This module is for students in the course-based M.A. and M.Sc. in Mathematics at NUI Galway, and for research students in the School of Mathematics, Statistics and Applied Mathematics. All interested students are very welcome to participate. Lectures begin on September 4 2017. The Course Outline document is here.
Lecturers: |
Dr Rachel Quinlan, Room
ADB-G007, Arás de Brún.
Email: rachel.quinlan@nuigalway.ie |
Dr Niall Madden, Room
ADB-1013, Arás de Brún.
Email: niall.madden@nuigalway.ie |
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Lectures: | Monday 11:00--11:50 in ADB-1020
Tuesday 12:00--12:50 in ADB-1020 Wednesday 12:00--12:50 in ADB-1020 |
Course Content |
This course is an exploration of some topics in linear algebra, from algebraic and algorithmic viewpoints. Linear algebra is a vast subject that pervades virtually all areas of mathematical work including (for example) algebra, analysis, geometry, coding theory, differential equations, numerical analysis, computational mathematics and mathematical modelling.
Mostly, we will investigate the spectrum (or list of eigenvalues) of
a square matrix. We will consider such questions as why we should care
about the spectrum, how to calculate a spectrum, and what can be
deduced about the spectrum from structural properties of a matrix or
from inspection of its entries. Both theoretical and computational
considerations will be included, and we will discuss connections to
graph theory and to other areas of mathematics and applied
mathematics.
The course will include some classical highlights of matrix theory and some of their implications, for example
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Assessment: | There will be three or four homework assignments during the semester, as well as a single 2-hour exam in the Winter exam session. |
The notes from the versions of this module that were taught by RQ and ran in 15/16 and 16/17 are here and here (but the content changes from year to year).