In intuitionistic mathematics, a species is a collection (similar to a classical set in that a species is determined by its members). A spread is a particular kind of species of infinite sequences defined via finite decidable properties. In modern terminology, a spread is an inhabited closed set of sequences. The notion of spread was first proposed by L. E. J. Brouwer (1918B), and was used to define the real numbers (also called the continuum). As Brouwer's ideas were developed, the use of spreads became common in intuitionistic mathematics, especially when dealing with choice sequences and the foundations of intuitionistic analysis (Dummett 77, Troelstra 77). Simple examples of spreads are: * the set of sequences of even numbers; * the set of sequences of the integers 1–6; * the set of sequences of valid terminal commands. Spreads are defined via a spread function, which performs a (decidable) "check" on finite sequences. The notion of a spread and its spread function are interchangeable in the literature; both are treated as one and the same. If all the finite initial parts of an infinite sequence satisfy a spread function's "check", then we can say that the infinite sequence is admissible to the spread. Graph theoretically, one may think of a spread as a rooted, directed tree with numerical vertex labels. (Wikipedia).
What is a Put Spread? | Options Trading Strategies | Option Combinations
What is a Put Spread? - Options Trading Strategies These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0 Check out our website http://www.onfinance.org/ Follow Patrick on twitter here: https://twitte
From playlist Class 2: An Introduction to Options
Lecture15. Cascades in networks. Influence maximization
Network Science 2021 @ HSE
From playlist Network Science, 2021
Credit Spread Options (Put & Call)
A credit spread option is a hedge/bet on the narrowing or widening of a credit spread (credit spread = risky yield - riskless yield). The credit spread put payoff = duration x notional x MAX [Credit Spread - Strike Spread, 0]. The Credit spread call payoff = duration x notional x MAX [Stri
From playlist Derivatives: Credit Derivatives
Data structure intuition is something that develops naturally for most software developers. In all languages, we rely heavily on standard containers and collections. Need fast insertion/lookup? Hashmap. Need a sorted data structure that stores unique values? Set. Duplicate values? Multiset
From playlist Software Development
Follow updates on Twitter: https://twitter.com/eigensteve This series discusses exponential growth, which is a ubiquitous phenomenon in science and engineering. This video will provide a high-level overview. Website: https://www.eigensteve.com/
From playlist Intro to Data Science
Sarah Coakley - Alternative Concepts of God?
Is God, if there is a God, a personal, conscious, all-powerful Supreme Being? Some offer radically different concepts of 'God', exploring novel ideas of what God may be like. They challenge theism - the God of Judaism, Christianity and Islam - with radically new kinds of gods. Is this 'her
From playlist Big Questions About God - Closer To Truth - Core Topic
What is a Butterfly Spread? - Options Trading Strategies Explained These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0 Check out our website http://www.onfinance.org/ Follow Patrick on twitter here:
From playlist Class 2: An Introduction to Options
The Spread law in Universal Hyperbolic Geometry | Universal Hyperbolic Geometry 27 | NJ Wildberger
The spread between two lines in hyperbolic geometry is exactly dual to the notion of the quadrance between two points. The Spread law is the third of the four main laws of trigonometry in universal hyperbolic geometry. Its proof also relies on a remarkable polynomial identity, just as did
From playlist Universal Hyperbolic Geometry
8ECM Public Lecture: Robin Wilson
From playlist 8ECM Public Lectures
LambdaConf 2015 - Introduction to Intuitionistic Type Theory Vlad Patryshev
Traditionally, in Computer Science, sets are assumed to be the basis of a type theory, together with Boolean logic. In this version of type theory, we do not need sets or Boolean logic; intuitionism is enough ("no principle of excluded middle required"). The underlying math is Topos Theory
From playlist LambdaConf 2015
Klaus Mainzer: Constructivity and Computability. Perspectives for Mathematics [...]
Title: Klaus Mainzer: Constructivity and Computability. Perspectives for Mathematics, Computer Science, and Philosophy The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: Since antiquity, mathematical proofs were realized by
From playlist Workshop: "Constructive Mathematics"
Giovanni Sambin: Pointfree topology is real and pointwise is ideal
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Both competing visions of mathematics in the past century, the thesis of formal- ism and the antithesis intuitionism, assume a notion of truth in which the quality of in
From playlist Workshop: "Constructive Mathematics"
Basic setup of tutorials and matlab - Amit Apte
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program
Sets, logic and computability | Math History | NJ Wildberger
In this video we give a very quick overview of a highly controversial period in the development of modern mathematics: the rise of set theory, logic and computability in the late 19th and early 20th centuries. Starting with the pioneering but contentious work of Georg Cantor in creating S
From playlist MathHistory: A course in the History of Mathematics
Spreads, determinants and chromogeometry (I) | WildTrig: Intro to Rational Trigonometry
We give a review of some formulas for the spread between two lines, and rewrite some of them using vector language and the theory of determinants. We get the important understanding that a spread between two vectors is just a renormalization of the squared area of the parallelogram spanned
From playlist WildTrig: Intro to Rational Trigonometry
Is Maths Discovered or Invented?
Tom Rocks Maths intern Kira Miller debates the age-old question of whether maths is discovered or invented by presenting the common arguments on each side. Arguments presented on the side of 'invented' include Formalism, Fictionalism, Art, and Social Construct. And in favour of 'discovere
From playlist Mathstars
Philosophy of Numbers - Numberphile
We revisit the philosophy department and the question of whether numbers really exist? Featuring Mark Jago from the University of Nottingham. More links & stuff in full description below ↓↓↓ Earlier video on numbers' existence: https://youtu.be/1EGDCh75SpQ Infinity paradoxes: https://yout
From playlist Infinity on Numberphile
Introduction to Exponential Distribution Probabilities
This video introduces the exponential distribution and exponential distribution probabilities. http://mathispower4u.com
From playlist Continuous Random Variables
(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
Modern Anomaly and Novelty Detection: Exercise - Session 8
GMM (gaussian mixture model) HBOS (histogram-based outlier detection)
From playlist Modern Anomaly and Novelty Detection