Numerical Linear Algebra (MATH3371)

MATH3371 is a Mathematics Level III course. See the course overview below.

Units of credit: 6

Prerequisites:  MATH2501 OR MATH2601 OR MATH2019 (DN) or MATH2099 (CR)

Exclusion courses: MATH5371 - jointly taught 

Cycle of offering:  Term 1 2023

Graduate attributes:

More information: The Course outline will be made available closer to the start of term - please visit this website: www.unsw.edu.au/course-outlines

Important additional information as of 2023

UNSW Plagiarism Policy

The University requires all students to be aware of its policy on plagiarism.

For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.

If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.d the syllabus. This will be provided closer to term. 

Please note the following recent changes to the programs 3956 and 3962, in Applied Mathematics.

1.       From 2022 there will be 3 new courses:

• MATH3051 to be offered in T3 every year. All students who will be doing level 3 in Applied Maths in 2022 and 2023 will be strongly advised to take this course as an elective course. From 2024 this course will be one of two core courses.
• MATH3371/5371 to be offered in T1 every year
• MATH3191/5191 to be offered in T3, alternate with MATH3171/5171

2.       From 2024 all level 3 students in Applied Maths should note that MATH3051 and MATH3041 will be one of two possible core courses.

The Online Handbook entry contains information about the course timetable. (The timetable is only up-to-date if the course is being offered this year.)

If you are currently enrolled in MATH3371, you can log into UNSW Moodle for this course.

• Understand algorithms for simple operations in linear algebra, and how their computational costs scale with problem sizes.
• Present the use of key matrix factorisations (LU, QR, SVD) for solving standard problems in linear algebra.
• Show how to recognise and exploit matrix structures (symmetry, band width, sparsity) for improving the efficiency of key algorithms.
• Explain the role and basic features of selected iterative methods (QR iteration, Jacobi, Richardson, conjugate gradient).
• Introduce some applications illustrating the wide range of applications of numerical linear algebra (data fitting, low-rank approximation, principal component analysis, image compression, machine learning).

Algorithms from numerical linear algebra are ubiquitous in scientific and statistical software.  The theoretical component of the course aims to impart an understanding of how these algorithms work as well as an appreciation of their potential limitations. Familiar pencil-and-paper methods suitable for solving small problems by hand calculation must typically be modified or replaced by different approaches when faced with large problems whose solution is feasible only with the help of a computer.

To illustrate the applications of numerical linear algebra, a variety of examples from statistics, data science and applied mathematics are described. The course includes a substantial computing component providing practical experience with widely used software libraries.