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Set Theory

2 rewiews
Comprehensive exploration of set theory fundamentals, covering key concepts and principles through structured lectures. Ideal for mathematics students seeking a deep understanding of this foundational topic.
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36 Lesons
1 day 5 hours
On-Demand
Free-Video
University of Chicago Department of Mathematics

Spectra and Definability in Combinatorial Sets of Reals

0 rewiews
Dive into the intricacies of spectra and definability in set theory with Vera Fischer's exploration of combinatorial sets of reals and cardinal characteristics of the continuum.
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1 Lesons
55 minutes
On-Demand
Free-Video

Mathematical Logic

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Explore statements, propositions, connectives, truth tables, tautology, and contradiction in mathematical logic.
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3 Lesons
30 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

O que é o Princípio da Casa dos Pombos?

0 rewiews
Explore o princípio da casa dos pombos, um conceito matemático fundamental, e suas aplicações em diversos campos da ciência e tecnologia.
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1 Lesons
23 minutes
On-Demand
Free-Video
BIMSA

Mathematical Logic: Unifications and Diversifications

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Explore mathematical logic's unifications and diversifications with Kazuyuki Tanaka, renowned expert in second-order arithmetic and reverse mathematics.
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1 Lesons
50 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Generic Absoluteness for the Definable Powerset of the Universally Baire Sets

0 rewiews
Explore generic absoluteness for the definable powerset of universally Baire sets in this advanced mathematical talk by Sandra Müller at the XVII International Luminy Workshop in Set Theory.
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1 Lesons
44 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Group Construction in C-minimal Structures

0 rewiews
Explorez la construction de groupes dans les structures C-minimales avec Françoise Delon, approfondissant les concepts mathématiques avancés en théorie des modèles.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

String Attractors of Rote Sequences

0 rewiews
Explore string attractors of Rote sequences in combinatorics on words, delving into mathematical concepts and their applications.
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1 Lesons
31 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Domino Snake Problems on Groups

0 rewiews
Explorez les problèmes de serpents de dominos sur les groupes mathématiques dans cette conférence approfondie de Nathalie Aubrun au CIRM.
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1 Lesons
42 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Automatic Actions in Geometric and Asymptotic Group Theory

0 rewiews
Explore geometric and asymptotic group theory, focusing on automatic actions in mathematics, with insights from Laurent Bartholdi's conference talk.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Böhm Trees and Taylor Expansion

0 rewiews
Explore Böhm trees and Taylor expansion in lambda calculus, delving into their mathematical properties and applications in differential linear logic.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Mestrado: Computação, Lógica e Teoria dos Conjuntos - Aula 01

0 rewiews
Explore fundamentos de computação, lógica e teoria dos conjuntos em aula de mestrado. Aborde linguagens formais, máquinas de registro, decidibilidade, complexidade algorítmica e lógica de primeira ordem.
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1 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Math TAU

Statistical Foundations of Common Knowledge

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Explore statistical foundations of common knowledge in game theory with Eduardo Faingold's insightful seminar presentation.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Models of Consciousness Conferences

The Strange Loops Inside Our Brains

0 rewiews
Explore the intriguing connection between Gödel's Incompleteness Theorem and consciousness, critically examining Hofstadter's analogies and their implications for understanding the mind-body problem.
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15 Lesons
18 minutes
On-Demand
Free-Video
Insights into Mathematics

Propositional Logic and the Algebra of Boole - N J Wildberger

0 rewiews
Overview of propositional logic, exploring atomic statements, connectives, truth values, and techniques for analysis. Covers tautologies, contradictions, truth tables, and equivalences, with a focus on Boole's algebraic approach.
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9 Lesons
33 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Usefulness of Useless Knowledge by Robbert Dijkgraaf - Followed by a Panel Discussion

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Explore the value of curiosity-driven research and its impact on technological progress, featuring insights from renowned scientists and a panel discussion on global science trends.
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49 Lesons
2 hours 31 minutes
On-Demand
Free-Video
Insights into Mathematics

A Brief History of Logic: From Leibniz to Boole - Math Foundations 254

0 rewiews
Explore the evolution of logic from Leibniz to Boole, covering key thinkers and innovations in systematic reasoning, diagram representations, and the introduction of mathematics to classical logic.
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1 Lesons
28 minutes
On-Demand
Free-Video
Write your own Operating System

Gödel's Proof of God - A Logician's Perspective

0 rewiews
Explore Gödel's ontological argument for God's existence through a logician's lens, examining key concepts and the proof's structure.
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9 Lesons
37 minutes
On-Demand
Free-Video
BunG Seminar

Higher Category Theory: DG Categories and Homological Algebra Applications - Talk 13

0 rewiews
Dive into higher category theory fundamentals, exploring DG categories and their applications in homological algebra through expert insights and practical examples.
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1 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Steve Brunton

Set Theory in Probability - Sample Spaces and Events

0 rewiews
Explore fundamental set theory concepts and their application in probability, including sample spaces, events, and key operations like unions and intersections through clear examples.
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9 Lesons
24 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Grothendieck Toposes as Unifying Bridges in Mathematics - Lecture 2

0 rewiews
Delve into Grothendieck toposes and their role as mathematical bridges, exploring how these structures enable the transfer of ideas between theories and lead to new discoveries in classical domains.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Insights into Mathematics

Logical Difficulties With the Modern Theory of Limits - Real Numbers + Limits Math Foundations

0 rewiews
Explores logical issues with the modern theory of limits in mathematics, examining the formal definition and its problems through examples and historical context.
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6 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

The Integral of X^n - Famous Math Problems

0 rewiews
Explores the integral of x^n, its historical development, and challenges in modern analysis. Proposes a new 'Algebraic Calculus' approach, addressing issues with continuum, infinite processes, and area theory.
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8 Lesons
44 minutes
On-Demand
Free-Video
IMSA

A Non-Archimedean Definable Chow Theorem

0 rewiews
Explore non-archimedean algebraization theorems and their applications in Diophantine geometry, focusing on a p-adic analogue of the definable Chow theorem.
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12 Lesons
45 minutes
On-Demand
Free-Video
IMSA

Model Theory - From Logic to Geometric Stability Theory and O-Minimality I

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Explore model theory principles, focusing on o-minimality and stability theory, with applications to complex geometry and arithmetic aspects.
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18 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Mixed Period Maps: Definability and Algebraicity

0 rewiews
Explore definable analytic spaces and their applications in algebraic geometry, focusing on period maps and mixed Hodge structures. Learn about o-minimal geometry and its role in proving key conjectures.
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14 Lesons
56 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Harry Altman- Lower Sets in Products of Well Ordered Sets

0 rewiews
Explore well partial orders, lower sets in products of ordinals, and weakly decreasing sequences. Gain insights into maximum linearizations and the surreal exponential.
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8 Lesons
33 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

David Cerna: Proof Schema and the Refutational Complexity of Their Cut Structure

0 rewiews
Explore proof schemas, refutational complexity, and cut structures in mathematical logic. Gain insights into CERES, ECA, and 1-SMA concepts for advanced theorem proving techniques.
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14 Lesons
39 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

A Stationary Set Method for Estimating Oscillatory Integrals

0 rewiews
Explore a stationary set method for estimating oscillatory integrals, with applications in number theory and Fourier analysis. Learn about o-minimal structures and geometric interpretations of upper bounds.
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19 Lesons
58 minutes
On-Demand
Free-Video
Fields Institute

Towards Reduction of Singularities of Generalized Analytic Functions

0 rewiews
Explore generalized analytic functions, focusing on singularity reduction techniques and their applications in tame geometry, with insights from complex analytic and nonarchimedean methods.
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19 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Applications of O-minimality to Hodge Theory - Lecture 4

0 rewiews
Explore infinitesimal thickening, definable spaces, and cell decomposition in o-minimality, with applications to Hodge theory and Abelian shields.
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11 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

Applications of O-minimality to Hodge Theory - Lecture 2

0 rewiews
Explore o-minimality's applications to Hodge Theory, covering definable spaces, fundamental domains, and Hodge metrics in this advanced graduate-level lecture.
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12 Lesons
46 minutes
On-Demand
Free-Video
Fields Institute

Tameness Beyond O-Minimality - Lecture 2

0 rewiews
Explore advanced mathematical concepts in tame geometry, focusing on o-minimality, metric dimensions, and related topics in real algebraic geometry.
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12 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Hilbert's 16th Problem and O-Minimality - Lecture 1

0 rewiews
Explore the topology of cycles, limit cycles, and related mathematical concepts in this advanced graduate-level lecture on Hilbert's 16th problem and o-minimality.
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9 Lesons
1 hour 43 minutes
On-Demand
Free-Video
Fields Institute

Decidability Bounds for Presburger Arithmetic Extended by Sine

0 rewiews
Explore decidability bounds in extended Presburger arithmetic with sine, covering previous results, methods, and the Channel conjecture in this mathematical seminar.
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18 Lesons
46 minutes
On-Demand
Free-Video
Fields Institute

Tameness Beyond O-Minimality - Lecture 1

0 rewiews
Explore advanced mathematical concepts beyond o-minimality, including real fields, partial orders, and postminimality in this graduate-level lecture on tame phenomena.
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10 Lesons
1 hour 28 minutes
On-Demand
Free-Video
Fields Institute

Complex Analysis in O Minimal Expansions of Real Closed Fields Lecture

0 rewiews
Explore complex analysis in o-minimal expansions, covering analytic functions, differentiability, and definability. Gain insights into advanced mathematical concepts and their applications.
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10 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

Complex Analysis in O-minimal Expansions of Real Closed Fields - Lecture 2

0 rewiews
Explore complex analysis in o-minimal expansions of real closed fields, covering topics from linearly ordered fields to finite extensions and K-linear matrices.
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10 Lesons
51 minutes
On-Demand
Free-Video
Fields Institute

O-minimality and the Pila-Wilkie Theorem - Lecture 1

0 rewiews
Explore o-minimality, its foundations, and key theorems in this graduate-level lecture, emphasizing mathematical concepts and their applications in tame geometry.
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15 Lesons
1 hour 40 minutes
On-Demand
Free-Video
Fields Institute

Introduction to O-Minimality and the Pila-Wilkie Theorem

0 rewiews
Explore o-minimality and the Pila-Wilkie Theorem, covering definitions, examples, proofs, and key concepts in tame geometry. Gain insights into this fundamental area of mathematical logic and its applications.
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17 Lesons
48 minutes
On-Demand
Free-Video
Fields Institute

Effectivity of Standard O-Minimal Results in the Sharply O-Minimal Setting

0 rewiews
Explore the effectiveness of o-minimal results in sharply o-minimal contexts, covering algebraic lemmas, cellular versions, and cylindrical parametrization techniques.
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9 Lesons
39 minutes
On-Demand
Free-Video
Fields Institute

Topics in Pure Model Theory - Lecture 10

0 rewiews
Explore advanced concepts in pure model theory, including simple theory, invariant types, and symmetry, with expert insights from Itay Kaplan of The Hebrew University of Jerusalem.
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8 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Fields Institute

Topics in Pure Model Theory - Lecture 8

0 rewiews
Explore stable theory, nonforking, and Kim's lemma in pure model theory with Prof. Itay Kaplan, delving into advanced concepts and proofs in this comprehensive lecture.
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10 Lesons
1 hour 32 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Why Study Fluid Mechanics?

0 rewiews
Explore the importance and applications of fluid mechanics in this engaging lecture by Rama Govindarajan, offering insights into this fundamental field of physics and engineering.
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1 Lesons
50 minutes
On-Demand
Free-Video
IMSA

Model Theory: From Logic to Geometric Stability Theory and O-Minimality II

0 rewiews
Explore model theory principles, focusing on o-minimality and stability theory, with applications to complex geometry and arithmetic aspects.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Tame Geometry and Hodge Theory II

0 rewiews
Explores applications of tame geometry in Hodge theory, covering algebraization results, tameness of period maps, functional transcendence, and atypical intersection conjectures in complex algebraic geometry.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
International Mathematical Union

Tameness in Geometry and Arithmetic: Beyond O-Minimality

0 rewiews
Explore advanced concepts in geometry and arithmetic, focusing on tameness beyond o-minimality, with mathematicians Dmitry Novikov and Gal Binyamini.
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1 Lesons
49 minutes
On-Demand
Free-Video
IMSA

Carlos A. Ruiz, UNAM - Quantum Toric Geometry, Generalized Geometries & O-Minimality Conference

0 rewiews
Explore advanced mathematical concepts in quantum toric geometry, generalized geometries, and o-minimality with expert Carlos A. Ruiz from UNAM in this in-depth conference presentation.
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1 Lesons
55 minutes
On-Demand
Free-Video
Fields Institute

Strongly Linear Maps on Bounded Hahn Fields- Applications to Derivations, Logarithms, Automorphisms

0 rewiews
Explore strongly linear maps on bounded Hahn fields and their applications to derivations, logarithms, and automorphisms in this advanced mathematics lecture.
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1 Lesons
57 minutes
On-Demand
Free-Video
Fields Institute

Partial Desingularization

0 rewiews
Explore partial desingularization in tame geometry, examining interactions between o-minimal, complex analytic, and nonarchimedean methods.
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1 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

Dichotomy Interlacement Versus Hardy in Definable ODE's

0 rewiews
Explore the interplay between dichotomy interlacement and Hardy's theory in definable ordinary differential equations, delving into advanced mathematical concepts and their applications.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Applications of O-minimality to Hodge Theory - Lecture 6

0 rewiews
Explore advanced concepts in o-minimality and their applications to Hodge Theory in this graduate-level lecture by Jacob Tsimerman from the University of Toronto.
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1 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

Applications of O-minimality to Hodge Theory - Lecture 1

0 rewiews
Explore o-minimality's applications in Hodge Theory, delving into advanced mathematical concepts and their interconnections in this graduate-level lecture by Jacob Tsimerman.
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1 Lesons
1 hour 41 minutes
On-Demand
Free-Video
Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 8

0 rewiews
Explore advanced concepts in complex analysis within o-minimal expansions of real closed fields, focusing on theoretical foundations and applications in mathematical logic.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 7

0 rewiews
Explore advanced concepts in complex analysis within o-minimal expansions of real closed fields, focusing on theoretical foundations and applications in mathematical logic.
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1 Lesons
1 hour 42 minutes
On-Demand
Free-Video
Fields Institute

Transseries, Model Theory, and Hardy Fields - Lecture 14

0 rewiews
Explore advanced mathematical concepts in transseries, model theory, and Hardy fields with expert Lou van den Dries in this graduate-level lecture from the Fields Institute.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 4

0 rewiews
Explore advanced concepts in complex analysis within o-minimal expansions of real closed fields, building on previous lectures in this graduate-level series.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 3

0 rewiews
Explore advanced concepts in complex analysis within o-minimal expansions of real closed fields, building on previous lectures in this graduate-level series.
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1 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 1

0 rewiews
Explore complex analysis in o-minimal expansions of real closed fields, delving into advanced mathematical concepts and their applications in this graduate-level lecture.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
Fields Institute

O-Minimality and Parametrizations

0 rewiews
Explore o-minimality theory and its applications in parametrizations, gaining insights into this fundamental concept in mathematical logic and model theory.
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1 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

O-minimality and the Pila-Wilkie Theorem - Lecture 2

0 rewiews
Explore o-minimality and the Pila-Wilkie theorem in this advanced graduate-level mathematics lecture, delving into complex algebraic geometry concepts and their applications.
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1 Lesons
48 minutes
On-Demand
Free-Video
Fields Institute

Transseries, Model Theory, and Hardy Fields - Lecture 1

0 rewiews
Explore advanced mathematical concepts in transseries, model theory, and Hardy fields with Professor Lou van den Dries in this graduate-level lecture series.
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1 Lesons
51 minutes
On-Demand
Free-Video
Fields Institute

Tameness in Geometry and Arithmetic - Beyond O-Minimality

0 rewiews
Explore geometric and arithmetic tameness beyond o-minimality, delving into advanced mathematical concepts and their applications in analysis and geometry.
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1 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Tameness Beyond O-Minimality

0 rewiews
Explore advanced concepts in tame geometry, focusing on tameness beyond o-minimality, with insights from Philipp Hieronymi's research in mathematical logic and model theory.
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1 Lesons
55 minutes
On-Demand
Free-Video
Fields Institute

Topics in Applied Model Theory - Lecture 12

0 rewiews
Explore advanced concepts in model theory, including risky closures, algebraic groups, and PAC fields, with expert insights from Zoé Chatzidakis of CNRS-ENS.
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8 Lesons
1 hour 34 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Computing with Gödel's Completeness Theorem

0 rewiews
Explore computational approaches to Gödel's completeness theorem, including Krivine's "exploding models," A-translation, and Kripke forcing, with insights on reifying validity proofs into derivability proofs.
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1 Lesons
46 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Derived Rules in Set Theory

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Explore intuitionistic set theories and learn about a general machinery for demonstrating derived rules in this advanced mathematical lecture.
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1 Lesons
42 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Triposes and Gödel's Dialectica Interpretation

0 rewiews
Exploring semantic presentation of Gödel's Dialectica interpretation using triposes, addressing previous work and suggesting solutions to related questions in mathematical logic.
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1 Lesons
30 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Two Observations on Intuitionistic Logic and Arithmetic

0 rewiews
Explore intuitionistic logic and arithmetic through finite type formalisation and negative translations. Gain insights into extensional and intensional models, decidable atomic formulas, and equality at higher types.
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1 Lesons
36 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

First Order Concatenation Theory vs First Order Number Theory

0 rewiews
Comparative analysis of first-order concatenation theory and number theory, exploring similarities, differences, and extensions with bounded quantifiers in string-based structures.
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1 Lesons
28 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Matthias Baaz - Fast Cut Elimination in Intuitionistic Logic

0 rewiews
Explores elementary procedure for eliminating prenex cuts in intuitionistic logic, with implications for classical logic. Discusses surprising results in quantifier-based cut elimination.
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1 Lesons
37 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Absorption Law for Slow Provability

0 rewiews
Explore the absorption law for slow provability, its simple proof, and application to Heyting Arithmetic's provability logic in this mathematical lecture by Albert Visser.
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1 Lesons
31 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Reverse Mathematics of Caristi's Fixed Point Theorem and Ekeland's Variational Principle

0 rewiews
Explore the mathematical strengths of Caristi's fixed point theorem and Ekeland's variational principle, examining their implications in complete separable metric spaces and their connections to various axiom systems.
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1 Lesons
33 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Hugo Herbelin- Investigations into Cubical Type Theory

0 rewiews
Exploration of a variant of cubical type theory with type-based equality, direct coercion, and primitive composition, aiming for a parametricity translation to identity type theory.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Ulrich Kohlenbach: Extraction of Information from Proofs

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Explore proof mining techniques and their applications in mathematics, focusing on extracting computational content from nonconstructive proofs in analysis and ergodic theory.
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1 Lesons
57 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Ulrich Kohlenbach - Extraction of Information from Proofs

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Explore proof theory and its applications in mathematics, focusing on extracting computational content from nonconstructive proofs for practical problem-solving.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
NIOS

Discrete Mathematics

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Explore logic, probability, graph theory, relations, and combinatorics in this comprehensive mathematics course, enhancing problem-solving skills and mathematical reasoning abilities.
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33 Lesons
1 day 4 hours
On-Demand
Free-Video
Fields Institute

Connections Between Boolean-Valued Logic and Ergodic Structure Theory

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Explore the intriguing links between Boolean-valued logic and ergodic structure theory in this insightful talk by Asgar Jamneshan, delving into advanced mathematical concepts and their applications.
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1 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

Tracially Complete C*-Algebras

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Explore the concept of tracially complete C*-algebras in this advanced mathematical lecture, delving into operator algebras and their applications in logic and analysis.
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1 Lesons
52 minutes
On-Demand
Free-Video
IEEE

On the Existence of Algebraically Natural Proofs

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Explore the concept of algebraically natural proofs in mathematics, examining their existence and implications for computational complexity theory.
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1 Lesons
23 minutes
On-Demand
Free-Video
Paul G. Allen School

On Making Mathematical Proof a Business - Allen School Distinguished Lecture

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Explore how Amazon leverages automated reasoning and mechanized proof search in mathematical logic for software development, with insights on challenges and future scalability.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Insights into Mathematics

How to Set Up Fractions - Famous Math Problems 24

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Rigorous exploration of fraction theory, covering fundamental operations, comparisons, proofs, and arithmetic laws. Emphasizes the importance of robust number systems in mathematics.
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9 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Inconvenient Truths About the Square Root of 2 - Real Numbers and Limits

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Explores the concept of sqrt(2), its historical significance, and modern approaches, challenging traditional views on irrational numbers and highlighting logical issues in mathematical analysis.
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10 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Pure and Applied Geometry - Understanding the Continuum - Universal Hyperbolic Geometry 20

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Explores the distinction between pure and applied geometry, challenging traditional views on real numbers and the continuum. Offers a rational number-based approach to understanding geometric concepts and continuums.
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10 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers as Cauchy Sequences - Limitations and Challenges - Math Foundations 114

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Explores logical weaknesses in using Cauchy sequences to define real numbers, challenging traditional approaches and highlighting ambiguities in fundamental mathematical concepts.
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13 Lesons
52 minutes
On-Demand
Free-Video
Insights into Mathematics

Dedekind Cuts and Computational Difficulties with Real Numbers - Famous Math Problems 19

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Explores the challenges and misconceptions surrounding 'real numbers', examining various approaches like infinite decimals, Dedekind cuts, and Cauchy sequences, while emphasizing the importance of concrete computations in mathematics.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Insights into Mathematics

Are All True Mathematical Statements Provable? - Famous Math Problems

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Explores the philosophical question of mathematical truth and provability, challenging conventional views with explicit examples of likely true but unprovable mathematical statements.
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9 Lesons
31 minutes
On-Demand
Free-Video
Insights into Mathematics

Infinite Sequences - Understanding Finite and Ongoing Sequences in Mathematics - Math Foundations 99

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Explore the concept of infinite sequences, focusing on natural numbers, primes, and Catalan numbers. Examine the distinctions between finite and ongoing sequences, and delve into various definitions and formulas.
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11 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

The Magic and Mystery of Pi - Real Numbers and Limits

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Explore the history, formulas, and philosophical implications of pi, from ancient calculations to modern computations, challenging traditional views on its nature and role in mathematics.
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11 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Logical Challenges in Abstract Algebra - Math Foundations 214

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Explores logical difficulties in abstract algebra, focusing on defining groups and the impact of different definitions on group theory development. Emphasizes critical thinking in mathematical foundations.
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1 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

A New Trichotomy for Integer Arithmetic - Math Foundations 206

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Novel approach to integer arithmetic using marks, anti-marks, and nothing. Explores symmetry between natural and negative numbers, foundational arithmetic of integers, and the role of multisets in organizing mathematical objects.
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1 Lesons
22 minutes
On-Demand
Free-Video
Insights into Mathematics

The Successor-Limit Hierarchy and Ordinals - Part 2

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Explores the connection between the successor-limit hierarchy and ordinal numbers in set theory, critiquing modern mathematical foundations and suggesting potential reinterpretations of ordinal theory.
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6 Lesons
25 minutes
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Insights into Mathematics

Logical Difficulties with Cyclotomic Fields - Famous Math Problems 20

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Explores logical issues in cyclotomic fields, focusing on the challenges of embedding roots of unity into complex numbers and the limitations of purely algebraic approaches.
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1 Lesons
29 minutes
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Insights into Mathematics

The Algebra of Boole and Boolean Algebra - Key Differences - Part 1

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Introduction to the Algebra of Boole, focusing on the bifield of two elements and n-tuples. Explores its role in circuit analysis and contrasts it with Boolean algebra, highlighting implications for 20th-century mathematics.
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1 Lesons
38 minutes
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Churchill CompSci Talks

Kolmogorov Complexity and Gödel's Incompleteness Theorems

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Explore Kolmogorov complexity, randomness, and compressibility in data, and discover their surprising connections to Gödel's incompleteness theorems in mathematical logic.
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1 Lesons
26 minutes
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Hausdorff Center for Mathematics

Beautiful Formalizations and Proofs in Mechanized Mathematics

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Explore the aesthetics of mathematical formalization, examining how beauty in mathematics adapts to mechanization and automation, with illustrative examples of elegant definitions and proofs.
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1 Lesons
40 minutes
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Hausdorff Center for Mathematics

Towards a Formalized Proof of Carleson's Theorem

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Explores formalizing Carleson's theorem on Fourier series convergence, discussing its significance, challenges, and recent generalizations in metric spaces using the Lean theorem prover.
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1 Lesons
39 minutes
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Hausdorff Center for Mathematics

Calculating Ordinal Invariants - Can You Do Better Than a Human?

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Explore ordinal invariants calculation techniques, comparing human and computational approaches in this advanced mathematics lecture by Mirna Džamonja.
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1 Lesons
56 minutes
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Hausdorff Center for Mathematics

Dialectica Categories for All

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Explore dialectica categories and their applications in logic, mathematics, and computer science with expert Valeria de Paiva in this insightful talk.
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1 Lesons
52 minutes
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Hausdorff Center for Mathematics

Capturing Mathematical Equality - Constructivism and Canonical Isomorphisms

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Explore the impact of rejecting constructivism in mathematics, examining the confusion between theorems and definitions and the overuse of "canonical isomorphism" in number theory.
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1 Lesons
35 minutes
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