MATH2070: Semester 2, 2025

Units MATH2070 Semester 2 2025 [Normal day]

Unit outline_

MATH2070: Optimisation and Financial Mathematics

Semester 2, 2025 [Normal day] - Camperdown/Darlington, Sydney

Overview

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 ?	{(MATH1X61 or MATH1971) or [(MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02)]} and (MATH1X62 or MATH1972 or MATH1X23 or MATH1933)
Corequisites ?	None
Prohibitions ?	MATH2970
Assumed knowledge ?	Multivariable calculus such as MATH1X23 or MATH1X62
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Caroline Wormell, caroline.wormell@sydney.edu.au

Assessment

The census date for this unit availability is 1 September 2025

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam ?	Final Exam Examination	60%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Out-of-class quiz	Early feedback task #earlyfeedbacktask Online quiz on the simplex method	2%	Week 03	40 minutes	AI allowed
Outcomes assessed:
Written work	Assignment Assignment	10%	Week 06 Due date: 11 Sep 2025 at 23:59 Closing date: 25 Sep 2025	2 weeks	AI allowed
Outcomes assessed:
In-person written or creative task	Quiz Quiz	12%	Week 09	40 minutes	AI prohibited
Outcomes assessed:
Written work	Project Computer project	10%	Week 12 Due date: 30 Oct 2025 at 23:59 Closing date: 13 Nov 2025	3 weeks	AI allowed
Outcomes assessed:
Out-of-class quiz	Online quiz Online quiz on CAPM	2%	Week 13	40 minutes	AI allowed
Outcomes assessed:
Conversation	Tutorial participation Participation in tutorials (8 out of 12)	2%	Weekly	50 minutes x 12 weeks	AI allowed
Outcomes assessed:
Conversation	Lab participation Participation in 8 out of 12 computer labs	2%	Weekly	50 minutes x 12	AI allowed
Outcomes assessed:
= early feedback task ?

Early feedback task

This unit includes an early feedback task, designed to give you feedback prior to the census date for this unit. Details are provided in the Canvas site and your result will be recorded in your Marks page. It is important that you actively engage with this task so that the University can support you to be successful in this unit.

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.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the Academic Integrity Policy.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

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 University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the Academic Honesty Education Module (AHEM) which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

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.

Support for students

The Support for Students Policy 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. 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

Weekly schedule

WK	Topic	Learning activity
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)
Weekly	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

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 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
Learning outcomes

Responding to student feedback

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

Assessment dates are revised.

Additional information

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.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

On this page

Useful links