Julia Sets and Polynomial Roots

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Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

General case of degree two polynomials

Explores Viète's formula for finding roots of degree two polynomials and their significance.

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Factorisation: Real Coefficients Examples

Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Complex Functions: Norm Equivalence

Explores norm equivalence in complex functions, covering homogeneity and triangular inequality.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Correlations of the Liouville function

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.