APP MTH 4049 - Applied Mathematics Topic D - Honours

North Terrace Campus - Semester 2 - 2017

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

  • General Course Information
    Course Details
    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 Staff

    Course Coordinator: Dr Giang Nguyen

    This is the same course as APP MTH 7049 - Applied Mathematics Topic D
    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    In 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
    all
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    1. 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 Learning
    The course will have an active MyUni website.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    The 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.
    Workload

    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 Summary
    Week 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
  • Assessment

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

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

    Assessment Summary
    Assessment task Task type Weighting Learning outcomes
    Assignments Formative and summative 30% All
    Exam Summative 70% All
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    There will be four assignments worth 30% of the total mark. The remaining 70% will come from the exam
    Submission
    Assignments must be handed in person to the lecturer or submitted in the assigned assignment box if they are to be marked.
    Course Grading

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

    M11 (Honours Mark Scheme)
    GradeGrade reflects following criteria for allocation of gradeReported 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.

  • 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
  • Fraud Awareness

    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’s disciplinary procedures.

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