MAT137 Questions & Guides
by Alfonso Gracia-Saz & Beatriz Navarro-Lameda
MAT137 (Calculus with Proofs)
MAT137, Calculus with Proofs, is a first-year calculus course at the University of Toronto. It is meant to be a first course on proofs as well as a first course on calculus. This is not a usual combination! At many universities, students study calculus without proofs first, and then take an Advanced Calculus or Introduction to Analysis that focuses on proving the results used in calculus.
MAT137 aims to split the difference. It introduces all the core calculus concepts, and also proves (and has students prove) many of the results along the way. Though, some results that can be very technical for a first-timer (like the proof of the intermediate value theorem) are stated without proof.
What's Included Here?
MAT137 is taught using an inverted classroom model. Students watch videos before class and class time is focused on problem-solving. This page includes problems designed for class time. Each unit has a Guide page with notes and tips for instructors about each exercise. On the Questions pages, you can select questions and download LaTeX/Beamer source code for the questions. Use this source code to compile slides for use in your class.
Copyright and Citation
Exercises here are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License (opens in a new tab). That means you can use the exercises in your course or share them with others, as long as you credit Alfonso Gracia-Saz. You may also modify the exercises to better suit your course.
The default slide template provided when you download slides includes an unobtrusive attribution which you may modify to fit your needs as long as an appropriate attribution is included.