Complex Roots: Conjugate Pairs and Quadratic Equations

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Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Introduces the argument of complex numbers and the polar method, demonstrating their application in finding roots.

Covers the Gauss-Wantzel Theorem and Fermat prime numbers.

Covers complex numbers, quadratic equations, solutions in C, and 2x2 matrices.

Covers the basics of polynomials, focusing on rings, operations, and properties.

Explores Fourier transform calculation and residue calculus in mathematical analysis.

Explores complex numbers, including modulus, conjugation, and Euler formula.

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, algebraic geometry, and intersection theory.

Explains Optimal Binary Search Trees using dynamic programming and covers a midterm exam from 2016.

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