Outline

Overview

This unit of study provides an introduction to mathematical computing and numerical analysis. Topics covered include floating-point arithmetic and computational errors, solution of (systems of) equations, numerical integration and differentiation, interpolation and approximation of functions, numerical methods to approximate solutions of differential equations, and basic concepts of numerical optimization with applications. This unit will cover the mathematical theory of numerical methods and their implementation in a modern programming language.

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

Assessment

The census date for this unit availability is 31 March 2026

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam	Final Exam In person exam.	50%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
In-person written or creative task	Quiz Quiz	20%	Week 09	45 minutes	AI prohibited
Outcomes assessed:
Out-of-class quiz	Tutorial Quiz Weekly quiz on content of lectures and tutorial/computational lab	30%	Weekly	Several coding and MC questions	AI allowed
Outcomes assessed:
= hurdle task ?

Assessment summary

Tutorial Quiz: There are weekly quizes covering the material covered in the lectures and tutorial/computational lab. Each must be submitted electronically by the deadline. Late submissions will receive a penalty. A mark of zero will be awarded for all submissions more than 6 days past the original due date. The maximum extension you can be awarded through Special Consideration for the assignments is 6 calendar days. If you are affected for more than 6 calendar days you will be granted a mark adjustment. This means that your final exam mark will count instead for the individual quiz 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. The worst mark of the individual quizes will be discarded in the computation of the final Tutorial Quiz mark (i.e., only the best N-1 marks out of the N individual quizzes will be used).

Quiz: One quiz will be held in person on campus during week 9. There is no replacement quiz. If you are unable to attend the quiz and you are awarded a special consideration, your final exam mark will be used instead of the quiz mark.

Final Exam: A mark of at least 40% in the exam is required to pass this unit. The final exam is compulsory and must be attempted in person. 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)

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.

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 6 days.

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	Introduction to Computational Mathematics. Floating point arithmetic.	Lecture (3 hr)
Week 01	Introduction to Computational Mathematics. Floating point arithmetic.	Tutorial (1 hr)
Week 02	Root finding methods. Iterations, recursions, and error quantification	Lecture (3 hr)
Week 02	Root finding methods. Iterations, recursions, and error quantification	Tutorial (1 hr)
Week 03	Systems of equations	Lecture (3 hr)
Week 03	Systems of equations	Tutorial (1 hr)
Week 04	Polynomial Interpolation	Lecture (3 hr)
Week 04	Polynomial Interpolation	Tutorial (1 hr)
Week 05	Trigonometric Interpolation and the Fast Fourier Transform	Lecture (3 hr)
Week 05	Trigonometric Interpolation and the Fast Fourier Transform	Tutorial (1 hr)
Week 06	Numerical Differentiation	Lecture (3 hr)
Week 06	Numerical Differentiation	Tutorial (1 hr)
Week 07	Numerical Integration	Lecture (3 hr)
Week 07	Numerical Integration	Tutorial (1 hr)
Week 08	Differential Equations: initial value problem in ODEs	Lecture (3 hr)
Week 08	Differential Equations: initial value problem in ODEs	Tutorial (1 hr)
Week 09	Differential Equations: boundary value problem in ODEs	Lecture (3 hr)
Week 09	Differential Equations: boundary value problem in ODEs	Tutorial (1 hr)
Week 10	Differential Equations: PDEs	Lecture (3 hr)
Week 10	Differential Equations: PDEs	Tutorial (1 hr)
Week 11	Unconstrained Optimisation	Lecture (3 hr)
Week 11	Unconstrained Optimisation	Tutorial (1 hr)
Week 12	Constrained Optimisation	Lecture (3 hr)
Week 12	Constrained Optimisation	Tutorial (1 hr)
Week 13	Optimisation in Data Science and Machine Learning	Lecture (3 hr)
Week 13	Optimisation in Data Science and Machine Learning	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. Learn and apply computational methods (e.g., root‑finding, numerical integration, linear system solvers, and ODE solvers) that solve problems arising in Mathematics, the Natural Sciences, and Engineering.
LO2. Understand and analyze the computational efficiency of different methods, the accuracy of numerical solutions, and sources of error in numerical calculations.
LO3. Apply mathematical ideas and tools to analyse numerical methods, derive their key properties, explain why they work, and justify their applicability to different classes of problems.
LO4. Apply computational methods to solve a concrete mathematical problem, analysing the errors in the numerical solutions, evaluating the suitability of different methods, and creating suitable solutions to the 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

Important: the University of Sydney regularly reviews units of study and reserves the right to change the units of study available annually. To stay up to date on available study options, including unit of study details and availability, refer to the relevant handbook.

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)

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, 2026 [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)

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