MATH203-18S1 (C) Semester One 2018

# Linear Algebra

 15 points, 0.1250 EFTS19 Feb 2018 - 24 Jun 2018

## 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.

This course will provide students with an opportunity to develop the Graduate Attributes specified below:

 Critically competent in a core academic discipline of their award Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

## Restrictions

MATH252, MATH254, EMTH203, EMTH204, EMTH211

## Timetable 2018

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 09:00 - 10:00 Jack Erskine 031 Lecture Theatre 19 Feb - 1 Apr 23 Apr - 3 Jun Lecture B 01 Thursday 14:00 - 15:00 A3 Lecture Theatre 19 Feb - 25 Mar 23 Apr - 3 Jun Lecture C 01 Friday 11:00 - 12:00 E9 Lecture Theatre 19 Feb - 25 Mar 23 Apr - 3 Jun Tutorial A 01 Thursday 09:00 - 10:00 Jack Erskine 442 19 Feb - 1 Apr 23 Apr - 3 Jun 02 Friday 12:00 - 13:00 Jack Erskine 442 19 Feb - 25 Mar 23 Apr - 3 Jun 03 Thursday 15:00 - 16:00 Jack Erskine 442 19 Feb - 1 Apr 23 Apr - 3 Jun 04 Thursday 10:00 - 11:00 Jack Erskine 442 19 Feb - 1 Apr 23 Apr - 3 Jun

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Thursday 14:00 - 15:00 A3 Lecture Theatre 26 Mar - 1 Apr

## Assessment

Assessment Due Date Percentage
Tutorials 10%
Test 30%
Final Examination 60%

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 \$749.00

International fee \$3,788.00

* 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

• MATH203-18S1 (C) Semester One 2018