Alfonso Gracia-Saz's Calculus Materials
Alfonso Gracia-Saz (1976–2021) was an award-winning (opens in a new tab) math professor at the University of Toronto. Before his passing (opens in a new tab), Alfonso put countless hours into redesigning MAT137: Calculus with Proofs (opens in a new tab) at the University of Toronto.
If you find these materials useful, consider donating to the Alfonso Gracia-Saz Memorial Scholarship (opens in a new tab).
On this page, you can find the materials Alfonso created for MAT137 as well as instructor guides for those materials that he made in collaboration with Beatriz Navarro-Lameda.
Alfonso's Philosophy
Alfonso believed in learning and growth. Below is an answer he gave to a student on Piazza (an online forum dedicated to the course) in 2020:
Student Question
This question is not really related to the course content, but I was just wondering if someone is not pursuing studies in mathematics, how much of the stuff we are learning right now will they retain? It just seems sad thinking that I'm probably gonna forget most of the stuff we're learning in 10, 15 years from now.
Alfonso's Answer
If you do not continue using math, you will probably forget a lot of the content quickly. However, things that you have figured out yourself (as opposed to being told) will stay with you for a long time, and you will always be able to re-figure them out.
What will absolutely stay with you? Hopefully all the skills you have sharpened in the last eight months. Resilience. Persistence. Being comfortable taking on unknown problems. Resourcefulness. Drawing from what you know and figuring out how to adjust it to novel situations. Understanding the difference between suspecting something is true and knowing is true because you have proven it. Wanting to understand why things are true rather than memorizing answers, knowing how much more satisfying it is to understand, and that you are capable of it. If you have experienced once the internal satisfaction of totally mastering and owning a concept inside out by yourself, through hard work, you will never be satisfied with less than that.
In essence what math is really about.
You know now that you are capable of much more than you thought possible if you are willing to embrace the struggle. It is only through the struggle that you learn. Don't believe me? Look at the first problem set. Remember how you thought back then it was extremely difficult? Look at Tutorial #3. Remember how you thought back then it was impossible? If you look at them again now you will wonder what made them so intimidating. That is how much you have grown, and it will stay with you. If MAT137 has done its job well, you are now a stronger, more resilient, more inquisitive, more audacious, and more persistent person than you were in September, and that will serve you good no matter what you choose to do in your future career, whether you become a mathematician, a programmer, a doctor, an entrepreneur, a politician, a teacher, or a farmer. So who cares if you forget what the Maclaurin series of arctan is? Embrace your newly-found powers. Use them wisely.