Complex Analysis/Real Analysis
Math Major Basics
BM4.1. Example of Complete Induction
BM6.1. Two Tough Set Equalities
BM8.2. Mappings: Basic Properties
BM8.3. Mappings: Composition and Inverse Functions
BM9.1. Cardinality 1: Finite Sets
BM9.2. Cardinality 2: Ininite Sets
BM10: Basic Properties of the Integers
BM10.1. The Euclidean Algorithm for the Integers
Complex Analysis
Complex Conjugate Roots of a Real Polynomial
Factoring 3x^4-2x^3+3x-2 Over The Complex Numbers
Overview of Complex Numbers (1 of 4)
Overview of Complex Numbers (2 of 4)
Overview of Complex Numbers (3 of 4)
Overview of Complex Numbers (4 of 4)
Example of De Moivre's Theorem
Largest Argument of Circle |z+4+2i|
Locus of arg(z-2) = arg(z+2) + pi/3
Locus of Complex equation Z^2 = 1+z/1-z for |z|=1
Parametrizing Curves in the Complex Plane 1
Parametrizing Curves in the Complex Plane 2
Real Analysis
Example of Proof by Induction: Increasing Sequence (Monotone Convergence Theorem)
Example of Countable Partition
Cardinality Example with [0,1]
Point Set Topology
Hausdorff Example 1: Cofinite Topology