MAS277 homepage
MAS277 Vector Spaces and Fourier Theory



Course details

  • Lecturer: Dr. Fionntan Roukema ("Fintan"),  K12 Hicks builing (office),   f.roukema (at) sheffield.ac.uk (email),   0114 222 3872 (phone)

  • Office hours: Wednesday mornings, by appointment, or pop by and hope for the best.

  • Lectures: Lectures will take place during weeks 1-11 on:
            Mondays 10:00-10:50 in Hicks building LT2,         Thursdays 09:00-09:50 in Hicks building LT7.

  • Tutorials: Tutorials will take place on weeks 1, 3, 5, 7, 9, 11 on Tuesdays at:
            11:00-11:50 Hicks Building F20 (Group 1)         14:00-14:50 Hicks building F20 (Group 2)         16:00-16:50 Hicks building F24 (Group 3).


About this course

This is a first course in abstract linear algebra. The first half of the course will focus on vector spaces and the second half will focus on inner product spaces. The course will finish by interpreting the convergence of Fourier series as a statement about projections in an inner product space.


Course material

Further material will be uploaded onto this site as the course progresses. For now, the following documents are available:



Lecture notes

These notes have been taken by MAS277 students during lectures. They have been put on this site with their permission to help everyone in the course. On behalf of all of us I would like to thank Jenna Hemsley and all other students who have/will contribute(d).

Lecture 1         Lecture 2        Lecture 3        Lecture 4        Lecture 5        Lecture 6        Lecture 7        Lecture 8        Lecture 9        Lecture 10        Lecture 11

Lecture 12       Lecture 13       Chapter 1 and 2 revision session       Lecture 14         Lecture 15         Lecture 16         Lecture 17         Lecture 18         Lecture 19

The remainder of the student notes will be made available here.