Evan Warner

I learned different integration techniques, sequences and series, and differential equations

How to write proofs, elementary logic, the basic building blocks of math through single-variable calculus. I also just learned a lot about how to learn math and do work effectively/efficiently.

Like the other reviewer, I took the both semesters of this class online, given the COVID-19 pandemic. For context, this was my first time taking a proof-based math class, and I had zero prior exposure to both linear algebra and multivariable calculus. I'd had nothing like that in high school (just the necessary scores to get into this class) and thought this would be a way for me to pressure-test whether or not I wanted to, or even could, be a math major. Overall, I think Warner was a solid professor, though (at least in my case) it was definitely worth it to take this class. For someone with my background (i.e. not very much), I could roughly follow what was going on in most lectures but needed to dedicate a substantial amount of time to develop more intuition. I dedicated a lot of time each weekend, especially in Honors A and the first few weeks of Honors B when I was still getting used to proof-writing and lin alg, in asking questions in class/office hours/via email to Warner (who makes himself SUPER accessible - literally I've sent him like 6 emails at one point and he always replied), reaching out to and discussing proofs with my more experienced and knowledgeable classmates, and just thinking very hard to make sure I understood the theorems from lecture and the HW readings and really made my best effort to get a perfect score on every pset. Like one past reviewer said, t…

Heavy - anywhere from 8-15 hours per week.

Integration series and differential equations

Proof-based math covering Calc 1 and Calc 2 from an incredibly rigorous perspective.

Weekly homework assignments. Quite difficult. 1 midterm, generously curved. Mostly "prove the following", a few "prove or give counterexample." 1 final, generously curved. "Pick 6 of 8 questions to answer" type deal.

He is a great great great professor. After a year in Columbia I can safely say that he is the best professor I've had. First of all, he is incredibly dedicated to teaching and will answer any doubt you have. There were several times where I emailed incredibly stupid questions (sometimes during a sunday) and he replied in a couple of hours at most. Additionally, he makes the class exciting and challenging (in a good way.) Just do yourself a favor and take this class with him

Integrals, differential equations, series/sequences

The most important skill I've taken away from this class was my proof-writing logical skills. I've put countless hours into thinking about how to format my proofs, how to precisely articulate my mathematical arguments based on things that I already know, and how to go about proving things in general. It has helped me be more precise in this class and in my general life. I also learned much more about Calculus from a fundamental perspective. I always wondered about how theorems we had assumed in AP Calculus BC were actually proven, and I can definitely say I've learned Calculus rigorously. I have learned a lot about how mathematics as a field itself works rather than the calculations commonly associated with math. I understand more about the properties of logic, functions, integrals, derivatives, sequences and series. Overall, I've definitely learned a lot and have improved my mathematical thinking skills a tremendous amount.