We aim to give students a guided tour of the subjects they will encounter in advanced university math courses. We will cover
- Number Theory
- Calculus
- Discrete Mathematics
- Differential Equations
- Linear Algebra
- Abstract Algebra
- Complex Analysis
- Topology
The tour is casually paced, with many stops along the way, so students have time to make friends with the subjects - what questions mathematicians asked about them, why mathematicians cared and what they have discovered thus far. We want students to 'break the ice' with these subjects now, so that when they run into them in the future, it will be like running into an old friend ('Oh me and finite fields...we go waaay back!'). This is especially important if they run into them in a much more formal context (dressed up in a tuxedo) where students might conclude a subject is just too intimidating to study. If they have taken our courses, they will instead see a formal presentation for what it is - one of many possible stylistic choices made by their instructor.
Each student is different, and we are happy to evaluate their readiness for a course on a case-by-case basis. Below is a sample path, with regular school courses in bold.
Algebra 1
↓
Intro to Number Theory
↓
Advanced Number Theory
↓
Group Theory
↓
Discrete Mathematics
↓
Linear Algebra
↓
Calculus (just the fun parts)
↓
Calculus
↓
Differential Equations
↓
Multivariable Calculus
↓
Complex Analysis
↓
Topology