Lectures related to Integer Cones

Composition of Applications in Mathematics

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

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

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

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Mapping Functions and Surjections

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

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Carathéodory's Theorem and Dimension Bound

Explores Carathéodory's Theorem and its dimension implications for set representation.

Cartesian Product and Induction

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

Information Measures: Entropy and Information Theory

Explains how entropy measures uncertainty in a system based on possible outcomes.

Functions: Definitions and Notations

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

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Proofs and Logic: Introduction

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

Finite Dimensional Spaces

Explores finite dimensional spaces, covering extraction process, bases generation, and space completion.

Correlations of the Liouville function

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Compression: Kraft Inequality

Explains compression and Kraft inequality in codes and sequences.

Hoare Logic: Foundations and Applications

Covers Hoare Logic, its foundations, applications, and significance in program verification.

Probability Theory: Integration and Convergence

Covers topics in probability theory, focusing on uniform integrability and convergence theorems.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.