Lectures related to Set Theory: Introduction and Operations

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.

Understanding Equivalence Relations and Integer Construction

Covers the construction of integers through equivalence relations and their properties in mathematics.

Injective Functions: Properties and Examples

Covers the properties of injective functions and demonstrates their proofs through examples and visual aids.

Commutation Groups: Euler's Totient Function

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

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.

Counting Basics: Set Theory and Permutations

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

Real Numbers: Sets and Operations

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.

Proofs and Sets: Applications

Covers the basics of proofs, defining sets, and applications between sets.

Sets and Operations: Introduction to Mathematics

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

Group Actions on Sets

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

Euclidean Spaces: Properties and Concepts

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

Linear Algebra: Propositions and Sets

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

Set Difference: Definition and Examples

Explains set difference and complement calculation with clear examples.

Cartesian Product: Sets and Recurrence

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

Propositional Calculus

Covers the basics of propositional calculus and its importance in computer science.

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Recursive Enumerability: Turing Machines and Undecidable Languages

Covers recursively enumerable languages, Turing machines, and the construction of undecidable languages.

Sets and Functions

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