Mathematical proofs | Probabilistic arguments

List of probabilistic proofs of non-probabilistic theorems

Probability theory routinely uses results from other fields of mathematics (mostly, analysis). The opposite cases, collected below, are relatively rare; however, probability theory is used systematically in combinatorics via the probabilistic method. They are particularly used for non-constructive proofs. (Wikipedia).

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Existence Proofs

Ben discusses constructive and non-constructive proofs with examples.

From playlist Basics: Proofs

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Introduction to Common Mathematical Proof Methods

This video introduces the common methods of mathematical proofs and provides a basic example of a direct proof. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Introduction to Direct Proofs: If n is even, then n squared is even

This video introduces the mathematical proof method of direct proof provides an example of a direct proof. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Introduction to Proof by Counter Example

This video provides an introduction to the proof method of proof by counter example. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Writing Proofs | Proof by Contradiction Example 2

We prove a statement using the method of proof by contradiction.

From playlist Abstract Algebra

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Proof by Cases: For Any Integer, n^3-n is Odd

This video provides an introduction to the proof method of proof by cases mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Proofs by contradiction -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

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Introduction to Proof by Contradiction: sqrt(2) is irrational

This video introduces the mathematical proof method of proof by contradiction and provides an example of a proof. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Proof Exercise: Determine the Type of Proof to be Used

This video provides 3 examples of statements and which proof method should be used. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Total Functions in the Polynomial Hierarchy - Robert Kleinberg

Computer Science/Discrete Mathematics Seminar I Topic: Total Functions in the Polynomial Hierarchy Speaker: Robert Kleinberg Affiliation: Cornell University Date: February 08, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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Bálint Tóth - Invariance principle for random Lorentz (type) gasbeyond kinetics limit

Bálint Tóth (University of Bristol & Alfréd Rényi Institute of Mathematics) Invariance principle for random Lorentz gas beyond the Boltzmann-Grad limit. I will present a survey of invariance principles for the Lorentz gas and some related models, in a scaling regime going beyond the Bolt

From playlist Large-scale limits of interacting particle systems

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The Abel lectures: László Lovász and Avi Wigderson

0:30 Introduction by the Abel Prize Committee Chair, Hans Munthe-Kaas 02:42 László Lovász: Continuous limits of finite structures 49:27 Questions and answers 1:00:31 Avi Wigderson: The Value of Errors in Proofs 1:41:24 Questions and answers 1:50:20 Final remarks by John Grue, Chair of the

From playlist Abel Lectures

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CTNT 2018 - "The Biggest Known Prime Number" by Keith Conrad

This is lecture on "The Biggest Known Prime Number", by Keith Conrad, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2018 - Guest Lectures

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Bayesian Inference by Program Verification - Joost-Pieter Katoen, RWTH Aachen University

In this talk, I will give a perspective on inference in Bayes' networks (BNs) using program verification. I will argue how weakest precondition reasoning a la Dijkstra can be used for exact inference (and more). As exact inference is NP-complete, inference is typically done by means of sim

From playlist Logic and learning workshop

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The Biggest Known Prime Number - Keith Conrad [2018]

Slides for this talk: https://ctnt-summer.math.uconn.edu/wp-content/uploads/sites/1632/2018/05/mersennetalkCTNT.pdf May 29: Keith Conrad (UConn) Title: The Biggest Known Prime Number. Abstract: There are infinitely many primes, but at any moment there is a biggest known prime. Earlier t

From playlist Number Theory

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Prime Numbers - What is Known and Unknown, by Keith Conrad

This talk by Keith Conrad (UConn) was part of UConn's Number Theory Day 2017.

From playlist Number Theory Day

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23. Probabilistic Computation, BPP

MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Defined probabilistic Turing machines

From playlist MIT 18.404J Theory of Computation, Fall 2020

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Diffeomorphism groups of critical regularity by Sang-hyun Kim

PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, India), Anish Ghosh (TIFR, Mumbai, India), Subhajit Goswami (TIFR, Mumbai, India) and Mahan M J (TIFR, Mumbai, India) DATE & TIME: 27 February 2023 to 10 March 2023 VENUE: Madhava Lecture Hall

From playlist PROBABILISTIC METHODS IN NEGATIVE CURVATURE - 2023

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Proof by Contradiction: There are infinitely many primes

This video provides an example of proof by contradiction. mathispower4u.com

From playlist Symbolic Logic and Proofs (Discrete Math)

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Derandomization and its connections throughout complexity theory - Roei Tell

Computer Science/Discrete Mathematics Seminar II Topic: Derandomization and its connections throughout complexity theory Speaker: Roei Tell Affiliation: Member, School of Mathematics Date: February 15, 2022 This is the first talk in a three-part series presented together with Lijie Ch

From playlist Mathematics

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Wiener process | Channel capacity | Hausdorff–Young inequality | Fundamental theorem of algebra | Noisy-channel coding theorem | Introduction to systolic geometry | Banach–Mazur compactum | Law of large numbers | Atiyah–Singer index theorem | Bernstein polynomial | Brownian motion | Combinatorics | Claude Shannon | Ivan Privalov | Boundary (topology) | Maximum-minimums identity | Normal number | Minimal surface | Dvoretzky's theorem | Variance | Random compact set | Rogers–Ramanujan identities | Doob's martingale convergence theorems | Basel problem | Computable number | Markov chain | Von Neumann algebra | Holomorphic function | Harmonic function | Local time (mathematics) | Picard theorem | Tensor product of Hilbert spaces | Weierstrass function | Probabilistic method | Probability theory | The Doctrine of Chances | Émile Borel | Coupling (probability) | Crossing number inequality | Loewner's torus inequality | Stochastic calculus