Lectures related to Permutations and Combinations

Explores the basic principles and applications of counting in computer science and mathematics.

Introduces Cartesian product and induction for proofs using integers and sets.

Covers the main rules of counting for combinatorial objects and introduces various counting techniques.

Covers the concepts of combinations and permutations in counting scenarios.

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

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

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

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

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Explores the Symmetric group, cycle decomposition, Orbit-Stabilizer theorem, and properties of cycles and transpositions.

Explores path integrals in quantum field theory, emphasizing the significance of Wick rotation and the classical case.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Introduces equivalence relations, partitions, partial orderings, and total ordering concepts with examples and definitions.

Covers the concept of natural numbers, including properties like commutativity and associativity.

Covers the fundamental concepts of sets and subsets in linear algebra, including operations and properties.

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