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Unit of study_

MATH4076: Computational Mathematics

Sophisticated mathematics and numerical programming underlie many computer applications, including weather forecasting, computer security, video games, and computer aided design. This unit of study provides a strong foundational introduction to modern interactive programming, computational algorithms, and numerical analysis. Topics covered include: (I) basics ingredients of programming languages such as syntax, data structures, control structures, memory management and visualisation; (II) basic algorithmic concepts including binary and decimal representations, iteration, linear operations, sources of error, divide-and-concur, algorithmic complexity; and (III) basic numerical schemes for rootfinding, integration/differentiation, differential equations, fast Fourier transforms, Monte Carlo methods, data fitting, discrete and continuous optimisation. You will also learn about the philosophical underpinning of computational mathematics including the emergence of complex behaviour from simple rules, undecidability, modelling the physical world, and the joys of experimental mathematics. When you complete this unit you will have a clear and comprehensive understanding of the building blocks of modern computational methods and the ability to start combining them together in different ways. Mathematics and computing are like cooking. Fundamentally, all you have is sugar, fat, salt, heat, stirring, chopping. But becoming a good chef requires knowing just how to put things together in creative ways that work. In a previous study, you should have learned to cook. Now you're going to learn how to make something someone else might want to pay for more than one time.


Academic unit Mathematics and Statistics Academic Operations
Unit code MATH4076
Unit name Computational Mathematics
Session, year
Semester 1, 2022
Attendance mode Normal day
Location Remote
Credit points 6

Enrolment rules

MATH3076 or MATH3976
[A mark of 65 or above in (12cp of MATH2XXX) or (6cp of MATH2XXX and 6cp of STAT2XXX or DATA2X02)] or (12cp of MATH3XXX)
Assumed knowledge

(MATH2X21 and MATH2X22) or (MATH2X61 and MATH2X65)

Available to study abroad and exchange students


Teaching staff and contact details

Coordinator Geoffrey Vasil,
Type Description Weight Due Length
Final exam (Take-home extended release) Type E final exam Summative assignment
See Canvas for more details
50% Formal exam period 48 hours
Outcomes assessed: LO2 LO1 LO6 LO5 LO4 LO3
Assignment Assignment 1
Python notebook questions and answers.
15% Mid-semester break standard assignment
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Assignment Modelling Project
2-part code & written report. Or, standard assignment precluding HD.
15% Multiple weeks Multi-stage project, 2-step submission.
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7
Assignment Assignment 0
Python notebook questions and answers. Early feedback on programming skill.
10% Week 03 short standard assignment
Outcomes assessed: LO1 LO2
Online task Online quiz
Short Python notebook testing mostly code skill.
10% Week 09
Due date: 07 May 2021 at 23:59

Closing date: 07 May 2021
24 hours
Outcomes assessed: LO1 LO2 LO4
Type E final exam = Type E final exam ?

Detailed information for each assessment can be found on Canvas.

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


High distinction

85 - 100

Representing complete or close to complete mastery of the material.


75 - 84

Representing excellence, but substantially less than complete mastery.


65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.


50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.


0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see

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 submissions without special consideration.

Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

Academic integrity

The Current Student website provides information on academic honesty, academic dishonesty, 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 dishonesty or plagiarism seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic dishonesty. If such matches indicate evidence of plagiarism or other forms of dishonesty, your teacher is required to report your work for further investigation.

WK Topic Learning activity Learning outcomes
Week 01 Python basics and fundamentals of computational algorithms. Lecture and tutorial (4 hr) LO1
Week 02 Functions, root finding, and numbers. Lecture and tutorial (4 hr) LO2 LO3
Week 03 Object-oriented programming and mathematical abstraction Lecture and tutorial (8 hr) LO1 LO4
Week 05 Integrals Lecture and tutorial (8 hr) LO2 LO4 LO5
Week 07 Derivatives Lecture and tutorial (4 hr) LO2 LO4
Week 08 Differential equations Lecture and tutorial (4 hr) LO2 LO5 LO6
Week 09 Numerical Fourier Transforms Lecture and tutorial (4 hr) LO2 LO6
Week 10 Intro to statistics, and data modelling Lecture and tutorial (8 hr) LO5 LO6
Week 12 Intro to Machine Learning and AI. Lecture and tutorial (8 hr) LO5 LO6

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. 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
No changes have been made since this unit was last offered


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