APP MTH 7048 - Applied Mathematics Topic A
North Terrace Campus - Semester 1 - 2020
General Course Information
Course Code APP MTH 7048 Course Applied Mathematics Topic A Coordinating Unit School of Mathematical Sciences Term Semester 1 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 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:
- Understand and apply various Monte Carlo techniques.
- Simulate and use models based on stochastic differential equations.
- Construct and simulate continuous time Markov chain (CTMC) models.
- Understand the scaling behaviour of certain CTMC models and how this relates to the scales of the process that is being observed.
- Derive and solve a hierarchy of approximate solutions for CTMCs.
- Understand and apply stochastic models and methods for inference of hidden dynamical processes.
- 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
Required ResourcesAccess to the intranet.
Recommended ResourcesP. Schuster, Stochasticity in Processes, Springer 2016.
D. P. Kroese, T. Taimre, Z. I. Botev, Handbook of Monte Carlo Methods, Wiley 2011
Online LearningThis 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 ModesThis course relies on lectures and exercises as the primary learning mechanism for the material. A sequence of written and/or online assignments provides assessment opportunities for students to gauge their progress and understanding.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lecture classes 30 100 Assignments 5 56 Total 156
Learning Activities Summary
- Monte Carlo methods (weeks 1-3)
- Stochastic differential equation models (weeks 4-5)
- Continuous-time Markov chain models (weeks 6-7)
- Scaling limits and approximate solution of CTMC models (week 8-9)
- Learning and inference for dynamical systems using stochastic models (weeks 10-12)
Specific Course RequirementsNone.
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 Objective Assessed Assignments 40% all Exam 60% all
Assessment Related RequirementsAn aggregate score of at least 50% is required to pass the course.
Assessment item Distributed Due date Weighting 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%
SubmissionAll assignments are to be submitted online through MyUni. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty.
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.
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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