APP MTH 7056 - Random Processes
North Terrace Campus - Semester 2 - 2021
General Course Information
Course Code APP MTH 7056 Course Random Processes Coordinating Unit School of Mathematical Sciences Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Available for Study Abroad and Exchange Y Assumed Knowledge (MATHS 1012 and MATHS 2103) or (MATHS 2201 and MATHS 2202) or (MATHS 2106 and MATHS 2107); knowledge of Markov chains, such as would be obtained from MATHS 2103 Course Description This course introduces students to the fundamental concepts of random processes, particularly continuous-time Markov chains, and related structures. These are the essential building blocks of any random system, be it a telecommunications network, a hospital waiting list or a transport system. They also arise in many other environments, where you wish to capture the development of some element of random behaviour over time, such as the state of the surrounding environment.
Topics covered are: Continuous-time Markov-chains: definition and basic properties, transient behaviour, the stationary distribution, hitting probabilities and expected hitting times, reversibility; Queueing Networks: Kendall's notation, Jackson networks, Loss Networks: truncated reversible processes, circuit-switched networks, reduced load approximations. Basic Queueing Theory: arrival processes, service time distributions, Little's Law; Point Processes: Poisson process, properties and generalisations; Renewal Processes: preliminaries, renewal function, renewal theory and applications, stationary and delayed renewal processes.
Course Coordinator: Dr Andrew Black
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes1. demonstrate understanding of the mathematical basis of continuous-time Markov chains
2. demonstrate the ability to formulate continuous-time Markov chain models for relevant practical systems
3. demonstrate the ability to apply the theory developed in the course to problems of an
appropriate level of difficulty
4. develop an appreciation of the role of random processes in system modelling
5. demonstrate skills in communicating mathematics orally and in writing
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 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 ResourcesStudents may wish to consult any of the following books, available from the Library as eBooks.
Essentials of Stochastic Processes (third edition), Richard Durrett, Springer, 2016.
Introduction to Probability Models, (currently the 10th edition), Sheldon Ross, Academic Press, 2009
Online LearningAll course materials will be made available on MyUni.
Learning & Teaching Activities
Learning & Teaching ModesEach week's material is presented via a number of sources that complement each other: the textbook, course notes and lecture videos that are posted on MyUni at the beginning of the week. Having studied the material from all sources, students test their initial understanding with an online quiz.
Students deepen their understanding of the material and their skills in applying it by working on tutorial exercises and attending a tutorial (face to face or online). Biweekly assignments provide students with further opportunities to practise and get feedback on their work. Students interact with the lecturer and with each other on a MyUni discussion platform. In addition, the lecturer offers weekly consulting and an hour of face to face teaching.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Study of notes, textbook and videos 80 Tutorials 11 24 Quiz 22 Assignment 5 30 Total 156
Learning Activities SummaryTopics
- Modelling with stochastic processes
- Poisson Processes
- Continuous-time Markov chains
- Renewal theory
- Queuing theory
- Brownian motion
Weekly tutorials cover the material of the previous few weeks.
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 Task type Due Weighting Assignments Formative and summative Odd weeks 20% Quizzes Formative and summative Weekly 10% Test Summative Week 8 10% Exam Summative Exam period 60%
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course.
No information currently available.
No information currently available.
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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