to use their deep knowledge and understanding of probability theory to formulate responses to complex concrete and abstract problems
- Ability to communicate their understanding and skills in probability theory with colleagues and non-experts and apply their knowledge in an occupational situation.
Additional Course Costs
None. Obtaining the textbook is completely optional, as it is available online via the ANU library.
Stochastics, 2nd revised and extended edition, by Hans-Otto Georgii, de Gruyter, 2013. ISBN 978-3-11-029254-1. (available for free online via the ANU Library)
Recommended student system requirements
ANU courses commonly use a number of online resources and activities including:
- video material, similar to YouTube, for lectures and other instruction
- two-way video conferencing for interactive learning
- email and other messaging tools for communication
- interactive web apps for formative and collaborative activities
- print and photo/scan for handwritten work
- home-based assessment.
To fully participate in ANU learning, students need:
- A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
- Speakers and a microphone (e.g. headset)
- Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
- Suitable location with minimal interruptions and adequate privacy for classes and assessments.
- Printing, and photo/scanning equipment
For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements
Students will be given feedback in the following forms in this course:
- written comments
- verbal comments
- feedback to whole class, groups, individuals, focus group etc
ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.
Adjustments to delivery in 2022
Course delivery in 2022 will be adjusted due to the COVID-19 pandemic. Where an activity is not referenced below, it remains unchanged.
- Lectures may be run online or pre-recorded and posted online.
- Some workshops will be held online.
|Week/Session||Summary of Activities||Assessment|
|1||Foundations of probability theory||Schedule is subject to change|
|2||Foundations of probability theory, standard probability distributions|
|3||Standard probability distributions, conditional probability and independence|
|4||Conditional probability and independence|
|5||Conditional probability and independence, expectation and variance|
|6||Expectation and variance|
|7||Expectation and variance, limit theorems|
|10||Limit theorems, Markov chains|
|12||Markov chains, Brownian motion|
Students are required to enrol in one of the available weekly workshop groups by following a process that will be detailed on the course Wattle page. Remote participation options will be provided for students who require them due to travel restrictions or COVID-safe guidelines. However not all times will be available for both remote and in-person attendance. Please refer to the course Wattle site for more information.
|Assessment task||Value||Due Date||Return of assessment||Learning Outcomes|
|Homework assignments||60 %||*||*||1,2,3,4,5,6|
|End-of-semester exam||40 %||02/06/2022||30/06/2022||1,2,3,4,5,6|
* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details
ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:
The ANU is using 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. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.
Moderation of Assessment
Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.
In Semester 1 2022, participation in workshops will be on campus with adjustments for remote participants.
This course includes a final examination.. The details and mode of delivery for the exam will be communicated through the course Wattle site.
Please note that, where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode of the exam.
Assessment Task 1
Learning Outcomes: 1,2,3,4,5,6
5 homework assignments, each worth 12%. Deadlines for assignments will be communicated at least two weeks before the deadline.
There are 5 assignments due over the semester. It is intended that the marked assignments will be returned within 7 days after submission. Further details can be found on the course Wattle site. Masters level students will complete extra and/or different questions to those set for the co-taught undergraduate course MATH3029.
Assessment Task 2
Learning Outcomes: 1,2,3,4,5,6
The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and mode of the exam. Final Exam will be online or take home, TBC. Students will need to get a mark of at least 40% on the exam to pass the course.
Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.
The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.
The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.
You will be required to agree to a declaration as part of the submission of your assignments, that will record your understanding of ANU academic integrity principles. Assignment submission will be via PDF upload to a Wattle Assignment Tool. Please keep a copy of the assignment for your records. MATH6109 does not use Turnitin, having been granted an exemption.
For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.
Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.
Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.
It is intended that the marked assignments will be returned within 7 days after submission, at which point late submissions will no longer be accepted.
Extensions and Penalties
Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.
Distribution of grades policy
Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.
Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.
Support for students
The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).
- ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
- ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
- ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
- ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
- ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
- ANUSA supports and represents undergraduate and ANU College students
- PARSA supports and represents postgraduate and research students