Lectures related to Proofs: Contraposition vs. Contradiction

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Proofs: Logic, Mathematics & Algorithms

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

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Cartesian Product and Induction

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

Introduction to Analysis

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Proof Techniques: Examples

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Properties of Real Numbers: Bounds, Density, Absolute Value

Covers the properties of real numbers, including bounds, density, and absolute value.

Square Roots and Irrationality

Explores even squares, irrationality of √2, gaps in rational numbers, and minorants in Q.

Proofs and Logic: Introduction

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

Concept of Proof in Mathematics

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

Stable Laws and Limit Theorems

Explores stable laws, limit theorems, and random variable properties.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Linear Algebra: Properties and Operations

Explores subset properties, contraposition, and equivalence in linear algebra.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Proof Techniques: Direct, Contraposition, Cases

Covers proof techniques like direct, contraposition, and cases with examples.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Introduction to Proofs

Introduces informal proofs and their practical applications in computer science and mathematics, emphasizing the importance of proving theorems through direct and indirect methods.

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.

Zig Zag Lemma

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.