Unit of study_

# MATH4076: Computational Mathematics

## Overview

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.

### Unit details and rules

Unit code MATH4076 Mathematics and Statistics Academic Operations 6 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) None (MATH2X21 and MATH2X22) or (MATH2X61 and MATH2X65) Yes

### Teaching staff

Coordinator Ayesha Sohail, ayesha.sohail@sydney.edu.au Ayesha Sohail

## Assessment

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
10% Week 03
Due date: 06 Mar 2024 at 23:59
Standard assessment
Outcomes assessed:
Assignment Assignment 2
Assignment
15% Week 08
Due date: 17 Apr 2024 at 23:59
Standard assignment
Outcomes assessed:
Quiz
10% Week 09 1 hour
Outcomes assessed:
Assignment Project
Written report on modelling project
15% Week 13
Due date: 22 May 2024 at 23:59
Standard assessment
Outcomes assessed:

### Assessment summary

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

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.

### 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.

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.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## 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 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)

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 Matlab basics, fundamentals of computational algorithms, and root finding methods (hint: Chapters 5 and 6 from Steven C Chapra). Lecture and tutorial (4 hr)
Week 02 Matrices (Iterative and non-iterative methods). You will learn basic concepts of numerical linear algebra and will learn some project-based activities. We will learn how it can help practically to deal with large matrices. Chapters 9, 10, 11, 12. Lecture and tutorial (4 hr)
Week 03 Worked examples and applications of topics learnt during weeks 1 and 2 practically. Lecture and tutorial (4 hr)
Week 04 Numerical integration with applications. Chapters 23 and 24. Lecture and tutorial (4 hr)
Week 05 Numerical differentiation with applications. Chapters 23 and 24 Lecture and tutorial (4 hr)
Week 06 Interpolation and Fourier transforms with applications. Chapters 18 and 19. Lecture and tutorial (4 hr)
Week 07 Review of what we learnt so far. Challenge questions. Project plans. Lecture and tutorial (4 hr)
Week 08 Differential equations and their numerical solution. Some applications. Lecture and tutorial (4 hr)
Week 09 Unconstrained optimization. Chapter 13. Some applications. Lecture and tutorial (4 hr)
Week 10 Constrained optimization. Chapters 15 and 16. Applications of optimization in science and engineering. Lecture and tutorial (4 hr)
Week 11 Some further understanding of optimization. Lecture and tutorial (4 hr)
Week 12 Machine learning. What we know. Lecture and tutorial (4 hr)
Week 13 Mathematical computing, machine learning and the future of AI tools. 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.

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.

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

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

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

Minor changes have been made since this unit was last offered