Course Info

Official course description

Review of the completeness properties of real numbers. Supremum and infimum, lim sup, lim inf. The topology of Rn. Uniform continuity. Compactness, Heine–Borel. The Riemann integral, the fundamental theorem of calculus, improper integrals. Sequences and series of functions, uniform convergence. Fourier series.


MAT1325 or MAT2122 or (MAT1322 and one of MAT1348, MAT1362, MAT2362).

Reference material


The following open access textbooks are recommended as references for the course material. They can both be downloaded free of charge.

Lecture notes

Click the above header to download lecture notes for the course. They are a single file that will be updated as the course progresses. They should be complemented by your own class notes. I will often say more in class than is in the lecture notes.


The DGDs are an important part of the course. They supplement the material covered in the lectures. You will be given an opportunity to ask questions about the lectures. In addition, we will go through the exercises in the course notes that correspond to the lectures from the past week. To get the most from the DGDs, you should attempt the exercises before the DGDs. That way, you can focus on clearing up any difficulties that you encounter. Graded homework assignments, quizzes, and midterm tests will also be handed back in the DGDs.

Extra help

The Math Help Centre does not serve this course. However, if you are looking for extra help beyond the DGDs and office hours, you can hire a private tutor using the tutor referral service of the Peer Help Centre.

Course website

There are two main locations for information regarding the course: