Lectures related to Mathematical Proofs: Induction, Inequalities, Divisibility, Subsets

Cartesian Product and Induction

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

Mathematical Induction: Proofs and Subsets

Covers proofs by mathematical induction and the number of subsets of a finite set.

Proofs: Logic, Mathematics & Algorithms

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

Formal Logic: Proofs and Sets

Covers the basics of formal logic, focusing on logical expressions and mathematical proofs.

Proofs by Induction: Principles and Examples

Explains the induction principle and proofs by induction with examples like 1 + 3 + 5 + ... + (2n-1) = n².

Recursively Defined Functions

Introduces recursively defined functions and demonstrates how to compute values and prove properties using mathematical induction.

Fourier Inversion Formula

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

Recursion and Induction: Understanding Mathematical Proofs

Explores recursion and induction for mathematical proofs through recursive algorithms and functions.

Strong Induction: The Power of Mathematical Proof

Explores strong induction as a powerful proof method with advantages over mathematical induction, demonstrated through a theorem about expressing integers as sums of powers of two.

Existence of Gibbs measures

Explores quasilocality in statistical mechanics and the existence conditions of Gibbs measures.

Inductive Propositions: Reasoning and Evaluation Techniques

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

Recurrence Demonstrations: Principle and Examples

Covers the principle of recurrence demonstrations with examples illustrating the process step by step.

Linear Algebra: Propositions and Sets

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.

Limits of Sequences: Induction, Bernoulli's Inequality, and Algebra

Explores induction, Bernoulli's inequality, and algebraic limits in sequences with examples and computations.

Induction and Recursion: Examples + Q&A

Covers examples and a Q&A session on induction and recursion.

Martingale Convergence Theorem: Proof and Stopping Time

Explores the proof of the martingale convergence theorem and the concept of stopping time in square-integrable martingales.

Wayl's Theorem: Polynomial Clarity

Focuses on the proof of Wayl's theorem through polynomial manipulation and induction.

Mathematical Induction: Basics and Applications

Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.

Formally Secure Compilation: Ensuring Component Security

Explores formally secure compilation, emphasizing the importance of mathematical proofs and compartmentalization in ensuring component security.

Generalization Error

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