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