# Difference between revisions of "Algebra/Intermediate"

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− | + | An intermediate-level study of geometry 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 Numbers]] | ||

+ | * [[Conic Sections]] | ||

+ | * [[Polynomials]] | ||

+ | ** [[Division Algorithm]] | ||

+ | ** [[Remainder theorem]] | ||

+ | ** [[Factor Theorem]] | ||

+ | ** [[Fundamental Theorem of Algebra]] | ||

+ | ** [[Rational root theorem]] | ||

+ | ** [[Complex Conjugate root theorem]] | ||

+ | ** [[Vieta's Formulas]] | ||

+ | ** [[Newton Sums]] | ||

+ | ** [[Symmetric Polynomial]] | ||

+ | ** [[Descartes Rule of Signs]] | ||

* [[Factoring]] | * [[Factoring]] | ||

+ | ** [[Simon's Favorite Factoring Trick]] | ||

** [[Differences of powers]] | ** [[Differences of powers]] | ||

− | ** [[ | + | ** [[Sums of powers]] |

** [[Sophie Germain Identity]] | ** [[Sophie Germain Identity]] | ||

− | ** [[ | + | * [[Sequences]] and [[Series]] |

− | * [[ | + | ** [[Arithmetic sequence]] |

− | ** [[ | + | ** [[Geometric sequence]] |

+ | ** [[Harmonic sequence]] | ||

+ | ** [[Arithmetic-Geometric sequence]] | ||

+ | ** [[Telescoping]] | ||

+ | ** [[Recursion]] | ||

+ | * Miscellanous [[Functions]] | ||

+ | ** [[Logarithms]] | ||

+ | ** [[Exponentials]] | ||

+ | ** [[Radicals]] | ||

+ | ** [[Absolute value]] | ||

** [[Greatest integer function]] | ** [[Greatest integer function]] | ||

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** [[Least integer function]] | ** [[Least integer function]] | ||

− | + | * [[Inequalities]] | |

− | + | ** [[Triangle Inequality]] | |

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− | ** [[ | ||

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** [[Trivial inequality]] | ** [[Trivial inequality]] | ||

+ | ** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] | ||

** [[Cauchy-Schwarz Inequality]] | ** [[Cauchy-Schwarz Inequality]] | ||

− | + | * [[Functional equations]] | |

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== Resources == | == Resources == | ||

=== Books === | === Books === | ||

* [https://artofproblemsolving.com/store/item/aops-vol2| AoPS Volume 2] | * [https://artofproblemsolving.com/store/item/aops-vol2| AoPS Volume 2] | ||

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=== Classes === | === Classes === | ||

* The [http://www.artofproblemsolving.com/Classes/classdetails.php?course_id=4 Intermediate Algebra Class] -- Intermediate Algebra Training. | * The [http://www.artofproblemsolving.com/Classes/classdetails.php?course_id=4 Intermediate Algebra Class] -- Intermediate Algebra Training. |

## Revision as of 13:14, 29 October 2021

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

## Contents

## Topics

- Techniques for Solving Equations
- System of equations
- Substitution
- Elimination

- Complex Numbers
- Conic Sections
- Polynomials
- Factoring
- Sequences and Series
- Miscellanous Functions
- Inequalities
- Functional equations

## Resources

### Books

### 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.