Deep Mathematics: Weekly Classes
Real mathematics for talented middle and high school students in Princeton
Weekly Sessions Are Part of Deep Mathematics
Deep Mathematics is advanced mathematics training tailored for talented students: genuine intellectual challenge and real depth. See the Deep Mathematics overview for full program benefits and philosophy.
Session Format
Each session combines theory with problem-solving. The instructor presents new material systematically, building concepts step by step. Students then work through problems of increasing difficulty that develop and test understanding. Students present solutions on the board, and the group discusses: comparing approaches, questioning reasoning, finding gaps, refining arguments together.
Explaining to others deepens your own understanding. Seeing different approaches expands your toolkit. Getting stuck and working through it together is where the real learning happens.
Group size: Up to 12 students per group.
No phones or computers. Pencil, paper, and thinking. Between sessions, students receive problems to work on if they choose.
Note: We teach responsible and efficient GenAI tools use in our Research Club Princeton, Research Skills courses, and Research Laboratories. Deep Mathematics sessions are dedicated to pure thinking and problem-solving without GenAI.
Topics
A 10-week module explores five areas of mathematics, two weeks each. Every area reveals a different face of what real mathematics is. Students discover which areas excite them most.
- Number Theory and Proof. Properties of integers, divisibility, primes, modular arithmetic. The ideal terrain for learning what proof actually means.
- Algebra and Structure. Why do the rules of algebra work? What happens when you change them? Equations, inequalities, polynomials, and the structures beneath them.
- Geometry and Spatial Reasoning. Classical geometry the way Euclid built it: from axioms to theorems through proof. Constructions, transformations, geometric insight.
- Combinatorics. Counting, arrangements, probability, and pigeonhole arguments. Problems where cleverness matters more than formulas.
- Foundations of Analysis. What are limits, really? What does it mean for a sequence to converge? The ideas beneath calculus, approached with care.
Prerequisites
Readiness and genuine interest in mathematics.
- Math: arithmetic and basic algebra (completed or in progress)
- No prior experience with proofs or advanced mathematics required. That is what we teach.
Deep Mathematics is conceptually demanding. Serious, deep, and rigorous. We designed it for students who want real challenge and are ready to work for it. Not everyone will be able to follow every session. That's normal, and it's part of why the program works.
Schedule, Cost & Refund Policy
10-Week Spring Module: Weekly classes starting March 2nd (holidays skipped). Location: Central Princeton.
- Princeton: Mondays, 5:00–6:30 PM at Arts Council of Princeton
102 Witherspoon St, Princeton, NJ 08542
Cost: $1,500 per 10-week module
Payment due at enrollment. Full refund if we cancel or minimum group size is not formed. If you need to cancel, the following refund policy applies:
| If you cancel at... | Refund |
|---|---|
| 1+ week before start | Full refund |
| Less than 1 week before start | No refund |
Mathematics in Practice: Research Skills & Computational Tools
Deep Mathematics develops the conceptual foundation. When you're ready to apply mathematics to research, we offer Research Skills courses in practical computational tools:
- Applied Statistics with R — Analyze data, build models, create publication-ready visualizations
- Modeling and Simulations with Wolfram Mathematica — Run advanced simulations, solve problems symbolically
- Applied Machine Learning with Python — Pattern recognition, prediction, and data-driven modeling
These courses teach the computational tools professional scientists use. Students who understand mathematics deeply find these tools more powerful and intuitive.
Different from Typical Math Enrichment in Princeton
Some students searching for math enrichment, a math tutor, or an advanced math program in Princeton may actually want something those options don't provide: the experience of doing real mathematics.
Acceleration programs move faster through the same material. Tutoring helps with the next test. Competition prep trains pattern recognition for specific contests. These all have value, and students who've done them arrive well prepared.
Deep Mathematics builds on that foundation with something different: learning to prove, derive, and reason from first principles. Students who develop this depth find competition problems, AP courses, and college mathematics more approachable, but that's a side effect. The goal is learning to think mathematically, the kind of understanding that lasts through college and beyond.