Lectures related to Axiom of countable choice

Fractals and Strange Attractors

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

Nonlinear Dynamics: Chaos and Complex Systems

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

Logical Structure: Choice and Bar Induction Principles

Covers the logical structure of principles equivalent to choice and bar induction, focusing on generalized dependent choice and its implications in mathematics.

Separable L^2 Spaces

Covers the concept of separable L^2 spaces, demonstrating properties and providing examples.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Relations, Sequences, Summation: Cantor Diagonalization

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

Absolute Value and Intervals

Introduces absolute value, intervals, triangle inequality, and complete numbers in the complex plane.

Dimension Theory: Vector Spaces and Bases

Explores dimension theory of vector spaces, covering bases, linear applications, and ranks.

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.

Market Opportunity Set: How to Generate

Explores the importance of selecting the right market opportunities for success and long-term impact in entrepreneurship.

Theory of Computation: Problems Definition and Counting (Denumerability)

Explores the theory of computation, emphasizing problems definition, counting, and the limits of algorithmic computation.

Properties of Real Numbers

Covers countability and bijections between sets, demonstrating the uncountability of real numbers.

Markov Chains: Definition and Examples

Covers the definition and properties of Markov chains, including transition matrix and examples.

Relations, Sequences and Summations

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

Cardinality of Sets: Countable and Uncountable

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

Theory of Computation: Counting and Decision Problems

Explores counting infinite sets and decision problems, showcasing the limits of computation in solving certain undecidable problems.

Discrete Random Variables: Functions and Probabilities

Explores discrete random variables, their functions, and probabilities in various scenarios.

Derivation of the logit model

Delves into the logit model's derivation, emphasizing the importance of the independence assumption and parameter normalization during estimation.

Deterministic Part: Utility Function Coding

Explores coding behavioral assumptions into a linear-in-parameter utility function.

Relations and Sequences: Well-ordered Sets and Geometric Series

Explores equivalence relations, well-ordered sets, geometric series, and countable sets.