APP MTH 4046 - Applied Mathematics Topic A - Honours

North Terrace Campus - Semester 1 - 2020

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 4046
    Course Applied Mathematics Topic A - Honours
    Coordinating Unit School of Mathematical Sciences
    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 Honours students only
    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 Andrew Black

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    In 2020 the topic of this course will be Advanced stochastic modelling and Monte Carlo methods

    Stochastic models are a broad class of mathematical models that are used to describe phenomena that are characterised by uncertainty or randomness. There are numerous examples of such phenomena: biological populations, epidemics, financial markets, traffic systems—one can find examples practically everywhere. What is common to all these is that they are very complex, with far too many factors to to be modelled perfectly. The randomness in our models reflects this inherent lack of knowledge in a principled way while still providing a meaningful description of the phenomena and the ability to make predictions. In this course we will learn how to specify stochastic models for realistic systems and how they can be used for prediction, inference and to gain basic insight into the underlying phenomena.

    Almost no useful models can be solved analytically, so instead we will use Monte Carlo approaches that involve the generation of random processes via a computer. These techniques are not just useful for simulation of stochastic models, but also a powerful method for solving many deterministic type problems.

    Assumed knowledge: Applied Probability III or Random Processes III is the best preparation, but a thorough knowledge of Probability and Statistics II is enough. This course will require programming (MATLAB or equivalent).

    On successful completion of this course, students will be able to:
    1. Understand and apply various Monte Carlo techniques.
    2. Simulate and use models based on stochastic differential equations.
    3. Construct and simulate continuous time Markov chain (CTMC) models.
    4. Understand the scaling behaviour of certain CTMC models and how this relates to the scales of the process that is being observed.
    5. Derive and solve a hierarchy of approximate solutions for CTMCs.
    6. Understand and apply stochastic models and methods for inference of hidden dynamical processes.
    7. Present analysis in written and graphical 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
    all
    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
    Access to the internet.
    Recommended Resources
    P. Schuster, Stochasticity in Processes, Springer 2016.
    D. P. Kroese, T. Taimre, Z. I. Botev, Handbook of Monte Carlo Methods, Wiley 2011.
    Online Learning
    This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions. Students should make appropriate use of these resources.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lectures as the primary delivery mechanism for the material.  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.

    ActivityQuantityWorkload Hours
    Lecture classes 30 100
    Assignments 5 56
    Total 156



    Learning Activities Summary
    1. Monte Carlo methods (weeks 1-3)
    2. Stochastic differential equation models (weeks 4-5)
    3. Continuous-time Markov chain models (weeks 6-7)
    4. Scaling limits and approximate solution of CTMC models (week 8-9)
    5. Learning and inference for dynamical systems using stochastic models (weeks 10-12)
    Specific Course Requirements
    None.
  • 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
    Component Weighting Objective Assessed
    Assignments 40% all
    Exam 60% all
    Assessment Related Requirements
    An aggregate score of at least 50% is required to pass the course.
    Assessment Detail
    Assessment itemDistributedDue dateWeighting
    Assignment 1 week 2 week 3 8%
    Assignment 2 week 4 week 5 8%
    Assignment 3 week 6 week 7 8%
    Assignment 4 week 8 week 9 8%
    Assignment 5 week 10 week 12 8%
    Submission
    All assignments are to be submitted online through MyUni. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty.
    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

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