Olympiad 1 (O1) Course
- Lessons: 20
- Fee: $1,100 AUD
- Current Time: Sun 17:30–19:30
- Workload: 4–6 hours
There will be 2 hours of teaching per week every over 20 weeks, and I expect students to spend about 4–6 hours per week reviewing the material and doing homework. The total time spent in this course should be around 120–180 hours over 2 terms. As this is the first Olympiad course, there will be a heavy emphasis on understanding and writing proofs, as well as a discussion of different problem-solving strategies more relevant to proofs.
Classes
| Name | Time | Students | Duration | Status |
|---|---|---|---|---|
| 2025-07-O1 | 8 | – | Active |
Syllabus (Provisional)
- Proofs (2 weeks): proof writing, contradiction, induction.
- Problem-Solving Strategies (6 weeks): try small cases, case bashing, extremal principle, pigeonhole principle, backsolving, representation and visualisation techniques, problem exploration.
- Combinatorics (3 weeks): double counting, bijections, invariants and monovariants, game theory, graph theory.
- Number Theory (3 weeks): prime factorisations, infinite descent, Euclidean algorithm, modular arithmetic, Fermat’s little theorem, Euler’s theorem, Diophantine equations.
- Algebra (3 weeks): graphing, sequences, polynomials, Vieta’s formulas, inequalities, functional equations.
- Geometry (3 weeks): geometry strategies and techniques, angle chasing, length chasing, important configurations, reverse reconstruction.
Learning Outcomes
- Understand what a proof is and be able to write one with an appropriate level of detail.
- Use contradiction and induction effectively in proofs.
- Be able to use a variety of soft and hard techniques in problem-solving.
- Apply a range of theorems and techniques across algebra, combinatorics, geometry, and number theory to prove results, especially in the areas covered in the C1 course.
- Understand what game theory, graph theory, and functional equations are.
- Understand how to manipulate inequalities.
Prerequisites
Before starting this course, students should be familiar with most of the concepts taught in the Competition Maths (C1) course. In particular, students should:
- have at least some experience with creative thinking and problem-solving in maths done outside the classroom,
- be able to use permutations and combinations, including the supermarket principle (aka stars and bars) to solve counting problems,
- be able to apply binomial theorem to determine coefficients of binomial expansions,
- be able to apply modular arithmetic (addition, subtraction, multiplication, exponentiation) in problems,
- be able to solve simultaneous equations and quadratic equations,
- be able to sum arithmetic and geometric series,
- understand the relationships between the equations and graphs of lines, quadratics, and circles,
- be able to angle chase on parallel lines, in triangles, in circles, and in cyclic quads, and
- be able to spot and utilise similar triangles in solving geometry problems.