Lectures related to Proof Techniques: Quiz Analysis

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.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Cartesian Product and Induction

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

Proof Techniques: Examples

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

Zig Zag Lemma

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

Inductive Propositions: Reasoning and Evaluation Techniques

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

Fourier Inversion Formula

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

The Languages of Isabelle: Isar, ML, and Scala

Explores the languages of Isabelle, focusing on Isar, ML, and Scala, covering proof schemes, Natural Deduction rules, inductive definitions, and the LCF approach.

Proofs: Contraposition vs. Contradiction

Covers the concepts of contraposition and contradiction in proofs.

Analysis IV: Measurable Sets and Properties

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

Proofs: Rules and Applications

Explores rules of inference, quantified statements, and proof methods in logic and mathematics.

Generalization Error

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Proofs and Logic: Introduction

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

Holomorphic Functions: Taylor Series Expansion

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

Proof of Convergence Rate Theorem

Covers the proof of the convergence rate theorem, emphasizing the correction of a missing factor sqrt{pi_j} in the proof.

Implicit Functions: Unique Solutions and Class C Functions

Covers the proof of the theorem of implicit functions and the concept of class C functions.

Prime Numbers: Euclid's Theorem

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

Coq Workshop: Introduction to Interactive Theorem Proving

Introduces Coq, an interactive theorem assistant based on the Curry-Howard isomorphism.

Compression: Kraft Inequality

Explains compression and Kraft inequality in codes and sequences.