APP MTH 7049 - Applied Mathematics Topic D
North Terrace Campus - Semester 2 - 2018
General Course Information
Course Code APP MTH 7049 Course Applied Mathematics Topic D Coordinating Unit School of Mathematical Sciences Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Available for Study Abroad and Exchange Y 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 Coordinator: Dr Andrew Black
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesIn 2016, the topic of this course is Infectious disease dynamics: Stochastic models and associated statistical methods.
Mathematical models are increasingly used to inform governmental policy-makers on issues that threaten human health or which have an adverse impact on the economy. It is this real-world success combined with the wide variety of interesting mathematical problems which arise that makes mathematical epidemiology one of the most exciting topics in applied mathematics. During the course, you will be introduced to mathematical epidemiology and some fundamental theory and numerical methods for studying and parametrising stochastic models of infectious disease dynamics. This will provide an ideal basis for addressing key research questions in this area; several such questions will be introduced and explored in this course.
Assumed knowledge for the course is DTMCs and CTMCs as, for example, covered in Applied Probability III and Random Processes III, ODEs as, for example, covered in Differential Equations II; and, some knowledge of Bayesian statistics would be useful, but not required.
On successful completion of this course, students will be able to:
1. understand and explain the basic model structures uesd in Mathematical Epidemiology;
2. develop ODE and CTMC models of infectious disease dynamics, giving consideration to the suitability of assumptions;
3. to derive and explain the Threshold, Escape and Final size results for the SIR ODE model;
4. understand and exploit linearisation, and associated Branching Processes, to study the early stages of epidemics;
5. numerically evaluate the distribution of the state of an epidemic model given initial conditions;
6. numerically evaluate the mean, and distribution, of the final size and duration of an epidemic for basic CTMC epidemic models, inluding Laplace-Stieljtes transform inversion and a general appreciation of Path Integral methods for CTMCs;
7. parameterise simple CTMC epidemic models within a Bayesian framework, including the use of the Metropolis-Hastings algorithm.
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
Recommended ResourcesG. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Models, ASA-SIAM Series on Statistics and Applied Probability, 1999.
Marcel F. Neuts, Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach, Courier Dover Publications, 1981.
Online LearningThe course will have an active MyUni website.
Learning & Teaching Activities
Learning & Teaching ModesThe 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.
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 66 Total 156
Learning Activities SummaryLecture outline
Introduction to Matrix Analytic Methods and example applications (2 Lectures).
Revision of Basic Probability, Discrete-time Markov chains, and Continuous-time Markov Chains (5 Lectures).
Phase-type distributions, renewal processes and Markovian Arrival Processes (10 Lectures).
The birth-and-death-process and Quasi-Birth-and-Death-process and the structure and derivation of the stationary distribution and other performance measures (13 Lectures).
The GI/M/1 and M/G/1-type Markov chains as QBDs (2 Lectures).
Summary (1 Lecture).
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- Assessment must encourage and reinforce learning.
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Assessment task Task type Weighting Learning outcomes Assignments Formative and summative 30% All Exam Summative 70% All
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course.
Assessment DetailThere will be four assignments worth 30% of the total mark. The remaining 70% will come from the exam
SubmissionAssignments must be handed in person to the lecturer or submitted in the assigned assignment box if they are to be marked.
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.
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