Below is a tentative list of topics:
- Sequences and Series, Linear Recursive Sequences, Patterns, Telescoping Series
- Introduction to Proofs: (Proof by Contradiction, Proof by Induction, Pigeonhole Principle)
- Introduction to Fractals
- Euler’s Number
- Complex Numbers
- Number systems
- Benford’s Law
- Set-Theoretic Topology
- Number Theory
- Linear Diophantine Equations
- 2D Geometry I: Properties of Chords-Secants-Tangents in Circles, Conics.
- Trigonometry: Radians, unit circle, trigonometric identities, trigonometric functions and equations
- Trigonometric Equations, Identities, and Transformations
- Modular Arithmetic: Equivalence relationship proofs and problems.
- Topology: Factorization and Divisibility, greatest common divisor, Unique factorization, Proofs and Problems
- Real Analysis-Functions: Limits of Functions, Continuous Functions, Derivatives, The Mean Value Theorem
- Limits, Implicit differentiation, and Related Rates Number Theory: Modular Arithmetic and its properties
- Multiplicative Functions, Dirichlet Product and Mobius Inversion, Euler Function, Proofs and Problems with Functions
- Proofs and Problems from previous ARML competitions
- Practice Questions for Waterloo Math Contest
