APP MTH 4046 - Applied Mathematics Topic A

North Terrace Campus - Semester 1 - 2015

Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au

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Course Details

Course Code	APP MTH 4046
Course	Applied Mathematics Topic A
Coordinating Unit	Applied Mathematics
Term	Semester 1
Level	Undergraduate
Location/s	North Terrace Campus
Units	3
Contact	Up to 2.5 hours per week
Available for Study Abroad and Exchange	Y
Restrictions	May only be presented towards some Engineering Programs
Assessment	ongoing assessment 30%, exam 70%

Course Staff

Course Coordinator: Dr Giang Nguyen

Course Timetable

The full timetable of all activities for this course can be accessed from .

Course Learning Outcomes

In 2014, the topic of this course will be Advanced Stochastic Processes.

Syllabus

Randomness is an important factor in modelling and analyzing various real-life situations. This course covers some key topics in continuous-time stochastic processes: measure-theoretic probability, filtration, martingales, Brownian motions and reflected Brownian motions, Markov-modulated Brownian motions, Ito integrals, convergence of processes, functional limit theorems, and applications to insurance, environmental modelling, and finance. Prerequisites: Students should have some background in probability and stochastic processes (for example, discrete-time or continuous-time Markov chains).

Learning Outcomes

1. Explain the basics of measure-theoretic probability

2. Demonstrate key properties of Brownian motions

3. Have a better appreciation for the roles of continuous-time stochastic processes in a wide variety of real-life applications, including insurance, environmental modelling, and finance

4. Explain the relevance and importance of Ito calculus to finance

5. Demonstrate the concept of convergence of processes and relevant proof techniques

6. Analyse, interpret, and predict the evolution of continuous-time stochastic processes

7. Present analysis and interpretations in written form

University Graduate Attributes

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute	Course Learning Outcome(s)
Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised.	all
The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner.	6, 7
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems.	2, 4, 5, 6, 7
Skills of a high order in interpersonal understanding, teamwork and communication.	7
A proficiency in the appropriate use of contemporary technologies.	2, 4, 5, 6, 7
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life.	all

Learning Resources

Required Resources

None.

Recommended Resources

1. G. R. Grimmett and D. R. Stirzaker, Probability and random processes, 3rd edition, Oxford University Press, 1985.
2. R. Durrett, Probability: theory and example, 3rd edition, 2010.
3. P. Billingsley, Convergence of probability measures, 2nd edition, Wiley, NY, 1999.
4. M. Harrison, Brownian motion and stochastic flow systems, John Wiley & Sons, 1985.

Online Learning

This course uses MyUni exclusively for providing electronic resources, such as assignments and handouts, and for making course announcements. It is recommended that students make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/

Learning & Teaching Modes

This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.

Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

Activity	Quantity	Workload Hours
Lectures Assignments	30 4	90 60
Total		150

Learning Activities Summary

Lecture Outline

1. Basics of measure-theoretic probability (Lectures 1-2)

2. Modes of convergence (Lectures 3-4)

3. Brownian motion and its applications (Lectures 5-8)

4. Quadratic variation property of Brownian motions (Lecture 9)

5. Filtration, martingales, and stopping times (Lectures 10-13)

6. Ito calculus and its applications to finance (Lectures 14-18)

7. Equivalent martingale measures (Lectures 19-20)

8. Probability on metric spaces (Lectures 21-22)

9. Weak convergence of stochastic processes (Lectures 23-24)

10. Functional limit theorems (Lectures 25-26)

11. Markov-modulated Brownian motions (MMBMs) and their applications (Lecture 27)

12. Stochastic fluid flows and their applications (Lecture 28)

13. Convergence of stochastic fluid flows to MMBMs (Lecture 29)

14. Summary (Lecture 30)

Specific Course Requirements

None.

The University's policy on Assessment for Coursework Programs is based on the following four principles:

Assessment must encourage and reinforce learning.
Assessment must enable robust and fair judgements about student performance.
Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
Assessment must maintain academic standards.

Assessment Summary

Component	Weighting	Objective Assessed
Assignments Exam	30% 70%	all all

Assessment Related Requirements

An aggregate score of at least 50% is required to pass the course.

Assessment Detail

Assessment Item	Distributed	Due Date	Weighting
Assignment 1 Assignment 2 Assignment 3 Assignment 4	Monday Week 1 Monday Week 4 Monday Week 7 Monday Week 10	Friday Week 3 Friday Week 6 Friday Week 9 Friday Week 12	7.5% 7.5% 7.5% 7.5%

Submission

Assignments will have a maximum two week turn-around time for feedback to students.

Course Grading

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
Grade	Mark	Description
FNS		Fail No Submission
F	1-49	Fail
P	50-64	Pass
C	65-74	Credit
D	75-84	Distinction
HD	85-100	High Distinction
CN		Continuing
NFE		No Formal Examination
RP		Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through .

Student Feedback

The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
Student Support
Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
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Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student鈥檚 disciplinary procedures.

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Authorised by:	Deputy Vice-Chancellor and Vice-President (Academic)
Maintained by:	Course Outlines Administrator

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