Lectures related to Cantor's first set theory article

Nonlinear Dynamics: Chaos and Complex Systems

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Lebesgue Integration: Cantor Set

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Analysis IV: Measurable Sets and Functions

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Fractals and Strange Attractors

Delves into renormalization, fractals, and strange attractors, exploring the properties of countable and uncountable sets.

Relations, Sequences and Summations

Covers strings, countable sets, cardinality, and the concept of countability, exploring the countability of various sets and Cantor diagonalization.

Fractal Uncertainty Principle and Spectral Gaps

Explores transfer operators, Patterson-Sullivan measure, FUP, spectral gaps, and resonances in Schottky groups.

Relations, Sequences, Summation: Cantor Diagonalization

Covers countable and uncountable sets, sequences, summation, and Cantor's Diagonalization proof.

Computing leading eigenvalues of the transfer operator

Explores computing the leading eigenvalue of a transfer operator beyond periodic points, focusing on mathematical settings, spectral radius estimation, and the Zaremba Conjecture.

Hausdorff Dimension and Brownian Motion

Explores the Hausdorff dimension of Brownian motion zeros, demonstrating a dimension of 1/2 with certainty.

Change of Variable Formula: Devil's Staircase

Explores a change of variable formula and the intriguing Devil's Staircase.

Different Infinities: Cantor's Theorem

Explains Cantor's theorem comparing cardinalities of different number sets.

Setting up arithmetic

Explores defining arithmetic operations through counting, with insights on cardinal numbers, Cantor's work, and Sudoku.

Additional Properties of Real Numbers

Explores the countability of subsets of real numbers and demonstrates that the set of real numbers is uncountable.

Cardinality of Sets: Countable and Uncountable

Explores countable and uncountable sets, demonstrating how to determine the cardinality of different sets through listing elements in a sequence.

Selected Topics in Mathematics

Covers selected topics in mathematics, including Taylor approximations and algebraic structures of Z and K[X].

Relations, Sequences, Summation: Quiz

Covers cardinality of sets, poset, equivalence relations, and geometric progressions through a quiz on Kahoot.

Cardinality of Sets: Countable and Uncountable

Explores cardinality, countable sets, and examples of countable and uncountable sets.