Lectures related to Square Roots and Irrationality

Real Numbers: Order and Completeness

Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.

Introduction to Analysis: Understanding Real Numbers and Proofs

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

Geometric Meanings: Euclidean Division and Divine Proportion

Explores the historical and mathematical significance of Euclidean Division and the Divine Proportion in geometry and art.

Dedekind Cuts: Rational Numbers

Explores Dedekind cuts in rational numbers, essential for constructing real numbers.

Roots of Real Numbers

Explores the properties and applications of roots of real numbers through practical examples.

Real Numbers: Axioms and Bounds

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Algebraic Fields: Transcendence Degree

Explores transcendence degree in algebraic fields and classical analytic functions.

Proofs and Logic: Introduction

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

Stable Laws and Limit Theorems

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