Lectures related to Countable set

Relations, Sequences, Summation: Summary of Week 5

Explores binary relations, sequences, and summation, including arithmetic and geometric progressions, recurrence relations, and cardinality of sets.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Signal Representations

Covers the properties of signal/data representations using Fourier transformations and matrices.

Probability Theory: Lecture 2

Explores toy models, sigma-algebras, T-valued random variables, measures, and independence in probability theory.

Implementation of Lists: Arrays and Iterators

Covers the implementation of lists using arrays, iterators, and various methods.

The Two-Holed Torus

Covers the construction of the connected sum of two tori in 10 minutes.

Definition of Indefinite Integral

Explains the definition and properties of indefinite integrals, highlighting the relationship between primitives and the set of all primitives of a function.

Permutations and Combinations

Covers the concepts of permutations and combinations, explaining how to calculate them with examples.