Real numbers and Cauchy sequences of rationals(I) | Real numbers and limits Math Foundations 111
We introduce the idea of a `Cauchy sequence of rational numbers'. The notion is in fact logically problematic. It involves epsilons and N's, much as does the notion of a limit, and suffers from similiar issues: how to guarantee that we can find an infinite number of N's for an infinite num
From playlist Math Foundations
Duality Theorem In this video, I use a neat little trick to show that the limit as n goes to infinity of 2^n is infinity, by using the fact (shown before) that the limit of (1/2)^n is 0. Exponential Limit: https://youtu.be/qxlSclbmh-w Other examples of limits can be seen in the playlis
From playlist Sequences
Infinite Limits (Limit Example 10)
Epsilon Definition of a Limit In this video, I illustrate the epsilon-N definition of a limit by doing an example with an infinite limit. More precisely, I prove from scratch that the limit of sqrt(n-2)+3 is infinity Other examples of limits can be seen in the playlist below. Check ou
From playlist Sequences
Here's a re-enactment of the famous paradox known as the "infinite monkey theorem."
From playlist Cosmic Journeys
Proof: Convergent Sequence is Bounded | Real Analysis
Any convergent sequence must be bounded. We'll prove this basic result about convergent sequences in today's lesson. We use the definition of the limit of a sequence, a useful equivalence involving absolute value inequalities, and then considering a maximum and minimum will help us find an
From playlist Real Analysis
Convergent sequences are bounded
Convergent Sequences are Bounded In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy! Other examples of limits can be seen in the
From playlist Sequences
Extremal Combinatorics with Po-Shen Loh - 04/27 Mon
Carnegie Mellon University is protecting the community from the COVID-19 pandemic by running courses online for the Spring 2020 semester. This is the video stream for Po-Shen Loh’s PhD-level course 21-738 Extremal Combinatorics. Professor Loh will not be able to respond to questions or com
From playlist CMU PhD-Level Course 21-738 Extremal Combinatorics
Epsilon delta limit (Example 3): Infinite limit at a point
This is the continuation of the epsilon-delta series! You can find Examples 1 and 2 on blackpenredpen's channel. Here I use an epsilon-delta argument to calculate an infinite limit, and at the same time I'm showing you how to calculate a right-hand-side limit. Enjoy!
From playlist Calculus
Lower bounds for subgraph isomorphism – Benjamin Rossman – ICM2018
Mathematical Aspects of Computer Science Invited Lecture 14.3 Lower bounds for subgraph isomorphism Benjamin Rossman Abstract: We consider the problem of determining whether an Erdős–Rényi random graph contains a subgraph isomorphic to a fixed pattern, such as a clique or cycle of consta
From playlist Mathematical Aspects of Computer Science
"Infinite sequences": what are they? | Real numbers and limits Math Foundations 99 | N J Wildberger
This lecture tries to clarify the big gap between the (finite) sequences we introduced in the last lecture, and "infinite" or "ongoing sequences" (we introduce the term "on-sequence") as are found in Sloane's Online Encyclopedia of Integer Sequences. We concentrate discussion on three such
From playlist Math Foundations
Nexus trimester - David Gamarnik (MIT)
(Arguably) Hard on Average Optimization Problems and the Overlap Gap Property David Gamarnik (MIT) March 17, 2016 Abstract: Many problems in the area of random combinatorial structures and high-dimensional statistics exhibit an apparent computational hardness, even though the formal resu
From playlist 2016-T1 - Nexus of Information and Computation Theory - CEB Trimester
Computing Limits from a Graph with Infinities
In this video I do an example of computing limits from a graph with infinities.
From playlist Limits
Anupam Gupta: The Independent Set problem on Degree d Graphs
Anupam Gupta: The Independent Set problem on Degree d Graphs The independent set problem on graphs with maximum degree d is known to be Ω(d/log2 d) hard to approximate, assuming the unique games conjecture. However, the best approximation algorithm was worse by about an Ω(log d) factor. I
From playlist HIM Lectures 2015
Structured Regularization Summer School - A. Montanari - 2/4 - 20/06/2017
Andrea Montanari (Stanford): Matrix and graph estimation Abstract: Many statistics and unsupervised learning problems can be formalized as estimating a structured matrix or a graph from noisy or incomplete observations. These problems present a large variety of challenges, and an intrigu
From playlist Structured Regularization Summer School - 19-22/06/2017
I present a mathematician's point of view on what AlphaGo is, and why it is important. The talk is intended for a general mathematical audience, with no prior knowledge about Go or deep reinforcement learning. In principle Go, and indeed any Markov game, can be solved by fixed point metho
From playlist Deep reinforcement learning seminar
Allesandro Lazaric: Reinforcement learning - lecture 2
CIRM HYBRID EVENT Recorded during the meeting "Mathematics, Signal Processing and Learning" the January 28, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians o
From playlist Virtual Conference
DQN - Playing Atari with Deep Reinforcement Learning | RL Paper Explained
❤️ Become The AI Epiphany Patreon ❤️ ► https://www.patreon.com/theaiepiphany ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ In this video, I cover the paper that started the hype for deep RL - Playing Atari with deep RL, which introduced the DQN or deep Q-network. You'll learn about: ✔️ All of the nitty-gritt
From playlist Reinforcement Learning
Anna Seigal: "Tensors in Statistics and Data Analysis"
Watch part 1/2 here: https://youtu.be/9unKtBoO5Hw Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensors in Statistics and Data Analysis" Anna Seigal - University of Oxford Abstract: I will give an overview of tensors as they arise in settings
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Definition of the Limit of a Sequence | Real Analysis
What are convergent sequences, and what is the definition of the limit of a sequence? We introduce the definitions, with examples and a proof in today's video lesson! In the definition of the limit of a sequence, we seek to capture what it means for a sequence to get arbitrarily close, or
From playlist Real Analysis
From playlist CS294-112 Deep Reinforcement Learning Sp17