Algebra/Intermediate

An intermediate-level study of algebra involves familiarity with introductory topics to a high level and a multitude of new topics.

Topics

• Techniques for Solving Equations
  • System of equations
  • Substitution
  • Elimination
• Complex number
• Quadratic equation
• Conic sections
• Polynomials
  • Division Algorithm
  • Remainder theorem
  • Factor Theorem
  • Fundamental Theorem of Algebra
  • Rational root theorem
  • Complex conjugate root theorem
  • Vieta's Formulas
  • Elementary symmetric polynomial
  • Newton's Sums
  • Descartes Rule of Signs
• Factoring
  • Simon's Favorite Factoring Trick
  • Sum and difference of powers
  • Sums of powers
  • Sophie Germain Identity
• Sequences and Series
  • Arithmetic sequence
  • Geometric sequence
  • Harmonic sequence
  • Arithmetico-geometric sequence
  • Telescoping
  • Recursion
• Miscellanous Functions
  • Logarithm
  • Exponential function
  • Radical
  • Absolute value
  • Greatest integer function
  • Least integer function
• Inequalities
  • Triangle Inequality
  • Trivial inequality
  • Arithmetic Mean-Geometric Mean Inequality
  • Cauchy-Schwarz Inequality
• Functional equations

Resources

Books

• AoPS Volume 2

Classes

• The Intermediate Algebra Class -- Intermediate Algebra Training.
• The Worldwide Online Olympiad Training (WOOT) Program -- Intermediate to Olympiad training in a variety of subjects, including algebra.

See also

• Introductory Algebra
• Olympiad Algebra