Transition to Proofs

When we are first introduced to mathematics, we are typically asked mathematical questions whose answers are numbers, or something similar to numbers. However, most of mathematics is not about finding numerical answers to problems, but rather understanding general patterns and explaining what makes them work. We aim to help students transition from numerical answer problems to proof-based mathematics.

Such transition to proofs classes are quite common at universities, since mathematicians need to be able to understand and write proofs. However, these classes are often fairly dull content-wise, as the entire goal is to learn what a proof is, and not to teach any new mathematics. Our class will be structured differently. We will teach students how to write and understand proofs while simultaneously teaching mathematics. To this end, we will run a three-quarter sequence, where each quarter is on a different topic and will introduce different typical techniques used in proofs. The classes are as follows:

Fall: Number theory
Winter: Combinatorics
Spring: Analysis

We strongly recommend that students take all three classes as a sequence.

These classes will be less challenging than our advanced classes, but we still expect that students will take them very seriously and will work hard. Getting used to proofs is not a trivial matter and will take a considerable amount of effort. Students who take this sequence and master the material in it will develop the mathematical maturity needed to follow our advanced classes in the following year.