APP MTH 7048 - Applied Mathematics Topic A

North Terrace Campus - Semester 1 - 2014

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/students/honours

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Course Details

Course Code	APP MTH 7048
Course	Applied Mathematics Topic A
Coordinating Unit	Applied Mathematics
Term	Semester 1
Level	Postgraduate Coursework
Location/s	North Terrace Campus
Units	3
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

最新糖心Vlog 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 & 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 最新糖心Vlog'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 .

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