Pre-requisites: A level Mathematics, or equivalent.
Co-requisites: None
Objectives
A first introduction to Linear Algebra, and in particular to the use
of matrices. Elementary row-operations are emphasised as a unifying
theme. On completion of this module, students should be able to: (a)
solve systems of linear equations; (b) perform elementary matrix
algebra; (c) solve simple eigenvalue problems.
Syllabus
Linear Algebra is the formal, detailed theory which covers the ideas
involved in solving simultaneous equations, and using matrices and
determinants. This course starts by treating simultaneous equations in
full generality, and introduces the notions involved in matrices and
vector spaces. These basic ideas will be used and expanded in a wide
variety of further mathematics modules, and are essential for
understanding much of numerical computing. Hence this (or an
equivalent) is an essential module for all students of mathematics and
many others.
Topics covered include:
General systems of linear equations: Reduction by elementary row
operations to echelon form; solution from echelon form by back
substitution.
Matrices and matrix algebra: Elementary matrices and inverse of
a matrix.
Determinants: Definition by expansion, effect of elementary
operations, evaluation. Concrete vector spaces and subspaces:
Definitions of span and linear combination; linear dependence. Basis
and dimensions of a vector space. Rank.
Eigenvalues and eigenvectors: Characteristic polynomial for
eigenvalues. Linear independence of eigenvectors for different
eigenvalues. Use in solving linear differential equations and in
computing powers.
Form of teaching:
Lectures (22 hours); tutorials (11 hours).
Form of assessment:
2 hour written examination at end of semester (85%), coursework (15%).
Lectures: on Wed at 12am (RSLT 25); on Thu
11am ( RSLT 18).
Lecturer: Dr Vladimir V Kisil, room 8.18L (Math).
Classes: run on even weeks (i.e., second,
fourth, ...) Thu at 3pm
(RSLT 19). They are dedicated to homework and exams
questions.
Classes on even weeks are shared by MATH1410 and MATH1610.
Attendance: will be collected during the lectures and
classes. A fact: absent from > 35% lectures
have 64% failure rate, in opposite to missing
< 15% lecture with only 9%!
Homework: 6 assignments during the
semester, contribute 15% toward the final mark.
Tutorials: (mainly) on Tuesdays 2pm, run by tutors by groups.