MATHS 2203 - Advanced Mathematical Perspectives II

North Terrace Campus - Semester 2 - 2019

The aim of this course is to foster a broad appreciation of the mathematical sciences with an exposure to the areas of major research strength within the School. It will be taught in four three week blocks covering Mechanics, Operations research, Pure Mathematics and Statistics. Students will be required to participate proactively in the course by possible involvement in open ended problems, independent reading and mini projects.

  • General Course Information
    Course Details
    Course Code MATHS 2203
    Course Advanced Mathematical Perspectives II
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3.5 contact hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 1012 and MATHS 1015
    Restrictions Available to BMaSc(Adv) students only
    Course Description The aim of this course is to foster a broad appreciation of the mathematical sciences with an exposure to the areas of major research strength within the School. It will be taught in four three week blocks covering Mechanics, Operations research, Pure Mathematics and Statistics. Students will be required to participate proactively in the course by possible involvement in open ended problems, independent reading and mini projects.
    Course Staff

    Course Coordinator: Dr Giang Nguyen

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    1. Be able develop rigorous mathematical arguments.
    2. Be able to understand and apply basic geometric arguments.
    3. Understand the connections between probability, statistical data and evidence.
    4. Be able to apply probabilistic reasoning in real contexts involving data and evidence.
    5. Appreciate the usefulness of both stochastic and deterministic modelling approaches. 
    6. Be able to analyse simple difference equation and Markov chain models.
    7. Be able to develop simple mathematical models.
    8. Be able to write project reports.
    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)
    1,2,3,4,5,6,7
    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
    1,2,3,4,5,6,7
    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
    8
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    Course materials will be provided by the lecturers.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    The course is taught in four blocks of three weeks.  In each block there are 9 lectures and 1 tutorial.
    Workload

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

    Activity Quantity Workload hours
    Lecture 36 108
    Tutorial 4 16
    Project 2 14
    Assignment 3 18
    Total 156
    Learning Activities Summary
    Geometry

    Week 1: Review from Multivariable and Complex Calculus. Examples of minimal surfaces. Second fundamental form and curvature of a surface.

    Week 2: Minimal surfaces, definition and examples.  Area minimising and minimal surfaces. Review complex analysis. Isothermal parameters.

    Week 3: Weiestrass-Enneper representation. Examples.  Test for non-minimising minimal surfaces. Examples.

    Statistics

    Week 4:  Probability, coincidence and evidence.  Review of basic probability axioms and properties.  Bayes’  Theorem and updating information. Decision rules.

    Week 5: Tests of statistical hypotheses, type 1 and type 11 error probabilities, the Neyman-Pearson Lemma. The power function. P-values as evidence and the posterior interpretation.

    Week 6: Probabilistic evidence in legal and forensic studies, and the prosecutor’s fallacy.

    Deterministic and stochastic models

    Week 7: Introduction to mathematical modelling - the process and its objectives. Thinking about simple problems, and turning words into equations. Linear difference equations - definitions and methods of solution. More complicated problems, and getting to grips with data.

    Week 8: Reflecting on the model. How good a fit is our model to the data? What is does it fail to take into account? Analytical methods for understanding the behaviour of diff erence equation models: cob-webbing, stability of a fixed point. A more detailed look at the discrete logistic equation - fixed points, periodic cycles, chaos, the idea of a bifurcation.

    Week 9: Introduction to discrete-time Markov chains. Development of a simple model (a stochastic logistic model). Transition probability matrices. Analytic evaluation of mean and variance. Ability to explain variability in data.

    Week 10: Introduction to the concepts of stationary and quasi-stationary behaviours. How can we find the parameters in the model? Evaluation of likelihood, and maximum likelihood estimation of parameters. Estimating parameters from data.

    Week 11: Applied Probability Extended. Expected hitting times of Discrete Time Markov Chain; applied to expected time to extinction of a population. The stochastic logistic model is equivalent to S-I-S epidemic model. Extension to modelling S-I-R epidemics. Models of interacting populations - systems of di fference equations. Host-parasitoid interactions: the Nicholson-Bailey model.

    Week 12: Analytical tools for systems of difference equations - stability of fixed points, the Jury conditions. Analysis of the Nicholson Bailey model. Further examples of interacting population models, e.g. spread of diseases - interactions between susceptible and infected. Summary and possible case study.


  • 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 Topic Objective assessed
    Project 1 25% Geometry 3, 4, 8
    Assignment 1 25% Statistics 1, 2, 8 
    Assignment 2 10% Deterministic models  5, 6, 7, 8
    Assignment 3 10% Stochastic models  5, 6, 7, 8
    Project 2 30% Deterministic and stochastic models  5, 6, 7, 8
    Assessment Related Requirements
    An aggregrate score of 50% or more is required to pass this course.
    Assessment Detail
    Assessment item Distributed Due
    Project 1 Week 3 Week 5
    Project 2 Week 4 Week 7
    Assignment 1 Week 8 Week 9
    Assignment 2 Week 9 Week 10
    Project 3 Week 10 Week 14
    Submission
    Reports are submitted to the relevant lecturer in either paper format (with a signed cover sheet) or electronically or a combination of both formats.  Late assignments are not accepted.  
    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 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.

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