MATH105 Linear Algebra

General course information

What is linear algebra?

Linear algebra provides us with a unified language for talking both about systems of simultaneous linear equations and about linear transformations of space (rotations, reflections, etc). It is the foundation for almost all mathematics you will study hereafter, because:
  • it is very well-understood: you will see that we have very simple algorithms for solving simultaneous linear equations;
  • to study more complicated nonlinear objects for which such methods are lacking, you often try to approximate them by linear ones. For example, calculus is the art of approximating curves and surfaces by straight lines or planes tangent to them.
  • We will see:
    • how matrices allow us to encode geometric transformations of space as finite arrays of numbers;
    • how to encode systems of simultaneous equations in matrix form;
    • how to solve matrix equations using row reduction to echelon form (Gaussian elimination);
    • how to compute the inverse of a matrix;
    • the determinant of a matrix: what it means geometrically and how to compute it;
    • eigenvalues and eigenvectors of matrices, with applications to differential equations, the geometry of ellipsoids, and the asymptotic behaviour of the Fibonacci sequence.
I'll assume you've seen basic trigonometry and calculus, but very little else.

Administration

This module will run in Weeks 21 - 25 (Term 3).
Lecturer
Jonny Evans
Email
j.d.evans at lancaster.ac.uk
Office hours
TBA.

Assessment

  • Four assessed courseworks plus one "end of module assessment" (basically a fifth coursework).
  • Four weekly Moodle quizzes.
  • Final exam (one component of the MATH100 exam).

Activities

Each week there will be:
  • one Workshop,
  • two in-person Live Sessions,
  • for each Live Session, a certain amount of pre-class video/notes you need to watch/read beforehand.

Live sessions

The Live Sessions will be an opportunity to discuss the material you have watched. I will ask you questions, you can ask me questions, we'll work as a group through examples and problems. It is important that you either watch the relevant videos or read the relevant notes before the Live Session.

Workshops

There will be four workshops over the term; these will be run in smaller groups (approx 15 students) with a tutor. I have provided worksheets as a focus for these workshops (1, 2, 3, 4).

Practice questions

In addition to the assessed question sheets and the workshop sheets, I have compiled a list of practice questions for you to test yourselves on.

Notes and videos

This page has a complete set of HTML notes with embedded (YouTube) videos. They are grouped according to which Live Session will discuss them. Note that some of the videos are completely optional and won't be covered in a live session.

If you click on the "Week 1", "Week 2", etc headings then you will see just the video links for the sessions that week.

The average length of video you'll need to watch for a Live Session mostly ranges from 55-80 minutes. Week 3 is the heaviest week (both sessions require around 80 minutes of pre-watching).

Video alternatives

If you are unable to view YouTube, you can access the videos on Planet eStream

If you do have access to YouTube, you can also just binge on the YouTube playlist