# Topics Covered in Math Challenge IV

The order of these topics may vary, and these topics might not be all covered. The coverage will depend on time schedule and overall progress.

### Summer Sample Topics for Algebra

- Polynomials
- Inequalities
- Functional equations
- Mathematical induction
- Complex numbers
- Sequences
- One-to-one correspondence
- Algebra problems in Math Olympiads

### Fall Sample Topics for Geometry

- Famous Theorems in Geometry
- Adding auxiliary lines
- Ratios in Geometry
- Straight line shapes
- Circles
- Transformations
- Concurrence and collinearity
- Analytical Geometry
- Proofs in Geometry
- Phantom points
- Area methods
- Analytical methods
- Vectors
- Solid Geometry
- Inequalities in Geometry
- Combinatorial Geometry
- Geometry problems in Math Olympiads

### Winter Sample Topics for Combinatorics

- Counting
- General functions
- Graph theory
- Combinatorial identities
- Pigeonhole Principle
- Calculating twice
- Combinatorial Geometry
- Ramsey Theory
- The extremal principle
- Coloring
- Covering
- Combinatorics problems in Math Olympiads

### Spring Sample Topics for Number Theory

- Integers
- The floor function
- Modular arithmetic
- Some important Number Theory Theorems
- Number base systems
- Diophantine equations
- Modular equations
- Quadratic residues
- Number Theory problems in Math Olympiads

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