MATH4412: Semester 2, 2020

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Units MATH4412 Semester 2 2020 [Normal day]

Unit outline_

MATH4412: Advanced Methods in Applied Mathematics

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

Overview

Mathematical approaches to many real-world problems are underpinned by powerful and wide ranging mathematical methods and techniques that have become standard in the field and should be in the toolbag of all applied mathematicians. This unit will introduce you to a suite of those methods and give you the opportunity to engage with applications of these methods to well-known problems. In particular, you will learn both the theory and use of asymptotic methods which are ubiquitous in applications requiring differential equations or other continuous models. You will also engage with methods for probabilistic models including information theory and stochastic models. By doing this unit you will develop a broad knowledge of advanced methods and techniques in applied mathematics and know how to use these in practice. This will provide a strong foundation for using mathematics in a broad sweep of practical applications in research, in industry or in further study.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	None
Corequisites ?	None
Prohibitions ?	None
Assumed knowledge ?	A thorough knowledge of vector calculus (e.g., MATH2X21) and of linear algebra (e.g., MATH2X22). Some familiarity with partial differential equations (e.g., MATH3X78) and mathematical computing (e.g., MATH3X76) would be useful.
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Nalini Joshi, nalini.joshi@sydney.edu.au
Lecturer(s)	Sean Gasiorek, sean.gasiorek@sydney.edu.au
Lecturer(s)	Nalini Joshi, nalini.joshi@sydney.edu.au

Type	Description	Weight	Due	Length
Final exam (Take-home extended release)	Final exam Take-home (long release). Answers must be submitted through Turnitin.	40%	Formal exam period	72 hours
Outcomes assessed:
Creative assessment / demonstration	Participation in tutorials Discussion of tutorial exercises.	4%	Ongoing	Ongoing
Outcomes assessed:
Assignment	Assignment 1 Written report	28%	Week 05	2 weeks
Outcomes assessed:
Assignment	Assignment 2 Written report	28%	Week 11	2 weeks
Outcomes assessed:
= Type E final exam ?

Assessment summary

Participation in tutorials: attend tutorials and explain how to tackle selected exercises.
Assignment 1: attempt all questions and provide full explanations of calculations.
Assignment 2: attempt all questions and provide full explanations of calculations.
Take home exam: attempt all questions and provide full explanations of calculations.

Detailed information for each assessment can be found on Canvas.

Assessment criteria

Assessment grading information.

Result name	Mark range	Description
Participation	0-4	Explain workings on selected exercises in tutorials to other participants.
Assignment 1	0-28	Submit answers with workings for Assignment 1.
Assignment 2	0-28	Submit answers with workings for Assignment 2.
Final exam	0-40	Submit answers with detailed workings for take home exam.

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.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

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
Multiple weeks	Asymptotic methods for finite dimensional deterministic systems	Lecture (3 hr)
	Asymptotic methods for infinite dimensional deterministic systems	Lecture (3 hr)
	Stochastic methods: General framework	Lecture (3 hr)
	Stochastic methods: asymptotics, averages, fluctuations, transitions, large deviations	Lecture (3 hr)
Weekly	Tutorial and/or computer lab on weekly topic	Tutorial (1 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.

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. Demonstrate a broad understanding of key concepts in applied mathematics
LO2. Create models and solve qualitative and quantitative problems in scientific contexts, using appropriate mathematical and computing techniques as necessary
LO3. Use the principles of applied mathematics to analyse and explore deterministic and stochastic systems
LO4. Evaluate the accuracy of approximate methods and assess their applicability
LO5. Communicate mathematical information deeply and coherently, both orally and through written work to a variety of audiences

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 first time this unit has been offered.

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

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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