APP MTH 4049 - Applied Mathematics Topic D - Honours
North Terrace Campus - Semester 2 - 2017
General Course Information
Course Code APP MTH 4049 Course Applied Mathematics Topic D - Honours Coordinating Unit School of Mathematical Sciences Term Semester 2 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 Course Description 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
Course Coordinator: Dr Giang NguyenThis is the same course as APP MTH 7049 - Applied Mathematics Topic D
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesIn 2017, 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, and Ito integrals.
Prerequisites: Students should have some background in probability and stochastic processes (for example, discrete-time or continuous-time Markov chains).
Learning Outcomes: On successful completion of this course, students will be able to:
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.
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) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
all Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
1,3 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
1,3 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
Recommended Resources1. L. C. Evans, An introduction to stochastic differential equations, AMS, 2012.
2. G. R. Grimmett and D. R. Stirzaker, Probability and random processes, 3rd edition, Oxford University Press, 1985.
3. R. Durrett, Probability: theory and example, 3rd edition, 2010.
4. M. Harrison, Brownian motion and stochastic flow systems, John Wiley & Sons, 1985.
5. T. Mikosch, Elementary Stochastic Calculus, World Scientific, 2002.
Online LearningThe course will have an active MyUni website.
Learning & Teaching Activities
Learning & Teaching ModesThe lecturer guides the students through the course material in 30 lectures. Students are expected to engage with the material in the lectures. Interaction with the lecturer and discussion of any difficulties that arise during the lecture is encouraged. Fortnightly homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Lectures 30 90 Assignments 4 68 Total 158
Learning Activities SummaryWeek 1: Measure-theoretic Probability
Week 2: Measure-theoretic Probability
Week 3: Modes of Convergence
Week 4: Brownian Motion
Week 5: Brownian Motion
Week 6: Filtrations, Conditional Probability
Week 7: Martingales
Week 8: Diffusions
Week 9: Diffusions
Weel 10: Stochastic Calculus
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 task Task type Weighting Learning outcomes Assignments Formative and summative 30% All Exam Summative 70% All
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course.
Assessment DetailThere will be four assignments worth 30% of the total mark. The remaining 70% will come from the exam
SubmissionAssignments must be handed in person to the lecturer or submitted in the assigned assignment box if they are to be marked.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M11 (Honours Mark Scheme) Grade Grade reflects following criteria for allocation of grade Reported on Official Transcript Fail A mark between 1-49 F Third Class A mark between 50-59 3 Second Class Div B A mark between 60-69 2B Second Class Div A A mark between 70-79 2A First Class A mark between 80-100 1 Result Pending An interim result RP Continuing Continuing CN
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 Access Adelaide.
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.
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