Pre-Olympiad Intensive and Research Initiation

Named after G. H. Hardy (1877–1947), the Cambridge mathematician who recognized Ramanujan’s genius from a letter and changed the course of mathematical history.
The Hardy Program is the institute’s most advanced offering. Students aged 12 to 16 who enter this program are not preparing for mathematics — they are already doing mathematics. They come to us having exhausted their school’s offerings, often self-taught, sometimes already recognized in regional competitions. What they need is structure, intellectual community, and the beginning of a research identity.

Core Curriculum

Advanced Algebra and Number Theory. Abstract algebra at the intuitive level (groups, rings, fields through examples), quadratic residues, Gaussian integers, Diophantine equations, analytic methods (p-adic numbers, zeta function introduced as an object of wonder, not of terror).

Olympiad Geometry.

Projective methods, inversive geometry, radical axes, power of a point, spiral similarities, advanced circle theorems.
Primary sources: Prasolov’s Problems in Plane Geometry, Evan Chen’s Euclidean Geometry in Mathematical Olympiads.

Combinatorics and Graph Theory

Generating functions, Ramsey theory, extremal combinatorics, probabilistic method (Erdős’s most beautiful tool). Students work through problems from IMO Shortlists 2000–present.

Calculus and Analysis — Introduction

Limits, continuity, differentiation, integration as area, sequences and series, epsilon-delta reasoning for the most advanced students. We use Spivak’s Calculus as our primary text — the most mathematically honest introductory calculus text in existence.

Mathematical Physics and Applications (elective)

For students who wish to extend into physics, cryptography, or theoretical computer science.

Research Initiation

Each Hardy Program student is assigned a Research Mentor — a working mathematician, PhD candidate, or advanced faculty member — and completes one individual research project per academic year. Projects may range from survey papers on unsolved problems to original computational explorations to proof attempts in elementary number theory.

Competition Track

Hardy Program students are prepared for the full IMO pipeline:

• OBMEP — National Final
• Brazilian IMO Selection Team Process
• Putnam Competition (for those approaching 17)
• International Mathematics Olympiad (IMO)
• Ibero-American Mathematical Olympiad

Mentorship

Every student in the Hardy Program has:

An Academic Mentor — a professional mathematician who meets monthly
A Wellbeing Mentor — a psychologist specializing in high-ability youth, who meets biweekly
Access to our Senior Student Network — former Hardy Program students now in undergraduate or graduate programs, available for informal guidance.

Format

• 6–8 hours of guided instruction per week
• Independent study with weekly problem set (graded and returned with written feedback)
• Monthly research seminar (students present their work)
• Annual Ramanujan Lecture Series — one internationally recognized mathematician per year, invited to speak and interact with students.

University Placement Support

For students in their final year (15–16), the institute provides:

• Application strategy for ITA, IME, UNICAMP, USP, and international universities
• Preparation for university entrance interviews
• Connection to scholarship opportunities nationally and internationally