Mathematical Acceleration and Competition Foundation

Named after Carl Friedrich Gauss (1777–1855), who at age 10 stunned his teacher by summing the integers 1 to 100 in seconds.
The Gauss Program serves students aged 7 to 11 who have moved beyond the pace and depth of standard school mathematics. These students are not simply “good at math” — they think in mathematics. They need problems that resist immediate solution, concepts that open onto further concepts, and peers who match their level of engagement.

Core Curriculum

Number Theory — Foundations. Divisibility, prime numbers, the Sieve of Eratosthenes, modular arithmetic introduced through clock problems, GCD and LCM, Euclidean algorithm. Students encounter Gauss’s own methods — including his proof of the formula for triangular numbers — as live mathematics, not historical footnote.

Combinatorics and Counting.

Multiplication principle, permutations, combinations, Pascal’s Triangle, pigeonhole principle, inclusion-exclusion at its elementary level.

Primary source: Problems from Arthur Engel’s Problem Solving Strategies (accessible chapters) and selections from the Russian Mathematical Olympiad archives.

Geometry — Euclidean Reasoning.

Triangles, circles, polygons, area and perimeter, similarity and congruence, introductory proof by construction. Emphasis on the ability to argue — to write “Because… therefore…” with mathematical precision.

Algebra — Thinking with Unknowns.

From pattern generalization to formal expressions. Word problems as translation exercises. Introduction to systems of equations through geometric interpretation.
Logic and Mathematical Proof.
What is a proof?
Direct proof, proof by contradiction, proof by cases. Students write their first proofs in structured natural language before any symbolic formalism.

Competition Track

Students in the Gauss Program are systematically prepared for:

• OBMEP (Olimpíada Brasileira de Matemática das Escolas Públicas)
• OBMC (Olimpíada Brasileira de Matemática — Colégio)
• Kangaroo Mathematics Brazil
• AMC 8 (for those with English proficiency)

Competition preparation is integrated into the curriculum — not a separate module — because the habits of mind required for competition mathematics are the same habits of mind required for research mathematics.

Methodology

Sessions follow the Hungarian method popularized by Paul Erdős’s teacher George Pólya, formalized in How to Solve It (1945): Understand → Plan → Execute → Reflect. Every session begins with an “impossible problem” — a problem students cannot immediately solve — and ends with every student having made genuine progress toward a solution.

Format

• 4 sessions per week, 90 minutes each
• Weekly problem set (10 problems, graded by difficulty, not by time)
• Monthly competition simulation under timed conditions
• Biannual individual progress report sent to families

Learning Outcomes

By the end of the Gauss Program, students will have: a working knowledge of elementary number theory, combinatorics, Euclidean geometry, and algebra; the ability to write a clear mathematical argument; and direct experience in at least two national competitions.

---