MATHS 2203 - Advanced Mathematical Perspectives II
North Terrace Campus - Semester 2 - 2017
General Course Information
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 Coordinator: Dr Raymond Vozzo
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
- Be able develop rigorous mathematical arguments.
- Be able to understand and apply basic geometric arguments.
- Understand the connections between probability, statistical data and evidence.
- Be able to apply probabilistic reasoning in real contexts involving data and evidence.
- Appreciate the usefulness of both stochastic and deterministic modelling approaches.
- Be able to analyse simple difference equation and Markov chain models.
- Be able to develop simple mathematical models.
- 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
Recommended ResourcesCourse materials will be provided by the lecturers.
Learning & Teaching Activities
Learning & Teaching ModesThe course is taught in four blocks of three weeks. In each block there are 9 lectures and 1 tutorial.
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 SummaryGeometry
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.
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 difference 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 difference 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.
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.
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 RequirementsAn aggregrate score of 50% or more is required to pass this course.
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
SubmissionReports 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.
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.
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.
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