Lectures related to Recurrence Demonstrations: Principle and Examples

Cartesian Product and Induction

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

Proofs by Induction: Principles and Examples

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

Linear Algebra: Propositions and Sets

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

Geometric Series: Convergence and Applications

Explores the convergence of geometric series and their applications in real-world problems.

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.

Recursion and Induction: Understanding Mathematical Proofs

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

Mathematical Recursion: Induction and Recursion

Explains mathematical induction for proving propositions true for all positive integers.

Mathematical Recursion: Induction and Recursion

Covers the principle of mathematical induction for proving propositions true for all positive integers.

Rigorous Proof of Differential Equations

Covers the rigorous proof of differential equations, emphasizing accuracy and precision.

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

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

Inductive Propositions: Reasoning and Evaluation Techniques

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

Induction and Recursion: Examples + Q&A

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

Strong Induction: Proof Method and Application

Explores strong induction as a proof method and demonstrates its application in proving a theorem about positive integers.

Induction and Recursion: Mathematical and Strong Induction - An Example

Covers the concepts of mathematical and strong induction through an example.

Mathematical Induction: Principle and Example

Introduces the principle of mathematical induction through an example.

Mathematical Induction: Basics and Applications

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

Linear Algebra: Multilinear Groin and Determinants

Explores multilinear groin and determinants, including the Sarrus rule and proof by induction.

Reasoning about lists

Covers laws of list concatenation, proof by induction, referential transparency, and structural induction.

Complexity & Induction: Algorithms & Proofs

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Formal Logic: Proofs and Sets

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