MATH 2315

This class is extremely rewarding and you will learn a TON of math, but it can be frustrating and very time-consuming. If you want to succeed, you have to go to office hours and collaborate with others in class.

The first few weeks cover foundations concepts very quickly (sets, functions, equivalence relations, etc.), then some proof-based linear algebra and multivariable calculus (with some other topics thrown in depending on what Sherman wants us to see, like permutations, means, and a rigorous multilinear map determinant definition). The content is really interesting and if you are interested in a math major, this course will definitely convince you. That being said, the textbook (Williamson Trotter) is not great: it has some interesting exercises but the exposition is a mix of unclear, redundant, and vague.

***If you are a CS or Engineering student who was "good at math" in high school and wants a challenge, this is maybe not the course for you (unless you love proofs). The vast majority of people in this category dropped within the first two weeks.

Sherman is great too! Wonderful first math professor to have at UVA, he really cares about you succeeding and prioritizes people building intuition on the material. Overall I highly recommend 2315 and its sequel course, it will certainly get you to appreciate math and learn a lot of it.

TLDR: Steep learning curve at first + very large workload but extremely interesting and valuable

Only take this class if you are genuinely interested in the theoretical side of math. This class is very challenging, if not almost impossible at times, and will push you to your limit. But over the course of this class and its successor (3315) I’ve learned so much about the subject material and more, and the effort I put into the class was definitely worth it.

Most of the learning is done on your own from a 50 year old textbook that’s mostly fine but is sometimes poorly worded and tends to overcomplicate many of the concepts. The lectures give bigger picture overviews of the readings, plus whatever extra topics Sherman feels like teaching. Sherman has high expectations but is an incredible professor and is especially good at breaking down complicated concepts into understandable bits and tying things back to physical intuition.

The class is very fast paced, and we go beyond Multi+Linear into some set theory and real analysis. The course aims to give a deeper understanding of the theory behind the material and shows how connected these fields are under the hood, but sometimes the extra content can be a little frustrating when you’ve already spent 10 hours on the homework and have to prove something wildly unrelated to what you’ve been learning about. Each homework consists of mostly book problems and 1-3 challenge problems (usually proofs) that range from slightly difficult to straight-up unfair. Group work is not only allowed but heavily encouraged, and office hours will probably become a part of your weekly schedule. Overall, this class will be an extremely valuable experience if you enjoy math for the sake of it and convinced me to major in math, but is definitely not for everyone.