MATHS 2203 - Advanced Mathematical Perspectives II
North Terrace Campus - Semester 2 - 2014
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General Course Information
Course Details
Course Code MATHS 2203 Course Advanced Mathematical Perspectives II Coordinating Unit Mathematical Sciences Term Semester 2 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 3.5 contact hours per week Prerequisites MATHS 1012 Mathematics IB. (Note: from 2015 the prerequisites for this course will be MATHS 1012 and MATHS 1015 . Please plan your 2014 enrolment accordingly). Restrictions Available to B. Mathematical Sciences (Advanced) students only Assessment ongoing assessment 100% Course Staff
Course Coordinator: Professor Michael Murray
Course Timetable
The full timetable of all activities for this course can be accessed from .
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Learning Outcomes
Course Learning Outcomes
- Be able develop rigorous mathematical arguments.
- Be able to understand and apply basic combinatorial 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) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 1, 3, 4, 7 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 1, 2, 4, 7 Skills of a high order in interpersonal understanding, teamwork and communication. 8 A proficiency in the appropriate use of contemporary technologies. 8 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all -
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 3 26 Assignment 2 6 Total 156 Learning Activities Summary
Combinatorics
Week 1: Elementary counting techniques: bijections, multiplication rule, addition rule, permutations, combinations, combinatorial arguments, inclusion-exclusion, pigeon hole principle.
Week 2: Generating functions: ordinary generating functions, exponential generating functions.
Week 3: Recurrence relations: solving homogenous and inhomogeneous generating functions.
Statistics
Week 4: Axioms of probability, the long-run interpretation of probability and laws of large numbers, conditional probability and Bayes' Theorem, subjective probabilities.
Week 5: Probability and data, assumptions, independence, rare events, understanding coincidences in context.
Week 6: Paradoxes and common fallacies, examples of probabilistic evidence in legal and forensic contexts.
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 di fference 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:
- 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 Summary
Component Weighting Topic Objective assessed Project 1 25% Combinatorics 1, 2, 8 Project 2 25% Statistics 3, 4, 8 Assignment 1 10% Deterministic models 5, 6, 7, 8 Assignment 2 10% Stochastic models 5, 6, 7, 8 Project 3 30% Deterministic and stochastic models 5, 6, 7, 8 Assessment Detail
Assessment item Distributed Due Project 1 Week 3 Week 5 Project 2 Week 6 Week 8 Assignment 1 Week 9 Week 10 Assignment 2 Week 10 Week 11 Project 3 Week 10 Week 12 Submission
No information currently available.
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 .
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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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Student Support
- Academic Integrity for Students
- Academic Support with Maths
- Academic Support with writing and study skills
- Careers Services
- Library Services for Students
- LinkedIn Learning
- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
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Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangements Policy
- Academic Integrity Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs Policy
- Copyright Compliance Policy
- Coursework Academic Programs Policy
- Intellectual Property Policy
- IT Acceptable Use and Security Policy
- Modified Arrangements for Coursework Assessment Policy
- Reasonable Adjustments to Learning, Teaching & Assessment for Students with a Disability Policy
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
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