Counting Basics: Set Theory and Permutations

Related lectures (25)

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Explores the Cartesian product in linear algebra and the method of induction for proving propositions.

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

Covers the concept of the Cartesian product, emphasizing the order of elements in pairs.

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.

Explores commutative groups, Euler's Totient Function, and Cartesian products in group theory.

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.

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

Covers the foundation of mathematics through set theory concepts like membership and unions.

Covers a recap of Analysis I and delves into the concept of open sets in R^n, emphasizing their importance in mathematical analysis.