This class was tough.
Course Overview:
I would recommend this class especially if one has a high interest in mathematics. In many calculus calculus classes, one learns mostly computation and maybe a small amount of theory. In this class, all the theorems are proven with mathematical rigor using definitions, axioms, and proper proof technique. One can achieve in-depth knowledge of the concepts of calculus and the underlying meaning of computations, and become familiar with reading proofs. Also, one learns how to think in terms of the mathematical theory instead of simply learning how to do certain types of problems.
Course highlights:
There was a significant amount of time spent on infinite sequences and series along with with uniform convergence of functions toward the latter half of the class. These are traditionally important subjects in mathematical theory, and they are certainly interesting to study. It was amazing to see how functions that I was so familiar could be equal to an infinite sum of a sequence of functions. Overall this course has many interesting concepts, and I would recommend to those with interest in mathematics.
Hours per week:
6-8 hours
Advice for students:
When one reads a mathematics textbook with rigorous proof, one cannot simply read it as if it were a novel. Large quantities of time must be spent on analyzing the proofs to the important theorems and understanding the logic used in the proof. One may even be forced to move on from it and come back to it later if it proves difficult. If it comes to it one should attend a TA session or go to the professor's office hours if they are completely stumped. However, if one puts in the appropriate amount of time and effort, the reward in knowledge is significant.