MAT157 at the University of Toronto: An Honest Review from a UofT Mathematics and Statistics Student

If you’re considering taking MAT157: Analysis I at the University of Toronto, you’re probably already aware it has a bit of a reputation. Whether you’re a math enthusiast, a theoretical dreamer, or just someone looking to challenge yourself, MAT157 is not your average first-year calculus course, and I’m here to break down exactly what to expect.

As a UofT student who took the course in 2023-2024, here’s my honest review of MAT157, what it covers, how it’s structured, and whether it’s worth the hype (or the headache).

Quick Summary:

• Difficulty: Very high  

• Workload: Heavy (proof-based weekly assignments and exams)  

• Recommended for: Strong interest in pure math  

• Not ideal if: You prefer computation over theory

What is MAT157?

MAT157 is the highest first-year calculus course at UofT. It’s officially titled Analysis I, but many students know it as “the proof-heavy calculus class.”

Course focus: you can find the official description here, but roughly covers real analysis fundamentals and proof-based approaches to calculus concepts.

If you’re coming from a high school calculus background and expecting more of the same, prepare for a big shift. I’m telling you, if you’re not prepared, this course will hit you like a sack of bricks.

Who Should Take MAT157?

I’ll be blunt: this course is not for everyone, and that’s okay. MAT157 is aimed at students who:

• Are considering a math specialist
• Love abstract thinking and proofs
• Are willing to spend serious time learning how to write and understand rigorous mathematics

If you’re someone who enjoys solving puzzles, finding elegant solutions, and thinking deeply about why things work, this course might be fun. If not, you’re going to struggle A LOT.

Course Content & Structure

MAT157 covers a lot, and it does so in a very formal way. Topics include:

• Logic and proofs
• Sequences and limits
• Continuity
• Differentiation and integration (with rigorous definitions)
• Theoretical underpinnings of calculus, including constructing real numbers (Yes, we had to PROVE that real numbers are indeed real).

Instead of applying formulas, you’re proving they work.

Lectures:
These were usually theoretical and fast-paced. Lecture attendance (and attention) is key here, since even missing one can set you back a lot. However, the professor was incredible; I truly admire how she was able to do such elegant proofs with novel ideas that I wouldn’t even begin to consider.

Problem Sets:
Expect weekly problem sets that require you to write full, formal proofs. They’re time-consuming but incredibly rewarding once you get the hang of it. The difficulty ranged from not too bad to absolutely mind boggling (Question 6, if you know, you know).

Exams:
Often proof-based, with a few computations later on. They test your understanding, not just your memorization. Don’t expect standard plug-and-chug questions; be prepared to write a full rigorous proof.

Pros of Taking MAT157

Deep understanding of math
Great foundation for upper-year pure math courses
Incredible professors (may be subject to change) 
Looks impressive for grad school/math-focused paths

Cons & Challenges

Workload is heavy – Problem sets can take hours, or even days
Not computational – If you want practical calculus, this isn’t it
Steep learning curve – Especially if you’ve never done proofs before
Can hurt your GPA if you’re not fully committed

My Personal Take

I won’t sugarcoat it: MAT157 was the hardest course I took in my entire academic career (so far). But it was also the most intellectually rewarding. It completely changed how I think about math, and honestly, about problem-solving in general.

For those who plan to take it or are taking it now, don’t feel discouraged if things don’t start well. I actually failed my first midterm and barely passed the second one. I even almost failed the final, but I still ended with an above average grade.

I have zero regrets about choosing this because it gave me a sense of mathematical maturity and a lot more respect for mathematics in general. The entire teaching team was also incredible and really supportive every step of the way, so you’ll be in good hands.

Final Verdict: Should You Take MAT157?

Yes, if:

• You love proofs and abstract reasoning
• You’re thinking about a math specialist or grad school in math
• You want a serious challenge and are ready to put in the work

No, if:

• You prefer computational or applied math
• You’re not comfortable with a heavy workload in first year
• You’re just trying to get a math requirement out of the way

Want more honest reviews like this? Let me know which UofT courses you’re curious about next, or if you’ve taken MAT157, drop your experience in the comments.