MATH203-17S1 (C) Semester One 2017

# Linear Algebra

 15 points, 0.1250 EFTS20 Feb 2017 - 25 Jun 2017

## 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

## Timetable 2017

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 16:00 - 17:00 A4 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Lecture B 01 Tuesday 13:00 - 14:00 A6 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Lecture C 01 Wednesday 12:00 - 13:00 E9 Lecture Theatre 20 Feb - 9 Apr 1 May - 4 Jun Tutorial A 01 Thursday 10:00 - 11:00 Erskine 442 20 Feb - 9 Apr 1 May - 4 Jun 02 Thursday 13:00 - 14:00 Erskine 442 20 Feb - 9 Apr 1 May - 4 Jun 03 Thursday 14:00 - 15:00 Erskine 442 20 Feb - 9 Apr 1 May - 4 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Thursday 18:30 - 19:30 E7 Lecture Theatre 27 Mar - 2 Apr

## Assessment

Assessment Due Date Percentage
Tutorials 15%
Test 25%
Final Examination 60%

## Indicative Fees

Domestic fee \$735.00

International fee \$3,525.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

## All MATH203 Occurrences

• MATH203-17S1 (C) Semester One 2017