Theory of computation | Hypercomputation
In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible to prove interesting statements such as "The complement of the Mandelbrot set is only partially decidable." These hypothetical computing machines can be viewed as idealised analog computers which operate on real numbers, whereas digital computers are limited to computable numbers. They may be further subdivided into differential and algebraic models (digital computers, in this context, should be thought of as topological, at least insofar as their operation on computable reals is concerned). Depending on the model chosen, this may enable real computers to solve problems that are inextricable on digital computers (For example, Hava Siegelmann's neural nets can have noncomputable real weights, making them able to compute nonrecursive languages.) or vice versa. (Claude Shannon's idealized analog computer can only solve algebraic differential equations, while a digital computer can solve some transcendental equations as well. However this comparison is not entirely fair since in Claude Shannon's idealized analog computer computations are immediately done; i.e. computation is done in real time. Shannon's model can be adapted to cope with this problem.) A canonical model of computation over the reals is Blum–Shub–Smale machine (BSS). If real computation were physically realizable, one could use it to solve NP-complete problems, and even #P-complete problems, in polynomial time. Unlimited precision real numbers in the physical universe are prohibited by the holographic principle and the Bekenstein bound. (Wikipedia).
Limits and algebra continued -- Calculus I
This lecture is on Calculus I. It follows Part I of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus I
Imaginary Numbers, Functions of Complex Variables: 3D animations.
Visualization explaining imaginary numbers and functions of complex variables. Includes exponentials (Euler’s Formula) and the sine and cosine of complex numbers.
From playlist Physics
What are Real Numbers? | Don't Memorise
Watch this video to understand what Real Numbers are! To access all videos on Real Numbers, please enroll in our full course here - https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=3YwrcJxEbZw&utm_term=%7Bkeyword%7D In this video, w
From playlist Real Numbers
Difficulties with real numbers as infinite decimals (II) | Real numbers + limits Math Foundations 92
This lecture introduces some painful realities which cast a long shadow over the foundations of modern analysis. We study the problem of trying to define real numbers via infinite decimals from an algorithmic/constructive/computational point of view. There are many advantages of trying
From playlist Math Foundations
RA1.1. Real Analysis: Introduction
Real Analysis: We introduce some notions important to real analysis, in particular, the relationship between the rational and real numbers. Prerequisites may be found in the Math Major Basics playlist.
From playlist Real Analysis
Real Analysis | The countability of the rational numbers.
We present a proof of the countability of the rational numbers. Our approach is to represent the set of rational numbers as a countable union of disjoint finite sets. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.ne
From playlist Real Analysis
Real Analysis | Compact set of real numbers.
We provide a definition of a (sequentially) compact subset of the real numbers and prove a classic theorem that says this definition is equivalent to the set being closed and bounded. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.co
From playlist Real Analysis
Fractions and repeating decimals | Real numbers and limits Math Foundations 89 | N J Wildberger
We introduce some basic orientation towards the difficulties with real numbers. In particular the differences between computable and uncomputable irrational numbers is significant. Then we discuss the relation between fractions and repeating decimals, giving the algorithms for converting
From playlist Math Foundations
Norbert Müller : Wrapping in exact real arithmetic
Abstract : A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Stanford Webinar: Visual Computing-Tracking the Top Trends and Opportunities
Computer graphics. Augmented reality and virtual reality. Computer Vision. Imaging technology. Deep Learning. Artificial Intelligence. In the field of visual computing, new tools and technologies are constantly emerging and evolving. With the relentless demand on computers to process ever
From playlist Engineering
Computation Ep34, Uncomputable numbers (Apr 29, 2022)
This is a recording of a live class for Math 3342, Theory of Computation, an undergraduate course for math and computer science majors at Fairfield University, Spring 2022. The course is about finite automata, Turing machines, and related topics. Homework and handouts at the class websi
From playlist Math 3342 (Theory of Computation) Spring 2022
Deep thoughts: Theory of Computation (Apr 27, 2021)
This is a recording of a live class for Math 3342, Theory of Computation, an undergraduate course for math & computer science majors at Fairfield University, Spring 2021. Download class notes from class website. Class website: http://cstaecker.fairfield.edu/~cstaecker/courses/2021s3342/
From playlist Math 3342 (Theory of Computation) Spring 2021
Computer Based Math: Rethinking the Curriculum for the Age of Computers
Speaker: Jon McLoone This presentation shares the thinking behind the new curriculum being developed by computerbasedmath.org and explores ways in which Wolfram technologies assist with Computer-Based Math™ instruction. For more training resources, please visit: http://www.wolfram.com/T
From playlist Wolfram Technologies for STEM Education 2014
Quantum generative adversarial networks | TDLS Author Speaking
Toronto Deep Learning Series, 18 June 2018 For slides and more information, visit https://tdls.a-i.science/events/2018-06-18/ Paper Review: https://arxiv.org/abs/1804.08641 Speaker: https://www.linkedin.com/in/pierre-luc-dallaire-demers-006540116/ Organizer: https://www.linkedin.com/in/
From playlist Quantum Machine Learning
Math Debate: Real numbers and the infinite in analysis (NJ Wildberger) | Ep. 16
What sense can we make of the part of mathematics that admits constructions we can never write down or compute? I take up this question in defense of infinite processes and analysis with NJ Wildberger, professor of mathematics at the University of New South Wales and host of the Youtube c
From playlist Daniel Rubin Show, Full episodes
Wolfram Physics Project: Working Session Tuesday, Nov. 2, 2021 [Topos Theory]
This is a Wolfram Physics Project working session about Topos Theory in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Lenore Blum - Alan Turing and the other theory of computing and can a machine be conscious?
Abstract Most logicians and theoretical computer scientists are familiar with Alan Turing’s 1936 seminal paper setting the stage for the foundational (discrete) theory of computation. Most however remain unaware of Turing’s 1948 seminal paper which introduces the notion of condition, sett
From playlist Turing Lectures
Ordered Fields In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms. Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0 COOL Construction of R (with sequences)
From playlist Real Numbers
On HOLD - Real Time Battery Pack Simulation Using Multicore Computers
Learn more on developing battery management systems: http://bit.ly/2P6Z6DA An accurate battery pack model is essential for hardware in-the-loop testing of Battery Management System (BMS). Get free resources on Battery Management systems: http://bit.ly/2P1PA4A Download a trial: http://bit
From playlist Power Electronics Control Design