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Video List


Algebra - General Topics


Real Numbers and Their Properties
Introduction to Modular Arithmetic
Introduction To Groups
Binomial Expansion Theorem
Partial Fraction Decompostion


Exponents


Basic Properties
Zero and Negative Exponents
Rational Exponents and Nth roots
Radicals - Simplifying and Basic Properties
The Exponential Function


Polynomials - Factoring and Zeros


Fundamentals of Factoring with 3 methods
Factoring Trinomials
Synthetic Division & Remainder Theorem
Finding Rational Zero's of Polynomials
Advanced Tools for finding Zero's of Polynomials


Inequalities


Solving & Graphing Linear Inequalities (1 variable)
Compound Inequalities - Working with AND and OR
Graphing Systems of Inequalities (2 variables)


Functions


Introduction from 4 views
Operations on functions
Inverses


Graphing


Slope and the Equation of a Line
Circles
Parabolas
Ellipses
Hyperbolas
Rotation of Axes
Polynomial Functions
Rational Polynomial Functions
Graphical Transforms - Translation, Reflection & Scaling
Parametric Equations of Curves
Introduction to Polar Coordinates


Complex Numbers


Introduction and operations
Working with Radicals
Complex plane and applications
DeMoivres Theorem - Powers and Roots of a + bi


Quadratic Equations


Completing the square
The Quadratic Formula


Graph Theory


Introduction via Konigsberg Bridge
Graph Theory - Basic Terminology
Euler and Hamilton Paths and Circuits


Game Theory


Introduction to Game Theory
Optimal Strategies and Nash Equilibrium
Mixed Strategy Solutions
How to play and win the game of Nim


Logic


Logical Connectives and Truth Tables
Properties and Applications
Valid Arguments


Counting Methods


Fundamental Counting Techniques with AND, OR and NOT
Counting Methods: Permutations and Combinations


Probability


Introduction and definitions
Using And, Or & Not
Binomial Probability - Patterns in Chaos


Statistics


Central Limit Theorem - Introduction
Central Limit Theorem - Applications


Geometry


Properties of Angles
Properties of Triangles
Similar and Congruent Triangles
Area: Properties and Formulas
Linear vs Angular Velocity


Trigonometry


Intro to Trig via Triangles
Intro to Trig via Unit Circle
Graphing the Sine and Cosine
Graphing Rational Trig Functions (tan, sec, ...)
Inverse Trig Functions
Solving Right Triangles
Solving Any Triangles
Introduction to Trig Identities
More Identities: Sum/Difference and Double Angle
Solving Trig Equations


Spherical Trigonometry


Introdution to Spherical Trigonometry
Polar Triangles
Terrestrial Navigation
Celestial Sphere


Logarithms


Introduction and definition
Solving Log & Exponent equations


Systems of Equations


Introduction & Substitution method
Elimination method
Gaussian Elimination with matricies
Cramer's Rule
Matrix Equations and Inverses


Matricies


Intro to Matrices - Basic Operations
Determinants of NxN Matrices


Vectors


Intro to Vectors - Basic Operations
Vectors - Dot Product
Vectors - Cross Product


Sequences and Series


Introduction to Sequences
Partial Sums and Series


Variation


Direct and Inverse Variation


Fuzzy Sets


Tools for an imprecise world
Operations and Applications


Geometric Modeling


Boundary representations
Projecting A Point to a Curve or Surface
Curve-Curve and Curve-Surface Intersection
Surface-Surface Intersections
Algorithm for Boolean Operations
Translating Geometry - Lost in Translation


Mathematical Induction


Introduction to Mathematical Induction



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