• Class Number 3555
• Term Code 3030
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Dr Jan Rozendaal
• Class Dates
• Class Start Date 24/02/2020
• Class End Date 05/06/2020
• Census Date 08/05/2020
• Last Date to Enrol 02/03/2020
• TUTOR
• Michael Howes
• Wenqi Zhang
SELT Survey Results

Probability Theory with Applications (MATH3029)

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 MATH3015 (Stochastic Analysis with Financial Applications), as well as other honours and post-graduate courses emphasizing the theory of mathematical finance and stochastic analysis.

Note: This is an HPC.

## Learning Outcomes

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

1. Understand and use fundamental concepts of probability theory
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

None. Obtaining the textbook is highly recommended but not obligatory.

Textbook:

Stochastics, 2nd revised and extended edition, by Hans-Otto Georgii, de Gruyter, 2013. ISBN 978-3-11-029254-1.

## Staff Feedback

Students will be given feedback in the following forms in this course:

• feedback to whole class, groups, individuals, focus group etc

## Student Feedback

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.

## Other Information

Course delivery and assessment in 2020 was adjusted due to the COVID-19 pandemic. Any information below that replaces what was published in the Class Summary for Semester 1, 2020 was approved by the Associate Dean Education (as is required after 10% commencement of a course). Where an activity or assessment is not referenced below, it remains unchanged.

Teaching Activities

• Lectures were pre-recorded and posted online.
• Workshops were done online.

Assessment

Adjustments were made to assignment due dates; for details see the course Wattle site.

• Midterm was cancelled.
• Final Exam was online.
• The final grade for the course was the maximum of the grades obtained using the following two forms of assessment:

1) 5 assignments, worth 10% each, and a final exam worth 50%;

2) 5 assignments, the first of which is worth 6% and the remaining four 10% each, and a final exam worth 54%

## Class Schedule

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
8 Limit theorems
9 Limit theorems
10 Limit theorems, Markov chains
11 Markov chains
12 Markov chains, Brownian motion

See Wattle

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Homework assignments 30 % 13/03/2020 05/06/2020 1,2,3,4
Mid-semester exam 25 % 03/04/2020 01/05/2020 1,2,3,4
End-of-semester exam 40 % 04/06/2020 02/07/2020 1,2,3,4
Workshop participation 5 % 24/02/2020 28/05/2020 1,2,3,4

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

## Policies

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:

## Assessment Requirements

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.

## Participation

Participation in workshops

## Examination(s)

Mid-semester and end-of-semester examination.

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 venue of the exam.

Value: 30 %
Due Date: 13/03/2020
Return of Assessment: 05/06/2020
Learning Outcomes: 1,2,3,4

Homework assignments

5 homework assignments, each worth 6%. Deadlines for assignments will be communicated at least two weeks before the deadline.

The date range for these tasks indicates the approximate due date for the first assignment, and the approximate return date for the last assignment. 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.

Value: 25 %
Due Date: 03/04/2020
Return of Assessment: 01/05/2020
Learning Outcomes: 1,2,3,4

Mid-semester exam

The date range is a general indication of when the mid-semester exam will be held. Please check the course Wattle site and the ANU Examination Timetable to confirm the date, time and location of the exam.

Value: 40 %
Due Date: 04/06/2020
Return of Assessment: 02/07/2020
Learning Outcomes: 1,2,3,4

End-of-semester exam

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 location of the exam.

Value: 5 %
Due Date: 24/02/2020
Return of Assessment: 28/05/2020
Learning Outcomes: 1,2,3,4

Workshop participation

You will be assessed based on your participation in the weekly workshops. Students are expected to contribute on an on-going basis throughout the semester. The date range for this task comprises the start of the semester and last day of the teaching period.

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.

## Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

## Hardcopy Submission

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

Individual assessment tasks may or may not allow for late submission. Policy regarding late submission is detailed below:

• Late submission permitted. 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 7 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.

## Referencing Requirements

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.

## Returning Assignments

It is intended that the marked assignments will be returned within 7 days after submission

## 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.

## Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

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).

## Convener

 Dr Jan Rozendaal 6125 2195 jan.rozendaal@anu.edu.au

### Research Interests

Microlocal analysis, harmonic analysis, partial differential equations, functional analysis

### Dr Jan Rozendaal

 Monday 15:00 16:00 Thursday 11:00 12:00

## Tutor

 Michael Howes 61252908 u6079887@anu.edu.au

## Tutor

 Wenqi Zhang WenQi.Zhang@anu.edu.au