Lectures related to Combinatorial Proofs: Frobenius Theorem

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

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.

Proofs and Logic: Introduction

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Mathematical Induction: Principle and Example

Introduces the principle of mathematical induction through an example.

Concept of Proof in Mathematics

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

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Recurrence: Induction

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

Neuro-symbolic Representations: Commonsense Knowledge & Reasoning

Delves into neuro-symbolic representations for commonsense knowledge and reasoning in natural language processing applications.

Proof of Main Lemma

Covers the proof of the main lemma and its mathematical properties.

Inductive Propositions: Reasoning and Evaluation Techniques

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

Linear Algebra: Injective Functions

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

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Neuro-symbolic Representations: Commonsense Knowledge & Reasoning

Explores neuro-symbolic representations for understanding commonsense knowledge and reasoning, emphasizing the challenges and limitations of deep learning in natural language processing.

Counting Poker Dices: Combinatorial and Analytical Proofs

Explores cable connections, poker dice rolls, and analytical proofs in mathematics.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Ordinary Differential Equations: Definitions and Methods

Explores ordinary differential equations, proof methods, and historical examples from Euclid, emphasizing logical reasoning and step-by-step derivations.

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Irreducible Representations of Rotations Group

Explores irreducible representations of the rotations group and their mathematical properties.