Combinatorics on words | Finite automata | Combinatorics | Theoretical computer science | Information theory | Number theory
Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S is a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. (Wikipedia).
http://www.teachastronomy.com/ Cosmology is the study of the universe, its history, and everything in it. It comes from the Greek root of the word cosmos for order and harmony which reflected the Greek belief that the universe was a harmonious entity where everything worked in concert to
From playlist 22. The Big Bang, Inflation, and General Cosmology
Covariance (1 of 17) What is Covariance? in Relation to Variance and Correlation
Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between the variance and the covariance. A variance (s^2) is a measure of how spread out the numbers of
From playlist COVARIANCE AND VARIANCE
Proving Law of Cosines - Trigonometry
This video goes through a proof of the Law of Cosines. The Cartesian x-y plane is utilized to prove the Law of Cosines. To understand this proof, the viewer should be familiar with the definition of the trigonometric functions, the Pythagorean Theorem, and the Pythagorean Identity. Stude
From playlist Trigonometry (old videos)
From playlist Courses and Series
Sir Alan Cobham returns to London (1929)
EMPIRE NEWS NEWSREEL (REUTERS) To license this film, visit https://www.britishpathe.com/video/VLVA35BGFYTPNMMRJKAGFNYD4BMXW-SIR-ALAN-COBHAM-RETURNS-TO-LONDON Aviation pioneer Sir Alan Cobham returns to London on completion of a tour of Britain. Full Description: SLATE CARD INFORMATION
From playlist EMPIRE NEWS NEWSREEL (REUTERS)
Boris Adamczewski : Aléa, automates et transcendance
HYBRID EVENT L'étude du caractère aléatoire de la suite des chiffres de certains nombres réels donne lieu à des problèmes classiques, comme la conjecture de normalité des nombres algébriques ou la conjecture de dimensions de Furstenberg (1969). Malheureusement, notre capacité à les appréhe
From playlist Combinatorics
TRANSPORT: Aviation: 22,000 Mile flight (1928)
EMPIRE NEWS NEWSREEL (REUTERS) To license this film, visit https://www.britishpathe.com/video/VLVA479R08Q8IQQJEZFHHB90OH12O-TRANSPORT-AVIATION-22000-MILE-FLIGHT Sir Alan and Lady Cobham reach Plymouth after their great round - Africa survey flight. Full Description: SLATE INFORMATION:
From playlist EMPIRE NEWS NEWSREEL (REUTERS)
This educational video delves into how you quantify a linear statistical relationship between two variables using covariance! #statistics #probability #SoME2 This video gives a visual and intuitive introduction to the covariance, one of the ways we measure a linear statistical relation
From playlist Summer of Math Exposition 2 videos
Fabien Durand - Sur le Théorème de Cobham (Part 1)
Sur le Théorème de Cobham (Part 1) Licence: CC BY NC-ND 4.0
From playlist École d’été 2013 - Théorie des nombres et dynamique
Émilie Charlier: Logic, decidability and numeration systems - Lecture 1
Abstract: The theorem of Büchi-Bruyère states that a subset of Nd is b-recognizable if and only if it is b-definable. As a corollary, the first-order theory of (N,+,Vb) is decidable (where Vb(n) is the largest power of the base b dividing n). This classical result is a powerful tool in ord
From playlist Mathematical Aspects of Computer Science
Fabien Durand - Sur le Théorème de Cobham (Part 2)
Sur le Théorème de Cobham (Part 2) Licence: CC BY NC-ND 4.0
From playlist École d’été 2013 - Théorie des nombres et dynamique
Order of Cosets Equals Order of Subgroup | Abstract Algebra
We prove that for a group G and a subgroup H, every coset Ha of H has the same order as H, and thus all the cosets of the subgroup H have the same order as each other. This is our final step to prove Lagrange's Theorem, which states for a finite group G and subgroup H, the order of G is a
From playlist Abstract Algebra
What is cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos(…?? // Banach Fixed Point Theorem
This weird expression of taking cos over and over again is just a sequence x_n=cos(x_{n-1}). There is a very cool theorem called the Banach Fixed Point Theorem that let's figure out the limit of sequences like this and depends on cos(x) being a so called contractible mapping. Check out m
From playlist Cool Math Series
In this first video on cosets, I show you the equivalence relation on a group, G, that will turn out to create equivalence classes, which are actually cosets. We will prove later that these equivalence classes created by an element in the group, G, are equal to the set of element made up
From playlist Abstract algebra
Teaching a computer to refuel an aeroplane
For a pilot, air-to-air refuelling is one of the most difficult and dangerous procedures to perform. Automating the process would not only eliminate the risk of human error but would also cut down the number of pilot hours required for training. Jonathan du-Bois, an engineer at Bristol Un
From playlist Ri Shorts
Jason P. Bell: Applications of algebra to automatic sequences and pattern avoidance - Lecture 1
Abstract: We will cover some of the more important results from commutative and noncommutative algebra as far as applications to automatic sequences, pattern avoidance, and related areas. Well give an overview of some applications of these areas to the study of automatic and regular sequen
From playlist Mathematical Aspects of Computer Science
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Air Refuelling - The Hidden Force Multiplier
Fasthosts Techie Test competition is now closed! Learn more about Fasthosts here: https://www.fasthosts.co.uk/curiousdroid Air refuelling is the hidden force enabler allowing those countries with this ability to project their airpower around the world. Far from just the process of refuell
From playlist Planes, Trains and Automobiles
This lecture is an informal introduction to the P=NP question in computer science: are nondeterministic polynomial time problems (NP) the same as polynomial time problems (P)? We describe what these terms mean, give a brief history, and examine some of the arguments for and against this qu
From playlist Math talks
Cosets in Group Theory | Abstract Algebra
We introduce cosets of subgroups in groups, these are wonderful little discrete math structures, and we'll see coset examples and several coset theorems in this video. If H is a subgroup of a group G, and a is an element of G, then Ha is the set of all products ha where a is fixed and h ra
From playlist Abstract Algebra