Outline

Overview

This unit of study provides an introduction to programming and numerical methods. Topics covered include computer arithmetic and computational errors, solution of nonlinear equations, systems of linear equations, numerical integration and differentiation, interpolation and approximation, initial value problems for ordinary differential equations. This course will cover basic concepts of numerical optimization and applications such as for instance numerical optimization in the rapidly evolving domain of machine learning.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	[A mark of 65 or above in (12 credit points of MATH2XXX) or (6 credit points of MATH2XXX and 6 credit points of STAT2XXX or DATA2X02)] or (12 credit points of MATH3XXX)
Corequisites ?	None
Prohibitions ?	MATH3076 or MATH3976
Assumed knowledge ?	(MATH2X21 and MATH2X22) or (MATH2X61 and MATH2X65)
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Eduardo Goldani Altmann, eduardo.altmann@sydney.edu.au
Lecturer(s)	Eduardo Goldani Altmann, eduardo.altmann@sydney.edu.au
Tutor(s)	Ayesha Sohail, ayesha.sohail@sydney.edu.au

Assessment

The census date for this unit availability is 31 March 2025

Details
Criteria

Type	Description	Weight	Due	Length
Supervised exam ?	Final Exam See Canvas for more details	50%	Formal exam period	2 hours
Outcomes assessed:
Assignment	Assignment 1 Assignment	7.5%	Week 03 Due date: 14 Mar 2025 at 23:59	Standard assessment
Outcomes assessed:
Assignment	Assignment 2 Assignment	7.5%	Week 08 Due date: 16 Apr 2025 at 23:59	Standard assignment
Outcomes assessed:
Tutorial quiz	Quiz Quiz	20%	Week 09	45 minutes
Outcomes assessed:
Assignment	Project Written report on modelling project	15%	Week 13 Due date: 30 May 2025 at 23:59	Standard assessment
Outcomes assessed:
= AI allowed ?

Assessment summary

Assignments and Project: There are two short release assignments and one project. Each must be submitted electronically, as one single typeset or scanned PDF file only, via Canvas by the deadline. Late submissions will receive a penalty. A mark of zero will be awarded for all submissions more than 7 days past the original due date. The maximum extension you can be awarded through Special Consideration for the assignments is 7 calendar days. If you are affected for more than 7 calendar days you will be granted a mark adjustment. This means that your final exam mark will count instead for the assignment mark. The closing date for submissions (with a late penalty) is the same for all students. It is not changed if you are granted an extension. This allows for timely release of the marks and feedback.

Quiz: One quiz will be held on campus during the Wednesday lecture in week 9.

Final Exam: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the course. 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.

Result name	Mark range	Description
High distinction	85 - 100	Representing complete or close to complete mastery of the material.
Distinction	75 - 84	Representing excellence, but substantially less than complete mastery.
Credit	65 - 74	Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.
Pass	50 - 64	Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.
Fail	0 - 49	When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

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

Except for supervised exams or in-semester tests, you may use generative AI and automated writing tools in assessments unless expressly prohibited by your unit coordinator.

For exams and in-semester tests, the use of AI and automated writing tools is not allowed unless expressly permitted in the assessment instructions.

The icons in the assessment table above indicate whether AI is allowed – whether full AI, or only some AI (the latter is referred to as “AI restricted”). If no icon is shown, AI use is not permitted at all for the task. Refer to Canvas for full instructions on assessment tasks for this unit.

Your final submission must be your own, original work. You must acknowledge any use of automated writing tools or generative AI, and any material generated that you include in your final submission must be properly referenced. You may be required to submit generative AI inputs and outputs that you used during your assessment process, or drafts of your original work. Inappropriate use of generative AI is considered a breach of the Academic Integrity Policy and penalties may apply.

The Current Students website provides information on artificial intelligence in assessments. For help on how to correctly acknowledge the use of AI, please refer to the  AI in Education Canvas site.

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:

Assignments and Project: 10% for each day, up to a maximum of 7 days.

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.

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	Introduction to Computational Mathematics. Floating point representation and arithmetic.	Lecture and tutorial (4 hr)
Week 02	Root finding and Newton-Raphson Method. Iterations, recursions, and error quantification.	Lecture and tutorial (4 hr)
Week 03	Interpolation and approximations of functions	Lecture and tutorial (4 hr)
Week 04	Numerical Differentiation	Lecture and tutorial (4 hr)
Week 05	Numerical Integration	Lecture and tutorial (4 hr)
Week 06	Linear systems of equations. Matrix operations.	Lecture and tutorial (4 hr)
Week 07	Fourier Transformation (FFT method)	Lecture and tutorial (4 hr)
Week 08	Differential Equations: numerical integration strategies (Euler and Runge-Kutta methods)	Lecture and tutorial (4 hr)
Week 09	Differential Equations: solutions of linear and non-linear ODEs	Lecture and tutorial (4 hr)
Week 10	Differential Equations: numerical methods for boundary value problems and PDEs	Lecture and tutorial (4 hr)
Week 11	Unconstrained Optimisation	Lecture and tutorial (4 hr)
Week 12	Constrained Optimisation	Lecture and tutorial (4 hr)
Week 13	Optimisation in Data Science and Machine Learning	Lecture and tutorial (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.

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. apply the basic ingredients of any programming language including syntax, definition of variables, control structures and memory management
LO2. investigate and resolve sources of error in numerical computation
LO3. explain how binary and floating-point decimal numbers are represented on a computer
LO4. critique the uses and dangers of iteration and recursion
LO5. leverage and compute linear operations on data
LO6. create numerical routines using fundamental numerical methods to solve computational problems in science, engineering and mathematics
LO7. create reports that combine a description of a practical problem, its numerical framing and the results of computation to solve this problem.

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.

There are minor modifications to the content that will be communicated through the course outline, Canvas, and Ed.

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

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

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

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

On this page

Useful links

MATH4076: Computational Mathematics

Semester 1, 2025 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

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

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

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

On this page

Useful links