Lecture

Proofs: Logic, Mathematics & Algorithms

Related lectures (30)

Concept of Proof in Mathematics

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

Cartesian Product and Induction

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

Proofs and Logic: Introduction

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

Composition of Applications in Mathematics

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

Elementary Algebra: Numeric Sets

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

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Fundamental Groups

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

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 Proofs

Introduces informal proofs, explores practical applications, and explains theorem proofs using direct and indirect methods.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Propositions and Proofs

Explores propositions, proofs, and contraposition in mathematical theory, emphasizing logical rules and proof methods.

Proof Techniques: Examples

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

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Sparsest Cut: ARV Theorem

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.

Correlations of the Liouville function

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

Proofs: Contraposition vs. Contradiction

Covers the concepts of contraposition and contradiction in proofs.

Fourier Inversion Formula

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.