Lectures related to Wayl's Theorem: Polynomial Clarity

Proofs: Logic, Mathematics & Algorithms

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

Rigorous Proof of Differential Equations

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

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Cartesian Product and Induction

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

Recurrence Exercise Correction

Covers the correction of an additional exercise on recurrence, demonstrating the step-by-step process.

Analysis IV: Measurable Sets and Properties

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

Fourier Inversion Formula

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

Formal Logic: Proofs and Sets

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

Modular Arithmetic: Foundations and Applications

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

Inductive Propositions: Reasoning and Evaluation Techniques

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

Concept of Proof in Mathematics

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

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Prime Number Theorem

Explores the proof of the Prime Number Theorem and its implications in number theory.

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Linear Independence: The Wronskian Concept

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

Injective Functions: Properties and Examples

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

Generalization Error

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

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.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Introduction to Coq: Arithmetic Expressions and Evaluators

Covers the basics of Coq, focusing on arithmetic expressions, evaluation, and proof techniques.