#MOC # Algebra For abstract algebra, see [[Category Theory]], which I'm treating as being equal. Algebra can be thought of as the [[Category]] of sets whose [[Morphism]]-s are [[Function (in Algebra)|functions]]. ## Concepts - [[Function (in Algebra)]] ![[Function (in Algebra)#^raszmz]] - [[The Quadratic Formula]] - [[The Cubic Formula]] - [[Sequence]] - [[Exponent Rules]] and [[Exponential Growth]] - [[Logarithm Rules]] and [[Logarithmic Scale]] - [[Square Root]] - [[Complex Numbers]] - [[Polar Coordinates]] - [[The Exponential Function]] and [[The Natural Constant]] ## Theorems - [[The Fundamental Theorem of Algebra]] - [[Descartes' Rule of Signs]] - [[Rational Root Theorem]] - [[Vieta's Formulas]] - [[Binomial Theorem]] - [[Euler's Formula]] - [[The Intermediate Value Theorem]] - [[The Extreme Value Theorem]] ## Proofs - [[A Complex Conjugate of a Root of a Polynomial with Real Coefficients Is Also a Root]] - [[All Polynomials With Real Coefficients Can Be Factored Into Linear And Irreducible Quadratic Terms]] - [[All Odd Degree Polynomials With Real Coefficients Must Have At Least One Real Root]] - [[Misconception About Multiplying Square Roots]] - [[Misconception About Roots and Fractions]] - [[Square Root of 2 Is Irrational]] - [[Squaring a Number Does Not Affect Its Parity]] ## Misc - The mnemonic used to teach the order of operations is [[PEMDAS]] - [[Solving a System of Two Linear Equations Using Cramer's Rule]] - [[The General Formula for the Difference of Two Nth Powers]]