Mathematical Induction: Principle and Example

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Recurrence: Induction

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.

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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.