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Complex Numbers in Geometry

• Complex Numbers and Geometry
• Triangles in Complex Plane

Mass Point Geometry

• Barycentric Coordinate for Math Olympiad: Part 1, Part 2

Combinatorics

Basic Combinatorics

• Multiplication and Addition Principle

Bijection Principle

• Concept and Application
• Integer Solutions

Invariance Principle

• Coloring Proof Application

Extremal Principle

• Part 1
• Part 2
• Application: Dancing Partner Problem

Combinatorial Argument

• Triangular Numbers

Partitions

• Partition of 𝑛 distinct objects into 2 classes
• Partition of 𝑛 distinct objects into 3 classes
• Partition and Recurrence Relation
• Partitions and Generating Functions

Number Theory

Modular Arithmetic

• Arithmetic of Remainders – the experiment
• Arithmetic of Remainders – the proof
• Theory of congruence – introduction
• Congruence relation is an equivalence relation
• Properties of Congruence Relation
• Euclid Algorithm and Modular Inverse
• GCD and Modular Inverse
• Application Problem: Part 1, Part 2, Part 3
• Application Problem: 7 divides 32𝑛+1+2𝑛+2

Divisibility

• Pairing of Divisors
• Solving Equations with primes
• Number Theoretic Function
• Bezout’s Theorem
• Multiplicative Function: Application

Advanced Topics

• Chinese Remainder Theorem
• Geometric Excursion in Number Theory: Part 1, Part 2, Part 3

Algebra

Inequality

• AM-GM Inequality
  • Part 1
  • Part 2
  • Part 3
• Cauchy Schwarz
  • Part 1
  • Part 2
• Quadratic Mean
• Jensen Inequality – Concept