First day of Calculus II happened Tuesday. Professor stated we are going through series and sums first. It's going to be a pain on top of all homeworks being online. This is my first time taking a math class in two years as well which is a bit of a pain having to go back and relearn (read: brush up on) many rules. Thanks for the article. I couldn't help but relate to this section of the comments. Thankfully, I'm also taking Proofs as a class, hired a tutor and plan to attend all the extra supplementary instruction sessions I can. As you can see, Devac, it really can be an odd system [from the outside].The most infuriating part of Calc II is that students are expected to be able to do basic convergence/divergence proofs for the series & sequences part without ever having learned how to write a proper proof in their lives. Grading those exams is painful because the class uses online math homework, so for many, the first time they have to write a proof for another human is on that exam. Each answer you have to read closely to see if they understand the ideas but can't explain them well or if they just wrote random words on the page.
I think sequences and series are quite cool, and they tend to pop up all over the place in other fields, including probability, combinatorics, computer science, and communications. I'm interested: what all does your proofs class cover? Is it something like a foundations class, where you start off with a few definitions and axioms and prove a bunch of stuff, or does it focus on logic and different proof techniques, or a mix? Perhaps the best thing I can recommend for this whole "why are things true" business is to find someone else in the class to compare and critique proofs with.
According to the syllabus, we'll be going through Logic, Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, and Functions. Some Proofs in Calc. Bless my HS Calc teacher for getting our toes wet early on since some of this sounds familiar. Just a matter of dusting of memories. My tutor has gone through the class so he's my first line of defense in the comparison department. If not, I'd like to start a study group (especially so if some from my Calc class are in the Proofs as well).