Difference between revisions of "Algebra/Intermediate"

 
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The following topics provide a good study of intermediate [[algebra]].
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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.
  
* [[Algebraic manipulation]]s
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== Topics ==
** Working with expressions involving [[radical]]s
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* Techniques for Solving Equations
* [[Equation | Equations]]
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** [[System of equations]]
** [[System of equations | Systems of equations]]
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** Substitution
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** Elimination
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* [[Complex number]]
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* [[Quadratic equation]]
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* [[Conic sections]]
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* [[Polynomials]]
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** [[Division Algorithm]]
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** [[Remainder theorem]]
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** [[Factor Theorem]]
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** [[Fundamental Theorem of Algebra]]
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** [[Rational root theorem]]
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** [[Complex conjugate root theorem]]
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** [[Vieta's Formulas]]
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** [[Elementary symmetric polynomial]]
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** [[Newton's Sums]]  
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** [[Descartes Rule of Signs]]
 
* [[Factoring]]
 
* [[Factoring]]
** [[Differences of powers]]
 
 
** [[Simon's Favorite Factoring Trick]]
 
** [[Simon's Favorite Factoring Trick]]
** [[Sums of powers]]
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** [[Sum and difference of powers]]
* [[Function | Functions]]
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** [[Sophie Germain Identity]]
** [[Exponential function | Exponentials]]
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* [[Sequence | Sequences]] and [[Series]]
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** [[Arithmetic sequence]]
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** [[Geometric sequence]]
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** [[Harmonic series | Harmonic sequence]]
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** [[Arithmetico-geometric series | Arithmetico-geometric sequence]]
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** [[Telescoping]]
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** [[Recursion]]
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* Miscellanous [[Functions]]
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** [[Logarithm]]
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** [[Exponential function]]
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** [[Radical]]
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** [[Absolute value]]
 
** [[Greatest integer function]]
 
** [[Greatest integer function]]
** [[Graph of a function| Graphing]]
 
 
** [[Least integer function]]
 
** [[Least integer function]]
** [[Logarithm | Logarithms]]
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* [[Inequalities]]
** [[Polynomial | Polynomials]]
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** [[Triangle Inequality]]
*** [[Descartes Rule of Signs]]
 
*** [[Division Algorithm]]
 
*** [[Factor Theorem]]
 
*** [[Remainder Theorem]]
 
*** [[Symmetric polynomial]]s
 
** [[Functional equation| Functional Equations]]
 
* [[Inequality | Inequalities]]
 
 
** [[Trivial inequality]]
 
** [[Trivial inequality]]
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** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]]
 
** [[Cauchy-Schwarz Inequality]]
 
** [[Cauchy-Schwarz Inequality]]
** [[Arithmetic Mean-Geometric Mean | Arithmetic Mean-Geometric Mean Inequality]]
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* [[Functional equations]]
** [[Triangle Inequality]]
 
* [[Newton sums]]
 
* [[Sequence]]s
 
** [[Arithmetic sequence]]s
 
** [[Geometric sequence]]s
 
** [[Harmonic sequence]]s
 
** [[Recursion]]
 
* [[Series]]
 
** [[Arithmetic series]]
 
** [[Arithmetico-geometric series]]
 
** [[Geometric series]]
 
** [[Telescoping]] series
 
* [[Substitution]] methods
 
* [[Trigonometry]]
 
** [[De Moivre's Theorem]]
 
** [[Roots of unity]]
 
* [[Continued expressions|Continued fractions]]
 
 
 
  
 
== Resources ==
 
== Resources ==
 
=== Books ===
 
=== Books ===
 
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* [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.
 
* 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.
 
  
 
== See also ==
 
== See also ==
* [[Algebra]]
 
 
* [[Algebra/Introduction | Introductory Algebra]]
 
* [[Algebra/Introduction | Introductory Algebra]]
 
* [[Algebra/Olympiad | Olympiad Algebra]]
 
* [[Algebra/Olympiad | Olympiad Algebra]]
  
[[Category:Intermediate Mathematics Topics]]
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[[Category:Algebra]] [[Category:Intermediate Mathematics Topics]]

Latest revision as of 16:47, 3 November 2021

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