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]] | ||
| − | |||
** [[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]] | |
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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| | + | * [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 == | ||
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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.
