Lectures related to Reasoning about lists

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Operations in Z

Covers addition properties and operations in the set of integers Z.

Model Extension and Composition of Functions

Explores model extension, function composition, graph uniqueness, and mathematical induction principles.

Group Theory: Definition and Examples

Covers the definition of a group, properties of symmetries, and group operations.

Group Theory Basics

Introduces the basics of group theory, including operations, properties, and Lie groups.

Cartesian Product and Induction

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

Properties of Rational Multiplication

Covers the properties of rational multiplication through fractions and simple calculations, leading to the resolution of division problems.

Elliptic Curves: Group Structure and Isomorphism

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Geometric Series: Convergence and Applications

Explores the convergence of geometric series and their applications in real-world problems.

Polynomials and Endomorphisms

Covers the properties of rings, examples of rings, and polynomials.

Groups and Numbers: Mathematical Elements on Groups

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Set Union: Properties and Operations

Explains the union of sets, its properties, operations, and intersection.

Mathematical Recursion: Induction and Recursion

Explains mathematical induction for proving propositions true for all positive integers.

Symmetries in Physics

Explores symmetries in physics through group theory, emphasizing how symmetries keep equations of motion unchanged.

Natural Transformations Composition

Covers the theory of categories, emphasizing the importance of naturalness in the composition of transformations.

Associative Operations: Fundamentals

Covers associative and commutative operations in parallel programming, using mathematical examples and discussing challenges in preserving associativity.

Lie Algebra: Group Theory

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Recurrence Demonstrations: Principle and Examples

Covers the principle of recurrence demonstrations with examples illustrating the process step by step.

Q is a Field

Covers the properties of rational numbers and introduces the concept of an ordered field in Q.