Lectures related to Mathematical Induction: Principle and Example

Covers the principle of induction for natural numbers and the importance of caution in its application.

Inductive Propositions: Understanding Evaluation in Coq

Covers inductive propositions in Coq, focusing on evaluation rules for arithmetic expressions and their applications in defining partial and non-deterministic functions.

Inductive Propositions: Reasoning and Evaluation Techniques

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

Recursion and Induction: Understanding Mathematical Proofs

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

Linear Algebra: Reciprocity and Equivalence

Explores reciprocity, equivalence, and proof techniques in linear algebra, emphasizing logical reasoning and mathematical rigor.

Untitled

Supremum Theorem

Explores the Supremum Theorem, its properties, proofs, and exercises.

Linear Algebra: Injective Functions

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Concept of Proof in Mathematics

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

Theorem: Regularity Conditions and Rigorous Proofs

Discusses regularity conditions and rigorous proofs in mathematical theorems, emphasizing precision and accuracy.

Injective Functions: Properties and Examples

Covers the properties of injective functions and demonstrates their proofs through examples and visual aids.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Convex Functions

Covers the definition of convex functions and their properties in optimization.

Coq Workshop: Introduction to Interactive Theorem Proving

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

Proofs by Induction: Principles and Examples

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

Cartesian Product and Induction

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

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Proof of Explicit Formula

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.