Lectures related to Linear Algebra: Sets and Propositional Language

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

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

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

Introduces fundamental concepts of linear algebra, focusing on sets and operations.

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

Covers sets, subsets, and their notation, including the power set concept.

Introduces sets and functions, covering union, intersection, complement, functions terminology, and set operations analogies.

Explores bijections in linear algebra and the concept of cardinality between sets.

Covers the basics of discrete mathematics, focusing on logic, structures, and algorithms for computer systems.

Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.

Covers the basics of discrete mathematics, including logic, structures, and algorithms.

Covers the construction of R and equivalence relations in sequences and linear recurrences.

Explores cardinality in sets and properties of groups, including commutativity and examples of abstract groups.

Introduces cardinality and mapping in linear algebra, illustrating concepts with examples and visual aids.

Explores recursively defined sets, natural numbers, strings, functions, string concatenation, and well-formed formulae.

Covers the definition of applications, image of elements, and direct and reciprocal images.

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

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

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

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