MATH203-23S1 (C) Semester One 2023

# Linear Algebra

15 points

Details:
 Start Date: Monday, 20 February 2023 End Date: Sunday, 25 June 2023
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 5 March 2023
• Without academic penalty (including no fee refund): Sunday, 14 May 2023

## Description

Linear algebra is a key part of the mathematician's toolkit and has applications to many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including vector spaces, linear transformations, eigenvalues, and orthogonality. Emphasis is placed on understanding both abstract mathematical structures and their concrete applications.

Course Information:
Linear algebra is a key part of the mathematician's toolkit and has applications to many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including vector spaces, linear transformations, eigenvalues, and orthogonality. Emphasis is placed on understanding both abstract mathematical structures and their concrete applications.

Topics Covered:
Vector spaces; Linear independence, bases and coordinate systems; Linear transformations, matrices, rank, nullity, and relationships between the fundamental matrix spaces; Eigenvalues, eigenvectors, diagonalisation and canonical forms of a matrix; Inner products and orthogonality; Gram-Schmidt process, QR-decomposition and orthogonal projections; Orthogonal diagonalization and the spectral theorem; Vector and matrix norms and condition numbers; LU-decompositions.

Applications:
Markov chains, population and economic models, coupled systems of linear ordinary differential equations, linear recurrence relations, Fourier series, least squares approximation, cryptography, coding theory, data compression.

## Learning Outcomes

• At the end of the course, students will:

• be proficient in the standard techniques of linear algebra;
• understand why these techniques work;
• be able to use these techniques in a variety of applications, including using MATLAB to solve standard problems;
• have developed problem solving skills both as part of a team and as an individual;
• have developed written and oral communications skills, emphasizing the ability to explain what the mathematics means.

## Restrictions

MATH252, MATH254, EMTH203, EMTH204, EMTH211, DATA203

## Timetable 2023

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 15:00 - 16:00 E5 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Lecture B 01 Tuesday 13:00 - 14:00 E9 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Lecture C 01 Wednesday 10:00 - 11:00 E9 Lecture Theatre 20 Feb - 2 Apr 24 Apr - 4 Jun Tutorial A 01 Thursday 11:00 - 12:00 Jack Erskine 442 Computer Lab 20 Feb - 2 Apr 24 Apr - 4 Jun 02 Friday 11:00 - 12:00 Jack Erskine 442 Computer Lab 20 Feb - 2 Apr 24 Apr - 4 Jun 03 Friday 10:00 - 11:00 Jack Erskine 442 Computer Lab 20 Feb - 2 Apr 24 Apr - 4 Jun 04 Friday 09:00 - 10:00 Jack Erskine 442 Computer Lab 20 Feb - 2 Apr 24 Apr - 4 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Wednesday 18:30 - 20:00 E5 Lecture Theatre 27 Mar - 2 Apr

## Assessment

To obtain a clear pass in this course, you must both pass the course as a whole (≥ 50%) and also obtain at least 40% in the final examination.

## Indicative Fees

Domestic fee \$824.00

International fee \$4,750.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

## All MATH203 Occurrences

• MATH203-23S1 (D) Semester One 2023 (Distance) - Not Offered - see department for alternatives
• MATH203-23S1 (C) Semester One 2023