Mathematics · Columbia University
As I said above, everything is taught that will be on tests and homework. You may NEED to go to office hours and if you do so, and take time on everything, you will do well. The homework is reasonable, not light, but not unfair. Same with the tests, very very fair. Its a hard math class, it has real work, but again, its all fair and he is readily available to help and appease.
We covered functions, limits, derivatives, curve sketching, and an introduction to integrals.
The first semester of this course focuses mostly on group theory.
set theory, compact, series, differentiable and integrable
I would recommend Professor Pineiro a million times! He is a great teacher and truly cares about his students' education and success. He teaches concepts thoroughly and prepares us to dive deeper into the topics on the homework. Although it is not an easy course and sometimes not obvious at first how to apply the concepts, Professor Pineiro gives examples that are really applicable to tests and lets you bring in any material. Everything on the tests are in some way taught on lecture and homework and truly if you study the course material, you can absolutely succeed. Not quite an easy A, but definitely a doable A and doable material with his excellent teaching style. Also note that he is extremely willing to answer questions and redo problems so don't hesitate to speak up.
A really clear refresh + additional information on the subject.
How to solve certain first and second order ordinary differential equations.
The rigorous proofs of limit, continuity, differentiation and integration.
I really learned calculus - not just to get by or to get through the course, but truly understand it, and apply it to other things.
We covered uniform convergence / spaces of continuous functions, Fourier series, multivariable differentiation / integration (in particular, the contraction mapping principle, the inverse function theorem, the implicit function theorem, and the fixed-point theorem), and Lebesgue theory (measure theory, Lebesgue integration, and L^p spaces). We also did a lecture on forms for fun.