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 more advanced classes in the following year.
In winter 2027, there will be two sections of this class. One section will meet Mondays from 5:00–6:00 PM Pacific time online and either Tuesdays from 5:30–7:30 PM Pacific time online or Wednesdays from 6:30–8:30 PM Pacific time in person in Palo Alto; students choose one of these two options. The other section will be Mondays from 11:00 AM–12:00 PM UTC and Thursdays from 10:30 AM–12:30 PM UTC online. Both sections will meet for ten consecutive weeks in winter 2027. Monday lectures run from January 4th through March 8th. The Tuesday problem sessions run from January 5th through March 9th, the Wednesday problem sessions from January 6th through March 10th, and the Thursday problem sessions from January 7th through March 11th.
Applications for the winter 2027 class are due November 22nd, 2026. After that, we will continue to accept applications on a rolling basis while space remains. Click here to apply!
