Algebra/Intermediate: Difference between revisions
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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]] | ||
** [[Simon's Favorite Factoring Trick]] | ** [[Simon's Favorite Factoring Trick]] | ||
** [[Sum and difference of powers]] | |||
** [[Sophie Germain Identity]] | ** [[Sophie Germain Identity]] | ||
** [[ | * [[Sequence | Sequences]] and [[Series]] | ||
* [[ | ** [[Arithmetic sequence]] | ||
** [[Exponential function | ** [[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]] | ||
** [[Least integer function]] | ** [[Least integer function]] | ||
* [[Inequalities]] | |||
** [[Triangle Inequality]] | |||
** [[ | |||
** [[Trivial inequality]] | ** [[Trivial inequality]] | ||
** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]] | |||
** [[Cauchy-Schwarz Inequality]] | ** [[Cauchy-Schwarz Inequality]] | ||
* [[Functional equations]] | |||
== Resources == | == Resources == | ||
=== Books === | === Books === | ||
* [https://artofproblemsolving.com/store/item/aops-vol2| | * [https://artofproblemsolving.com/store/item/aops-vol2| AoPS Volume 2] | ||
=== 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. | ||
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== See also == | == See also == | ||
* [[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 15:06, 7 December 2024
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
- System of equations
- 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.
