0001. Relations
0002. Set Theory
0003. Define W, N, +, X
0004. Build group axioms
0005. Symmetry groups
0006. Permutations groups
0010. Ring Axioms, Z, axiom of inequality
0020. The Chinese Remainder Theorem
0014. Divisibility and Remainder
0016. Divisibility Rules
0018. Euclidean Algorithm
0022. Encryption algorithms
0023. Field axioms and division
0024. Define Q
0026. Finite sequences and series
Define convergent series
Define neighborhoods, balls
Define closures
Define R
Define irrational numbers
Continued fractions
Measuring degrees of irrationality
The most irrational number
Fibonacci sequence
0011. Representing numbers with bases, adding, subtracting and multiplying in base 10.
0008. Mappings
Graphing Functions
Polynomials
Polynomial Roots
Solving Quadratics
Solving Cubics
Solving Quartics
Algebraic Numbers
Transcendental Numbers
0007. Subgroups
0015. Factoring Numbers, Primes, Composites, Fundamental Theorem of Algebra
Continuous Functions
Uniform Continuity
0009. Cosets and Lagrange's Theorem
0013. Metric Spaces and number lines
Slope
Conics
Derivative
Integral
Vector Space
Cartesian Plane
Matrices
Lines, rays, line segments
Parallel and Perpendicular Lines
Intersections, angles
Triangles - constant sum of angles
Parallelograms
Area of a shape
Pythagorean Theorem
Squares, cubes the geometric way
Geometric square roots
Determinants
Matrix inverses
Solving linear systems
Operators
Derivates of polynomials with matrices
Eigenvalues, eigenvectors
Characteristic polynomial
Common applications of derivatives
Derivatives of trigonometric functions
Newton's method: polynomial roots
Distributions
Gaussian distribution
Poisson distribution
Queue theory
Probability
Permutations, Combinations
Ordinary differential equations
Partial differential equations
Inner Products
Signal Processing
Pattern recognition
Regression
Imaginary and Complex Numbers
Decimal representation
Terminating and repeating decimals
0012. Other bases (2, 8, 16)
Long division
Right Triangles
Sine, Cosine, Tangent
Isomorphisms
Random Number Generators
Graph Theory
Deterministic Automata
Genetic Algorithms
Infinite Series - Axioms that break
Statistics
Contraction mappings
0017. Modular arithmetic and rings
0021. Totients
0019. Linear Diophantine Equations
Inductive sets
Graphing points
Prove existence of irrational numbers
2^(1/2) is a valid number that is not rational
0025. Infinite Processes