Notes Handouts 51
- Warm Up (Combinatorics)
- Coloring proofs
- Warm Up (Algebra)
- $a^3 + b^3 + c^3 - 3abc$
- Invariance principle
- Polynomials
- Quadratic polynomials
- Cubic polynomials
- Quartics
- Viete's relations
- Differentiation and multiple roots
- Finite differences
- Telescoping
- Growth of polynomials
- Binomial theorem
- More on polynomials
- Arithmetic progressions
- Rational and irrational numbers
- Auxiliary configuration
- Induction
- Inclusion-exclusion principle
- Invariance principle
- Pigeonhole principle
- Extremal principle
- Arrange in order
- Grouping in pairs
- Counting
- Counting via bijections
- Counting the complement
- Counting in two different ways
- Generating functions
- Size of the roots
- Roots of unity
- Crossing the $x$-axis
- Lagrange interpolation
- Integer divisibility
- Functional equations
- System of equations
- Inequalities
- Induction
- Quadratic polynomials
- Cubic polynomials
- Using identities
- Binomial coefficients
- Primes, divisors, and congruences
- System of equations
- Chinese remainder theorem
- Gauss's lemma
- Orders
- Primes
- Triangles