2022-2023

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