Lecture

Counting: The Product Rule

Related lectures (28)

Cartesian Product and Induction

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

Cartesian Product: Sets and Recurrence

Explores the Cartesian product of sets, subsets, and recurrence in mathematics with examples and exercises.

Sets and Relations

Introduces sets, Cartesian product, order importance, and relations on sets.

Sets and Functions

Introduces sets, functions, and proofs in mathematics, covering set equality, subsets, Cartesian products, and truth sets of predicates.

Mathematics: Sets and Functions

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Operations on Sets: Parts, Intersection, and Difference

Explores operations on sets, Cartesian products, and functions' properties.

Advanced Analysis II: Recap and Open Sets

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

Cartesian Product in Linear Algebra

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

Cartesian Product

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

Euclidean Spaces: Properties and Concepts

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

Cartesian Products and Equivalence Relations

Introduces Cartesian products, equivalence relations, and functions, emphasizing the importance of order and discussing injective, surjective, and bijective functions.

Sets, Functions and Relations: Q&A

Covers examples of relation composition, Cartesian product, and injective functions.

Mapping Functions and Surjections

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

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Cartesian Product and Equivalence Classes

Covers the Cartesian product of sets and binary relations with detailed examples and graphical representations.

Sets and Operations: Introduction to Mathematics

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

Properties of Cartesian Products and Disjoint Unions

Introduces essential properties of Cartesian products and disjoint unions in the theory of groups and categories.

Commutation Groups: Euler's Totient Function

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

Group Actions on Sets

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

Counting Basics: Set Theory and Permutations

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