Algebra 24

• 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
• Size of the roots
• Roots of unity
• Crossing the $x$-axis
• Lagrange interpolation
• Integer divisibility
• Functional equations
• System of equations
• Inequalities