MATH4414: Semester 2, 2020

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Units MATH4414 Semester 2 2020 [Normal day]

Unit of study_

MATH4414: Advanced Dynamical Systems

Semester 2, 2020 [Normal day] - Camperdown/Darlington, Sydney

Overview

In applied mathematics, dynamical systems are systems whose state is changing with time. Examples include the motion of a pendulum, the change in the population of insects in a field or fluid flow in a river. These systems are typically represented mathematically by differential equations or difference equations. Dynamical systems theory reveals universal mechanisms behind disparate natural phenomena. This area of mathematics brings together sophisticated theory from many areas of pure and applied mathematics to create powerful methods that are used to understand and control the dynamical building blocks which make up physical, biological, chemical, engineered and even sociological systems. By doing this unit you will develop a broad knowledge of methods and techniques in dynamical systems, and know how to use these to analyse systems in nature and in technology. This will provide a strong foundation for using mathematics in a broad sweep of applications and for research or further study.

Unit details and rules

Unit code	MATH4414
Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prohibitions ?	None
Prerequisites ?	None
Corequisites ?	None
Assumed knowledge ?	Assumed knowledge is vector calculus (e.g., MATH2X21), linear algebra (e.g., MATH2X22), dynamical systems and applications (e.g., MATH4063 or MATH3X63) or equivalent. Some familiarity with partial differential equations (e.g., MATH3978) and mathematical computing (e.g., MATH3976) is also assumed.
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Geoffrey Vasil, geoffrey.vasil@sydney.edu.au

Type	Description	Weight	Due	Length
Assignment	Final take-home exam Combination analytical/computational work. Typed written report	50%	Formal exam period Due date: 03 Dec 2020 at 23:59	4 days
Outcomes assessed:
Assignment	Assignment 1 Combination analytical/computational work. Type written report.	25%	Week 06	4 weeks
Outcomes assessed:
Assignment	Assignment 2 Combination analytical/computational work. Typed written report	25%	Week 11	4 weeks
Outcomes assessed:

Assessment summary

Assignment 1: Will cover the fundamentals of finite maps. Among other things, this will involve the use of composition and transfer operators.
Assignment 2: Will cover the dynamics of continuous systems. Among other things, this will involve studying chaos and sensitive dependance on initial conditions.

Final Exam: This will involve synthesising concepts througout the semester.

In each case, the topics will be presented with much reference to soecific examples.

Assessment criteria

The work will include a mixture of analytical and computer work. The computer results will be presented in the form of figures and text. Not code specifically. The work will be marked on the basis of correctness and quality of presentation.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

No late assessments will be accepted.

Academic integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Weekly schedule

WK	Topic	Learning activity
Week 01	Introduction to definitions and examples	Block teaching (4 hr)
Week 02	Further explore foundational definitions and examples	Block teaching (4 hr)
Week 03	Explore classic discrete models in depth.	Block teaching (4 hr)
Week 04	Explore classic discrete models in depth	Block teaching (4 hr)
Week 05	Explore classic discrete models in depth	Block teaching (4 hr)
Week 06	Investigate classic continuous models in dynamical systems	Block teaching (4 hr)
Week 07	Investigate classic continuous models in dynamical systems	Block teaching (4 hr)
Week 08	Investigate classic continuous models in dynamical systems	Block teaching (4 hr)
Week 09	Investigate classic continuous models in dynamical systems	Block teaching (4 hr)
Week 10	Study chaotic dynamics via classic modest. E.g Double pendulum, Lorentz equations, Logistic map, and renormalisation group theory.	Block teaching (4 hr)
Week 11	Study chaotic dynamics via classic modest. E.g Double pendulum, Lorentz equations, Logistic map, and renormalisation group theory.	Block teaching (4 hr)
Week 12	Consider the stochastic dynamics and its relation to fast-slow chaotic dynamics.	Block teaching (4 hr)

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

None required. Students can consult the book “Nonlinear Dynamics and Chaos” by Steve Strogatz as a reference.

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

At the completion of this unit, you should be able to:

LO1. Understand the distinction between continuous, discrete, and finite dynamical systems.
LO2. Understand the concept of transfer and composition operators.
LO3. Explain how the single and double pendulum are important paradigms for much of general dynamical systems.
LO4. Be able to gain intuition about a system by computing examples numerically.
LO5. Understand bifurcations, period doubling, and transition to chaos,
LO6. Understand the statistical nature of ensembles of deterministic and stochastic solutions to dynamical systems.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

This is the course is being taught by a new lecturer.

Additional information

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Disclaimer

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