# Difference between revisions of "Algebra/Intermediate"

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− | + | 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]] | * [[Factoring]] | ||

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

− | ** [[ | + | ** [[Sum and difference of powers]] |

− | * [[ | + | ** [[Sophie Germain Identity]] |

− | ** [[Exponential function | + | * [[Sequence | Sequences]] and [[Series]] |

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

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

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

+ | ** [[Arithmetico-geometric series | Arithmetico-geometric sequence]] | ||

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

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

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

+ | ** [[Logarithm]] | ||

+ | ** [[Exponential function]] | ||

+ | ** [[Radical]] | ||

+ | ** [[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] | |

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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. | ||

* The [http://www.artofproblemsolving.com/Classes/AoPS_C_WOOT.php Worldwide Online Olympiad Training (WOOT) Program] -- Intermediate to Olympiad training in a variety of subjects, including algebra. | * The [http://www.artofproblemsolving.com/Classes/AoPS_C_WOOT.php Worldwide Online Olympiad Training (WOOT) Program] -- Intermediate to Olympiad training in a variety of subjects, including algebra. | ||

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== See also == | == See also == | ||

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* [[Algebra/Introduction | Introductory Algebra]] | * [[Algebra/Introduction | Introductory Algebra]] | ||

* [[Algebra/Olympiad | Olympiad Algebra]] | * [[Algebra/Olympiad | Olympiad Algebra]] | ||

− | [[Category:Intermediate Mathematics Topics]] | + | [[Category:Algebra]] [[Category:Intermediate Mathematics Topics]] |

## Latest revision as of 16:47, 3 November 2021

An intermediate-level study of algebra 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 number
- Quadratic equation
- 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.