Lectures related to Philosophy of Mathematics: Ontology and Structures

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

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.

Sequences and Convergence: Understanding Mathematical Foundations

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

Propositional Logic: Basics and Applications

Covers the basics of propositional logic, its history, language, and computing applications.

Logic and Truth Tables

Covers logic, truth tables, and mathematical propositions, demonstrating how to analyze logical statements.

Introduction & Propositional Logic

Covers the basics of propositional logic, logical connectives, truth tables, and compound propositions.

Sets and Operations: Introduction to Mathematics

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

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Logic Systems: Basics and Operators

Covers the basics of logic systems, including digital versus analog circuits, logic operators, truth tables, and Boolean algebra.

FSM Design and Synthesis

Explains the design and synthesis of Finite State Machines in logic systems.

Boolean Algebra: Properties and Theorems

Covers the properties and theorems of Boolean algebra in logic systems.

Injective Functions: Properties and Examples

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

Sets and Functions

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

Discrete Mathematics: Logic & Structures

Covers propositional logic, truth tables, and problem-solving strategies in discrete mathematics.

Monstrous Moonshine

Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.

Logic in Mathematics: Properties and Propositions

Explores the significance of logic in mathematics and science through properties and propositions.

Propositional Logic: Basics and Equivalences

Covers the basics of propositional logic and explores logical equivalences and proof techniques.

Optimizing Logic Functions

Covers the optimization of logic functions using Karnaugh diagrams and dealing with incomplete defined functions.

Proofs: Logical Equivalence and Inference Rules

Covers the concept of logical equivalence in proofs and inference rules.

Understanding Equivalence Relations and Integer Construction

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