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Unit outline_

MATH2070: Optimisation and Financial Mathematics

Semester 2, 2024 [Normal day] - Camperdown/Darlington, Sydney

Problems in industry and commerce often involve maximising profits or minimising costs subject to constraints arising from resource limitations. The first part of this unit looks at programming problems and their solution using the simplex algorithm; nonlinear optimisation and the Kuhn Tucker conditions. The second part of the unit deals with utility theory and modern portfolio theory. Topics covered include: pricing under the principles of expected return and expected utility; mean-variance Markowitz portfolio theory and the Capital Asset Pricing Model. Some understanding of probability theory including distributions and expectations is required in this part. Theory developed in lectures will be complemented by computer laboratory sessions using Python. Minimal computing experience will be required.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites
? 
(MATH1061 or MATH1961 or MATH1971) or [(MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02)]
Corequisites
? 
None
Prohibitions
? 
MATH2970
Assumed knowledge
? 

MATH1X23 or MATH1933 or MATH1X03 or MATH1907

Available to study abroad and exchange students

Yes

Teaching staff

Coordinator Caroline Wormell, caroline.wormell@sydney.edu.au
Lecturer(s) Caroline Wormell, caroline.wormell@sydney.edu.au
The census date for this unit availability is 2 September 2024
Type Description Weight Due Length
Supervised exam
? 
Final exam
Examination
60% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6
Assignment Assignment
Assignment
15% Week 06
Due date: 04 Sep 2024 at 23:59

Closing date: 16 Sep 2024
2 weeks
Outcomes assessed: LO1 LO6
Small test Quiz
Quiz
10% Week 09
Due date: 25 Sep 2024 at 23:59

Closing date: 04 Oct 2024
40 minutes
Outcomes assessed: LO1 LO6 LO4 LO3 LO2
Assignment Computer project
Project
15% Week 13
Due date: 30 Oct 2024 at 23:59

Closing date: 13 Nov 2024
3 weeks
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6

Assessment summary

Detailed information for each assessment can be found on Canvas.

Final exam: If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator. 

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

For more information see sydney.edu.au/students/guide-to-grades.

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.

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.

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.

Support for students

The Support for Students Policy 2023 reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy 2023. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

WK Topic Learning activity Learning outcomes
Week 01 1. Introduction; 2. Introduction to optimisation and linear programming Lecture (3 hr)  
Week 02 1. Graphical solution to LP problems; 2. Simplex algorithm Lecture (3 hr)  
Week 03 Non-standard LP problems and two-phase simplex algorithm Lecture (3 hr)  
Week 04 1. Non-standard LP problems; 2. Duality Lecture (3 hr)  
Week 05 Nonlinear optimisation without constraints Lecture (3 hr)  
Week 06 Nonlinear optimisation with constraints Lecture (3 hr)  
Week 07 Probability review Lecture (3 hr)  
Week 08 1. Decision under uncertainty; 2. Utility theory Lecture (3 hr)  
Week 09 1. Utility theory; 2. Portfolio basics Lecture (3 hr)  
Week 10 Portfolio theory: portfolio selection rules and 2-asset portfolios Lecture (3 hr)  
Week 11 Portfolio theory: unrestricted n-asset portfolios Lecture (3 hr)  
Week 12 1. Portfolio theory: restricted n-asset portfolios; 2. Capital asset pricing model Lecture (3 hr)  
Week 13 Revision Lecture (3 hr)  
Weekly Problems linked with lectures with one week lag Tutorial (1 hr)  
Computer problems linked with lectures with one week lag Computer laboratory (1 hr)  

Attendance and class requirements

  • Unless otherwise indicated, students are expected to attend a minimum of 80% of timetabled activities for a unit of study, unless granted exemption by the Associate Dean.
  • For some units of study the minimum attendance requirement, as specified in the relevant table of units or the unit of study outline, may be greater than 80%. The Associate Dean may determine that a student has failed a unit of study because of inadequate attendance. Further details are available from the Science Undergraduate Handbook 2019: https://sydney.edu.au/handbooks/science/coursework/faculty_resolutions and the Science Postgraduate Handbook 2019: https://sydney.edu.au/handbooks/science_PG/ 

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 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.

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

  • LO1. demonstrate familiarity with the concepts in linear programming (standard and non-standard) and simplex algorithm, and apply them to solve concrete problems
  • LO2. demonstrate familiarity with the concepts in non-linear optimisation without constraints. Explain how the rule based on Hessian can be used to determine minima and maxima, and apply it to solve concrete problems
  • LO3. demonstrate familiarity with the concepts in non-linear optimisation with constraints, and apply suitable methods (Lagrange multipliers and KKT conditions) to solve concrete problems
  • LO4. demonstrate understanding of the notions from utility theory and explain the difference between principles of expected return and expected utility. Apply this knowledge to solve practical problems
  • LO5. demonstrate a coherent and advanced knowledge of the fundamental concepts in portfolio theory and capital asset pricing model
  • LO6. identify, formulate and solve original practical problems that can be addressed using mathematical and computational techniques you learned in this unit.

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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

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

Assessment dates are revised.

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

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.