Intro to Higher Mathematics · Mathematics
Some introduction to proofs and abstract math
Set theory, functions and relations, basic propositional logic, epsilon delta proofs, series convergence, modulo arithmetics—overall a hodgepodge of topics from analysis and algebra slow-cooked with logic
How to write proofs, definitions of a function, ways to categorize numbers, etc.
Weekly problem sets graded by the TA. Definitely needed to go to office hours for homework help. Two midterms and a final. Midterms were curved and Prof McDuff made the class right before midterms a review session. Good grade is achievable but you need to put in the work.
psets & exams. not the easiest exams but nice curve and also gives hints if you are stuck on problems
Problem sets every week. They are pretty long, and you will probably need to consult your classmates and the professor to finish them, but it's rewarding. (But this might be specific to Rachel's class? Other professors teaching may not demand so much.) Midterm and final exam. Do your HW well every week and these will not be a problem. The class is not at all an easy A (or an easy B+/A- for that matter...) but if you give an honest effort you will do well. 'You get what you deserve' is very true for this course.
10 Moderately Difficult - Very Challenging HW Sets (25%) Class participation (5%) <-- (Free points) Two Midterms (not too tough, not too easy, each 15%) Extra Problems or a Presentation (10%) Final (30%)
basic abstract mathematical thinking/prep for analysis
I learned a wide variety of skills, from fundamentals of set theory to working with proof-based language. Understanding how to write logical proofs was the most important skill I gained, although our discussions of basic analysis and number theory were interesting as well, and certainly were great ways of building the mathematical language used in proofs.
One of the first introductory math classes to abstract concepts. First few weeks were a difficult transition, especially having never taken a proofs-based class before. Lectures are well-structured and notes are (usually) posted in advance. Prof McDuff is clearly very smart and accomplished, and will make passing comments in class about how concepts are "really very simple" when they are not - but she is very good about taking questions in class and during office hours. Overall would recommend. Definitely one of the more unique and well-taught math courses I've taken and prepared me well in terms of proofs.