Algebra

In mathematics, algebra is the study of examining, manipulating, and solving equations, inequalities, and other mathematical expressions. Algebra revolves around the concept of the variable, an unknown quantity denoted by a letter. Many contest problems test one's fluency with algebraic manipulation.

Introductory Topics

• Algebraic expressions
  • Algebraic manipulation
  • Substitution
• Equations
  • Linear equations
  • Systems of equations
• Factoring
• Functions
  • Exponentials
  • Graphing
  • Logarithms
  • Polynomials
• Inequalities
  • Trivial inequality

Intermediate Topics

• Equations
  • Systems of equations
• Factoring
  • Simon's Favorite Factoring Trick
• Functions
  • Exponentials
  • Greatest integer function
  • Graphing
  • Least integer function
  • Logarithms
  • Polynomials
• Inequalities
  • Trivial inequality
  • Cauchy-Schwarz Inequality
• Newton's Sums
• Trigonometry
  • DeMoivre's Theorem
  • Roots of unity