- published: 09 Jan 2019
- views: 287
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remove the playlistLarge Set (ramsey Theory)
- remove the playlistLarge Set (ramsey Theory)
- Large (film)
- Large (surname)
- Large set (Ramsey theory)
- Quasar (brand)
- Group
- Stratigraphic unit
- 1994 Group
Large (film)
Large is a 2001 feature film directed by Justin Edgar for FilmFour.
Plot
Large is a gross-out teen comedy which centres on Jason, the son of a fading rock star, and his comic attempts to fulfill the conditions of his father's will in order to inherit a fortune.
Cast
Luke de Woolfson as Jason Mouseley
Simon Lowe as Rob
Phil Cornwell as Barry Blaze Mouseley
Melanie Gutteridge as Sophie
Morwenna Banks as Lorraine
Lee Oakes as Ian
Andrew Grainger as Norman Gates
Production
Large was produced by Alex Usburne.The pre-production period was relatively long, with writers Mike Dent and Justin Edgar draughting 20 versions of the script.Large was filmed and edited at Pebble Mill Studios and on location in Birmingham, UK, for six weeks in March and April 2000 on a budget of £1.4 million. The line producer was Paul Ritchie (Slumdog Millionaire, Bend It Like Beckham). It was the first film of Director of Photography Robbie Ryan (Fish Tank, Wuthering Heights) and Editor Eddie Hamilton (Kick Ass, X-Men: First Class). It was also Edgar's feature film debut.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Large_(film)
Large (surname)
Large is an English surname, with variants including Lardge, Lurge, and Large. Its meaning is variable, though it may derive from the Norman French adjective, large (meaning "generous" or "big" [as in, "that's big of you", meaning generous, as well as large in size]), as it is found in the surname "le Large" in English records dating back as far as the 13th century. Harrison's work on English surnames gives the following: "LARGE (adjectival: French, Latin) BIG; GENEROUS [Middle English Old French large; Latin larg-us, -a, [meaning] abundant, liberal]"
He gives an early citation for the name: Austin Belz from the Hundred Rolls, a reference dating to 1273.
He also provides a quotation showing the word in its older sense of generous, full, liberal or ample in its literary context:
So large of yift [gift] and free was she (from Chaucer's Romance of the Rose I168)
Another variant surname, "de Large", appears to be continental European rather than English in origin.
Henry Brougham Guppy's survey circa 1881, based on local British directories, places Large as a surname local to North Wiltshire, and considers it to have particular prevalence among yeoman farmers.(Guppy, 1890)
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Large_(surname)
Large set (Ramsey theory)
In Ramsey theory, a set S of natural numbers is considered to be a large set if and only if Van der Waerden's theorem can be generalized to assert the existence of arithmetic progressions with common difference in S. That is, S is large if and only if every finite partition of the natural numbers has a cell containing arbitrarily long arithmetic progressions having common differences in S.
Examples
Properties
Necessary conditions for largeness include:
is large, it is not the case that sk≥3sk-1 for k≥ 2.Two sufficient conditions are:
where 
is a polynomial with 
and positive leading coefficient, then 
is large.The first sufficient condition implies that if S is a thick set, then S is large.
Other facts about large sets include:
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Large_set_(Ramsey_theory)
Quasar (brand)
Quasar is a North American brand of electronics, first used by Motorola in 1967 for a model line of transistorized color televisions. These TVs were known for containing all serviceable parts in a drawer beside the picture tube. It was soon established as its own brand, with all Motorola-manufactured televisions being sold as Quasar by Motorola.
Quasar Electronics, Inc.
On May 29, 1974, Motorola, Inc., sold its television manufacturing division — including its plants in Pontiac, Illinois; Franklin Park, Illinois; and Markham, Ontario — to Matsushita, who continued production of home television receivers under a newly incorporated entity, Quasar Electronics, Inc., an American-managed subsidiary of Matsushita Electronic Corporation of America (MECA). Motorola continued to operate its plant in Quincy, Illinois for two years (until 1976), when plant ownership passed to the new company. Later, Quasar Company, the sales company, was split off from Matsushita Industrial Company, the manufacturing entity.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Quasar_(brand)
Group
Group may refer to:
Groups of people
In science and technology
In mathematics
In chemistry
In computing and the internet
Other uses in science and technology
Other uses
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Group
Stratigraphic unit
A stratigraphic unit is a volume of rock of identifiable origin and relative age range that is defined by the distinctive and dominant, easily mapped and recognizable petrographic, lithologic or paleontologic features (facies) that characterize it.
Units must be mappable and distinct from one another, but the contact need not be particularly distinct. For instance, a unit may be defined by terms such as "when the sandstone component exceeds 75%".
Lithostratigraphic units
Sequences of sedimentary and volcanic rocks are subdivided on the basis of their lithology. Going from smaller to larger in scale, the main units recognised are Bed, Member, Formation, Group and Supergroup.
Bed
A bed is a lithologically distinct layer within a member or formation and is the smallest recognisable stratigraphic unit. These are not normally named, but may be in the case of a marker horizon.
Member
A member is a named lithologically distinct part of a formation. Not all formations are subdivided in this way and even where they are recognized, they may only form part of the formation.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Stratigraphic_unit
1994 Group
The 1994 Group was a coalition of smaller research-intensive universities in the United Kingdom, founded in 1994 to defend these universities' interests following the creation of the Russell Group by larger research-intensive universities earlier that year. The 1994 Group originally represented seventeen universities, rising to nineteen, and then dropping to eleven. The Group started to falter in 2012, when a number of high performing members left to join the Russell Group. The 1994 Group ultimately dissolved in November 2013.
Role
The group sought "to represent the views of its members on the current state and the future of higher education through discussions with the government, funding bodies, and other higher education interest groups" and "[made] its views known through its research publications and in the media".
University Alliance, million+, GuildHE and the Russell Group were its fellow university membership groups across the UK higher education sector.
Members
1994 Group position in league tables
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/1994_Group
Podcasts:
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Natasha Dobrinen - Ramsey theory on trees and applications to big Ramsey degrees
Mini-course “Infinitary Ramsey Theory”, part II: Ramsey theory on trees and applications to big Ramsey degrees Natasha Dobrinen (University of Denver, Colorado, USA) This is part II of a two-part mini-course given at the Kurt Gödel Research Center, Universität Wien on January 9, 2019. Part I has been given on January 8, 2019. The slides for part II (this part) are available at https://drive.google.com/open?id=1I7h8Cwxhk2Or-F_tWaiuiFmimsQg2GDX (The slides for part I (the previous part) are available at https://drive.google.com/open?id=1TSzT6D9n8W0UtXVLFz6JKWkMTlPgW5dl) Abstract The Infinite Ramsey Theorem states that given $n,r\ge 1$ and a coloring of all $n$-sized subsets of $\mathbb{N}$ into $r$ colors, there is an infinite subset of $\mathbb{N}$ in which all $n$-sized subsets have ...
published: 09 Jan 2019 -
Biggest Breakthroughs in Math: 2023
Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery. Read about more math breakthroughs from this year at Quanta Magazine: https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/ 00:05 Ramsey Numbers One of the biggest mathematical discoveries of the past year was in graph theory where the proof of a new, tighter upper bound to Ramsey numbers. These numbers measure the size that graphs must reach before inevitably containing structures called cliques. The discovery, announced in March, was the first advance of its type since 1935. - Original story with links to research papers can be found here: https://www.quantamagazine.org/after-ne...
published: 23 Dec 2023 -
Alexander Clifton: "Ramsey Theory for Diffsequences"
Abstract: Van der Waerden's theorem states that any coloring of the natural numbers with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number W(r,k)$which is the smallest $n$ such that any $r$-coloring of {1,2,...,n} guarantees the presence of a monochromatic arithmetic progression of length k. It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a D-diffsequence, which is an increasing sequence a_1,a_2...,a_k in which the consecutive differences a_i-a_{i-1} all lie in some given set D. For each D that exhibits a van der Waerden-type result, we let Delta(D,k;r) represent the analogue of the ...
published: 26 Feb 2022 -
Ramsey Theory: Lecture 2 - Finite Ramsey's Theorem and Ramsey's Theorem for r-sets
This is the second lecture in my course on Ramsey Theory. Email for queries: [email protected]
published: 01 Sep 2021 -
Why complete chaos is impossible || Ramsey Theory
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription! Normal tic-tac-toe can always be drawn. But what if it lives in high dimensions? It turns out that no matter how large a tic-tac-toe board you have or how many players want to play, there always is a dimension long enough that guarantees the 1st player will always win. The theorem behind this, Hales-Jewett, is part of a family of theorems in Ramsey theory that show how lower level structures (like straight lines of the same colour) are always going to occur if the dimension is large enough. That is, you can't have a system that is totally without order. In this video we explore these tic-tac-toe generalizations, the Van Der Waerden...
published: 27 Aug 2023 -
Graph Theory 9-2: Ramsey's Theorem
In this second video of Week 9, we prove Ramsey's theorem and some of its generalizations; in particular, this involves finding order in the midst of chaos.
published: 04 Feb 2021 -
Advances on Ramsey numbers - Jacob Fox
https://www.math.ias.edu/seminars/abstract?event=83564
published: 23 Nov 2015 -
Ramsey Theory: An Introduction
This video is created as a study project by Class Math 303 Group 1B from Simon Fraser University. The purpose of this video is to create a gentle introduction about Ramsey Theory. Credits: Director: Naiyuan Guo Animation: Naiyuan Guo,Rose (Rong) Luo Design: Biying Xu Sound: Chrisitine Yang Academic Proof: Nicole Cossey Editing: Zen So Production Supervisor: Rose (Rong) Luo
published: 06 Apr 2014 -
2022.09.27, Alexander Clifton, Ramsey Theory for Diffsequences
Alexander Clifton, Ramsey Theory for Diffsequences September 27 2022, Tuesday @ 4:30 PM ~ 5:30 PM Room B332, IBS (기초과학연구원) Speaker Alexander Clifton IBS Discrete Mathematics Group https://sites.google.com/view/alexander-clifton/home Van der Waerden's theorem states that any coloring of $\mathbb{N}$ with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number $W(r,k)$ which is the smallest $n$ such that any $r$-coloring of $\{1,2,\cdots,n\}$ guarantees the presence of a monochromatic arithmetic progression of length $k$. It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a $D$-diffsequence,...
published: 27 Sep 2022 -
Probability and Ramsey Theory part 1
Date: April 13, 2017 Speaker: Aaron Robertson, Colgate University Title: Probability and Ramsey Theory Abstract: We will find a threshold function f(k;r) such that almost all r-colorings of more than f(k;r) consecutive integers admit a monochromatic k-term arithmetic progression while almost no r-colorings do if we have less than f(k;r) consecutive integers. We will then move on to investigate the distribution of the random variable X = number of monochromatic k-term arithmetic progressions in [1,n] under random coloring of each integer. It is known that X tends to a Poisson distribution as k tends to infinity. We investigate what X is for small k.
published: 18 Apr 2017
developed with YouTube
1:24:37
Natasha Dobrinen - Ramsey theory on trees and applications to big Ramsey degrees
- Order: Reorder
- Duration: 1:24:37
- Uploaded Date: 09 Jan 2019
- views: 287
Mini-course “Infinitary Ramsey Theory”, part II: Ramsey theory on trees and applications to big Ramsey degrees
Natasha Dobrinen (University of Denver, Colorado...
Mini-course “Infinitary Ramsey Theory”, part II: Ramsey theory on trees and applications to big Ramsey degrees
Natasha Dobrinen (University of Denver, Colorado, USA)
This is part II of a two-part mini-course given at the Kurt Gödel Research Center, Universität Wien on January 9, 2019. Part I has been given on January 8, 2019.
The slides for part II (this part) are available at https://drive.google.com/open?id=1I7h8Cwxhk2Or-F_tWaiuiFmimsQg2GDX
(The slides for part I (the previous part) are available at https://drive.google.com/open?id=1TSzT6D9n8W0UtXVLFz6JKWkMTlPgW5dl)
Abstract
The Infinite Ramsey Theorem states that given $n,r\ge 1$ and a coloring of all $n$-sized subsets of $\mathbb{N}$ into $r$ colors, there is an infinite subset of $\mathbb{N}$ in which all $n$-sized subsets have the same color. There are several natural ways of extending Ramsey's Theorem. One extension is to color infinite sets rather than finite sets. In this case, the Axiom of Choice precludes a full-fledged generalization, but upon restricting to definable colorings, much can still be said. Another way to extend Ramsey's Theorem is to color finite sub-objects of an infinite structure, requiring an infinite substructure isomorphic to the original one. While it is not possible in general to obtain substructures on which the coloring is monochromatic, sometimes one can find bounds on the number of colors, and this can have implications in topological dynamics.
In Part I, we traced the development of Ramsey theory on the Baire space, from the Nash-Williams Theorem for colorings of clopen sets to the Galvin-Prikry Theorem for Borel colorings, culminating in Ellentuck's Theorem correlating the Ramsey property with the property of Baire in a topology refining the metric topology on the Baire space. This refinement is called the Ellentuck topology and is closely connected with Mathias forcing. Several classical spaces with similar properties will be presented, including the Carlson-Simpson space and the Milliken space of block sequences. From these we derived the key properties of topological Ramsey spaces, first abstracted by Carlson and Simpson and more recently given a refined presentation by Todorcevic in his book {\em Introduction to Ramsey spaces}. As the Mathias forcing is closely connected with Ramsey ultrafilters, via forcing mod finite initial segments, so too any Ramsey space has a $\sigma$-closed version which forces an ultrafilter with partition properties. Part I showed how Ramsey spaces can be used to find general schemata into which disparate results on ultrafilters can be seen as special cases, as well as obtain fine-tuned results for structures involving ultrafilters.
Part II (the part you are watching) will focus on Ramsey theory on trees and their applications to Ramsey theory of homogeneous structures. An infinite structure is {\em homogeneous} if each isomorphism between two finite substructures can be extended to an automorphism of the infinite structure. The rationals as a linearly ordered structure and the Rado graph are prime examples of homogeneous structures. Given a coloring of singletons in the rationals, one can find a subset isomorphic to the rationals in which all singletons have the same color. However, when one colors pairs of rationals, there is a coloring due to Sierpinski for which any subset isomorphic to the rationals has more than one color on its pairsets. This is the origin of the theory of {\em big Ramsey degrees}, a term coined by Kechris, Pestov and Todorcevic, which investigates bounds on colorings of finite structures inside infinite structures. Somewhat surprisingly, a theorem of Halpern and Läuchli involves colorings of products of trees, discovered en route to a proof that the Boolean Prime Ideal Theorem is strictly weaker than the Axiom of Choice, is the heart of most results on big Ramsey degrees. We will survey big Ramsey degree results on countable and uncountable structures and related Ramsey theorems on trees, including various results of Dobrinen, Devlin, Džamonja, Hathaway, Larson, Laver, Mitchell, Shelah, and Zhang.
https://wn.com/Natasha_Dobrinen_Ramsey_Theory_On_Trees_And_Applications_To_Big_Ramsey_Degrees
Mini-course “Infinitary Ramsey Theory”, part II: Ramsey theory on trees and applications to big Ramsey degrees
Natasha Dobrinen (University of Denver, Colorado, USA)
This is part II of a two-part mini-course given at the Kurt Gödel Research Center, Universität Wien on January 9, 2019. Part I has been given on January 8, 2019.
The slides for part II (this part) are available at https://drive.google.com/open?id=1I7h8Cwxhk2Or-F_tWaiuiFmimsQg2GDX
(The slides for part I (the previous part) are available at https://drive.google.com/open?id=1TSzT6D9n8W0UtXVLFz6JKWkMTlPgW5dl)
Abstract
The Infinite Ramsey Theorem states that given $n,r\ge 1$ and a coloring of all $n$-sized subsets of $\mathbb{N}$ into $r$ colors, there is an infinite subset of $\mathbb{N}$ in which all $n$-sized subsets have the same color. There are several natural ways of extending Ramsey's Theorem. One extension is to color infinite sets rather than finite sets. In this case, the Axiom of Choice precludes a full-fledged generalization, but upon restricting to definable colorings, much can still be said. Another way to extend Ramsey's Theorem is to color finite sub-objects of an infinite structure, requiring an infinite substructure isomorphic to the original one. While it is not possible in general to obtain substructures on which the coloring is monochromatic, sometimes one can find bounds on the number of colors, and this can have implications in topological dynamics.
In Part I, we traced the development of Ramsey theory on the Baire space, from the Nash-Williams Theorem for colorings of clopen sets to the Galvin-Prikry Theorem for Borel colorings, culminating in Ellentuck's Theorem correlating the Ramsey property with the property of Baire in a topology refining the metric topology on the Baire space. This refinement is called the Ellentuck topology and is closely connected with Mathias forcing. Several classical spaces with similar properties will be presented, including the Carlson-Simpson space and the Milliken space of block sequences. From these we derived the key properties of topological Ramsey spaces, first abstracted by Carlson and Simpson and more recently given a refined presentation by Todorcevic in his book {\em Introduction to Ramsey spaces}. As the Mathias forcing is closely connected with Ramsey ultrafilters, via forcing mod finite initial segments, so too any Ramsey space has a $\sigma$-closed version which forces an ultrafilter with partition properties. Part I showed how Ramsey spaces can be used to find general schemata into which disparate results on ultrafilters can be seen as special cases, as well as obtain fine-tuned results for structures involving ultrafilters.
Part II (the part you are watching) will focus on Ramsey theory on trees and their applications to Ramsey theory of homogeneous structures. An infinite structure is {\em homogeneous} if each isomorphism between two finite substructures can be extended to an automorphism of the infinite structure. The rationals as a linearly ordered structure and the Rado graph are prime examples of homogeneous structures. Given a coloring of singletons in the rationals, one can find a subset isomorphic to the rationals in which all singletons have the same color. However, when one colors pairs of rationals, there is a coloring due to Sierpinski for which any subset isomorphic to the rationals has more than one color on its pairsets. This is the origin of the theory of {\em big Ramsey degrees}, a term coined by Kechris, Pestov and Todorcevic, which investigates bounds on colorings of finite structures inside infinite structures. Somewhat surprisingly, a theorem of Halpern and Läuchli involves colorings of products of trees, discovered en route to a proof that the Boolean Prime Ideal Theorem is strictly weaker than the Axiom of Choice, is the heart of most results on big Ramsey degrees. We will survey big Ramsey degree results on countable and uncountable structures and related Ramsey theorems on trees, including various results of Dobrinen, Devlin, Džamonja, Hathaway, Larson, Laver, Mitchell, Shelah, and Zhang.
19:12
Biggest Breakthroughs in Math: 2023
- Order: Reorder
- Duration: 19:12
- Uploaded Date: 23 Dec 2023
- views: 1847135
Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical d...
Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.
Read about more math breakthroughs from this year at Quanta Magazine: https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/
00:05 Ramsey Numbers
One of the biggest mathematical discoveries of the past year was in graph theory where the proof of a new, tighter upper bound to Ramsey numbers. These numbers measure the size that graphs must reach before inevitably containing structures called cliques. The discovery, announced in March, was the first advance of its type since 1935.
- Original story with links to research papers can be found here: https://www.quantamagazine.org/after-nearly-a-century-a-new-limit-for-patterns-in-graphs-20230502/
06:21 Aperiodic Monotile
The most attention-getting result of the year was the discovery of a new kind of tile that covers the plane but only in a pattern that never repeats. A two-tile combination that does this has been known since the 1970s, but the single tile, discovered by a hobbyist named David Smith and announced in March, has been a sensation.
CORRECTION: In the video, the image presented as the 'turtle' tile is in fact a rotated 'spectre' tile. To see the correct version of the turtle tile, you can visit Dave Smith's webpage: https://hedraweb.wordpress.com/2023/03/23/its-a-shape-jim-but-not-as-we-know-it/
- Original story with links to research papers can be found here: https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/
- Build your own aperiodic tiling patterns with Kaplan's online tool: https://cs.uwaterloo.ca/~csk/hat/h7h8.html
14:20 Three Arithmetic Progressions
Two computer scientists, Zander Kelley and Raghu Meka, stunned mathematicians with news of an out-of-left-field breakthrough on an old combinatorics question: How many integers can you throw into a bucket while making sure that no three of them form an evenly spaced progression? Kelley and Meka smashed a long-standing upper bound on the number of integers smaller than some cap N that could be put in the bucket without creating such a pattern.
- Original story with links to research papers can be found here: https://www.quantamagazine.org/surprise-computer-science-proof-stuns-mathematicians-20230321/
- VISIT our Website: https://www.quantamagazine.org
- LIKE us on Facebook: https://www.facebook.com/QuantaNews
- FOLLOW us Twitter: https://twitter.com/QuantaMagazine
Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/
https://wn.com/Biggest_Breakthroughs_In_Math_2023
Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.
Read about more math breakthroughs from this year at Quanta Magazine: https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/
00:05 Ramsey Numbers
One of the biggest mathematical discoveries of the past year was in graph theory where the proof of a new, tighter upper bound to Ramsey numbers. These numbers measure the size that graphs must reach before inevitably containing structures called cliques. The discovery, announced in March, was the first advance of its type since 1935.
- Original story with links to research papers can be found here: https://www.quantamagazine.org/after-nearly-a-century-a-new-limit-for-patterns-in-graphs-20230502/
06:21 Aperiodic Monotile
The most attention-getting result of the year was the discovery of a new kind of tile that covers the plane but only in a pattern that never repeats. A two-tile combination that does this has been known since the 1970s, but the single tile, discovered by a hobbyist named David Smith and announced in March, has been a sensation.
CORRECTION: In the video, the image presented as the 'turtle' tile is in fact a rotated 'spectre' tile. To see the correct version of the turtle tile, you can visit Dave Smith's webpage: https://hedraweb.wordpress.com/2023/03/23/its-a-shape-jim-but-not-as-we-know-it/
- Original story with links to research papers can be found here: https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/
- Build your own aperiodic tiling patterns with Kaplan's online tool: https://cs.uwaterloo.ca/~csk/hat/h7h8.html
14:20 Three Arithmetic Progressions
Two computer scientists, Zander Kelley and Raghu Meka, stunned mathematicians with news of an out-of-left-field breakthrough on an old combinatorics question: How many integers can you throw into a bucket while making sure that no three of them form an evenly spaced progression? Kelley and Meka smashed a long-standing upper bound on the number of integers smaller than some cap N that could be put in the bucket without creating such a pattern.
- Original story with links to research papers can be found here: https://www.quantamagazine.org/surprise-computer-science-proof-stuns-mathematicians-20230321/
- VISIT our Website: https://www.quantamagazine.org
- LIKE us on Facebook: https://www.facebook.com/QuantaNews
- FOLLOW us Twitter: https://twitter.com/QuantaMagazine
Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/
- published: 23 Dec 2023
- views: 1847135
51:15
Alexander Clifton: "Ramsey Theory for Diffsequences"
- Order: Reorder
- Duration: 51:15
- Uploaded Date: 26 Feb 2022
- views: 76
Abstract: Van der Waerden's theorem states that any coloring of the natural numbers with a finite number of colors will contain arbitrarily long monochromatic a...
Abstract: Van der Waerden's theorem states that any coloring of the natural numbers with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number W(r,k)$which is the smallest $n$ such that any $r$-coloring of {1,2,...,n} guarantees the presence of a monochromatic arithmetic progression of length k.
It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a D-diffsequence, which is an increasing sequence a_1,a_2...,a_k in which the consecutive differences a_i-a_{i-1} all lie in some given set D. For each D that exhibits a van der Waerden-type result, we let Delta(D,k;r) represent the analogue of the van der Waerden number W(r,k). One question of interest is to determine the possible behaviors of Delta as a function of k. In this talk, we will demonstrate that it is possible for Delta(D,k;r) to grow faster than polynomial in k. Time permitting, we will also discuss a class of D's for which no van der Waerden-type result is possible.
https://wn.com/Alexander_Clifton_Ramsey_Theory_For_Diffsequences
Abstract: Van der Waerden's theorem states that any coloring of the natural numbers with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number W(r,k)$which is the smallest $n$ such that any $r$-coloring of {1,2,...,n} guarantees the presence of a monochromatic arithmetic progression of length k.
It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a D-diffsequence, which is an increasing sequence a_1,a_2...,a_k in which the consecutive differences a_i-a_{i-1} all lie in some given set D. For each D that exhibits a van der Waerden-type result, we let Delta(D,k;r) represent the analogue of the van der Waerden number W(r,k). One question of interest is to determine the possible behaviors of Delta as a function of k. In this talk, we will demonstrate that it is possible for Delta(D,k;r) to grow faster than polynomial in k. Time permitting, we will also discuss a class of D's for which no van der Waerden-type result is possible.
- published: 26 Feb 2022
- views: 76
57:21
Ramsey Theory: Lecture 2 - Finite Ramsey's Theorem and Ramsey's Theorem for r-sets
- Order: Reorder
- Duration: 57:21
- Uploaded Date: 01 Sep 2021
- views: 189
This is the second lecture in my course on Ramsey Theory.
Email for queries: [email protected]
This is the second lecture in my course on Ramsey Theory.
Email for queries: [email protected]
https://wn.com/Ramsey_Theory_Lecture_2_Finite_Ramsey's_Theorem_And_Ramsey's_Theorem_For_R_Sets
This is the second lecture in my course on Ramsey Theory.
Email for queries: [email protected]
- published: 01 Sep 2021
- views: 189
23:00
Why complete chaos is impossible || Ramsey Theory
- Order: Reorder
- Duration: 23:00
- Uploaded Date: 27 Aug 2023
- views: 48139
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!
...
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!
Normal tic-tac-toe can always be drawn. But what if it lives in high dimensions? It turns out that no matter how large a tic-tac-toe board you have or how many players want to play, there always is a dimension long enough that guarantees the 1st player will always win. The theorem behind this, Hales-Jewett, is part of a family of theorems in Ramsey theory that show how lower level structures (like straight lines of the same colour) are always going to occur if the dimension is large enough. That is, you can't have a system that is totally without order. In this video we explore these tic-tac-toe generalizations, the Van Der Waerden theorem and sketch it's proof.
Reference: This undergrad level book introducing Ramsey Theory has lots more detail on all the theorems and more: https://www.sfu.ca/~vjungic/RamseyNotes/sec_Intro.html
0:00 Friends and Strangers Theorem
2:56 What is Ramsey Theory?
3:36 High dimensional Tic-Tac-Toe
7:58 Hales-Jewett Theorem
10:37 Van der Waerden's theorem
14:42 Proof sketch of Van der Waerden's theorem
21:23 Summary
21:57 Brilliant.org/TreforBazett
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►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
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OTHER PLAYLISTS:
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https://wn.com/Why_Complete_Chaos_Is_Impossible_||_Ramsey_Theory
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!
Normal tic-tac-toe can always be drawn. But what if it lives in high dimensions? It turns out that no matter how large a tic-tac-toe board you have or how many players want to play, there always is a dimension long enough that guarantees the 1st player will always win. The theorem behind this, Hales-Jewett, is part of a family of theorems in Ramsey theory that show how lower level structures (like straight lines of the same colour) are always going to occur if the dimension is large enough. That is, you can't have a system that is totally without order. In this video we explore these tic-tac-toe generalizations, the Van Der Waerden theorem and sketch it's proof.
Reference: This undergrad level book introducing Ramsey Theory has lots more detail on all the theorems and more: https://www.sfu.ca/~vjungic/RamseyNotes/sec_Intro.html
0:00 Friends and Strangers Theorem
2:56 What is Ramsey Theory?
3:36 High dimensional Tic-Tac-Toe
7:58 Hales-Jewett Theorem
10:37 Van der Waerden's theorem
14:42 Proof sketch of Van der Waerden's theorem
21:23 Summary
21:57 Brilliant.org/TreforBazett
Check out my MATH MERCH line in collaboration with Beautiful Equations
►https://beautifulequations.net/pages/trefor
COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
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- published: 27 Aug 2023
- views: 48139
32:53
Graph Theory 9-2: Ramsey's Theorem
- Order: Reorder
- Duration: 32:53
- Uploaded Date: 04 Feb 2021
- views: 730
In this second video of Week 9, we prove Ramsey's theorem and some of its generalizations; in particular, this involves finding order in the midst of chaos.
In this second video of Week 9, we prove Ramsey's theorem and some of its generalizations; in particular, this involves finding order in the midst of chaos.
https://wn.com/Graph_Theory_9_2_Ramsey's_Theorem
In this second video of Week 9, we prove Ramsey's theorem and some of its generalizations; in particular, this involves finding order in the midst of chaos.
- published: 04 Feb 2021
- views: 730
59:19
Advances on Ramsey numbers - Jacob Fox
- Order: Reorder
- Duration: 59:19
- Uploaded Date: 23 Nov 2015
- views: 4502
https://www.math.ias.edu/seminars/abstract?event=83564
https://www.math.ias.edu/seminars/abstract?event=83564
https://wn.com/Advances_On_Ramsey_Numbers_Jacob_Fox
https://www.math.ias.edu/seminars/abstract?event=83564
- published: 23 Nov 2015
- views: 4502
3:58
Ramsey Theory: An Introduction
- Order: Reorder
- Duration: 3:58
- Uploaded Date: 06 Apr 2014
- views: 85546
This video is created as a study project by Class Math 303 Group 1B from Simon Fraser University. The purpose of this video is to create a gentle introduction a...
This video is created as a study project by Class Math 303 Group 1B from Simon Fraser University. The purpose of this video is to create a gentle introduction about Ramsey Theory.
Credits:
Director: Naiyuan Guo
Animation: Naiyuan Guo,Rose (Rong) Luo
Design: Biying Xu
Sound: Chrisitine Yang
Academic Proof: Nicole Cossey
Editing: Zen So
Production Supervisor: Rose (Rong) Luo
https://wn.com/Ramsey_Theory_An_Introduction
This video is created as a study project by Class Math 303 Group 1B from Simon Fraser University. The purpose of this video is to create a gentle introduction about Ramsey Theory.
Credits:
Director: Naiyuan Guo
Animation: Naiyuan Guo,Rose (Rong) Luo
Design: Biying Xu
Sound: Chrisitine Yang
Academic Proof: Nicole Cossey
Editing: Zen So
Production Supervisor: Rose (Rong) Luo
- published: 06 Apr 2014
- views: 85546
1:07:57
2022.09.27, Alexander Clifton, Ramsey Theory for Diffsequences
- Order: Reorder
- Duration: 1:07:57
- Uploaded Date: 27 Sep 2022
- views: 93
Alexander Clifton, Ramsey Theory for Diffsequences
September 27 2022, Tuesday @ 4:30 PM ~ 5:30 PM
Room B332, IBS (기초과학연구원)
Speaker
Alexander Clifton
IBS Discr...
Alexander Clifton, Ramsey Theory for Diffsequences
September 27 2022, Tuesday @ 4:30 PM ~ 5:30 PM
Room B332, IBS (기초과학연구원)
Speaker
Alexander Clifton
IBS Discrete Mathematics Group
https://sites.google.com/view/alexander-clifton/home
Van der Waerden's theorem states that any coloring of $\mathbb{N}$ with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number $W(r,k)$ which is the smallest $n$ such that any $r$-coloring of $\{1,2,\cdots,n\}$ guarantees the presence of a monochromatic arithmetic progression of length $k$.
It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a $D$-diffsequence, which is an increasing sequence $a_1, a_2, \cdots, a_k$ ($a_i$ is smaller than $a_{i+1}$) in which the consecutive differences $a_i-a_{i-1}$ all lie in some given set $D$. We say that $D$ is $r$-accessible if every $r$-coloring of $\mathbb{N}$ contains arbitrarily long monochromatic $D$-diffsequences. When $D$ is $r$-accessible, we define $\Delta(D,k;r)$ as the smallest $n$ such that any $r$-coloring of $\{1,2,\cdots,n\}$ guarantees the presence of a monochromatic $D$-diffsequence of length $k$.
One question of interest is to determine the possible behaviors of $\Delta$ as a function of $k$. In this talk, we will demonstrate that is possible for $\Delta(D,k;r)$ to grow faster than polynomial in $k$. We will also discuss a broad class of $D$'s which are not $2$-accessible.
https://wn.com/2022.09.27,_Alexander_Clifton,_Ramsey_Theory_For_Diffsequences
Alexander Clifton, Ramsey Theory for Diffsequences
September 27 2022, Tuesday @ 4:30 PM ~ 5:30 PM
Room B332, IBS (기초과학연구원)
Speaker
Alexander Clifton
IBS Discrete Mathematics Group
https://sites.google.com/view/alexander-clifton/home
Van der Waerden's theorem states that any coloring of $\mathbb{N}$ with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number $W(r,k)$ which is the smallest $n$ such that any $r$-coloring of $\{1,2,\cdots,n\}$ guarantees the presence of a monochromatic arithmetic progression of length $k$.
It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a $D$-diffsequence, which is an increasing sequence $a_1, a_2, \cdots, a_k$ ($a_i$ is smaller than $a_{i+1}$) in which the consecutive differences $a_i-a_{i-1}$ all lie in some given set $D$. We say that $D$ is $r$-accessible if every $r$-coloring of $\mathbb{N}$ contains arbitrarily long monochromatic $D$-diffsequences. When $D$ is $r$-accessible, we define $\Delta(D,k;r)$ as the smallest $n$ such that any $r$-coloring of $\{1,2,\cdots,n\}$ guarantees the presence of a monochromatic $D$-diffsequence of length $k$.
One question of interest is to determine the possible behaviors of $\Delta$ as a function of $k$. In this talk, we will demonstrate that is possible for $\Delta(D,k;r)$ to grow faster than polynomial in $k$. We will also discuss a broad class of $D$'s which are not $2$-accessible.
- published: 27 Sep 2022
- views: 93
29:59
Probability and Ramsey Theory part 1
- Order: Reorder
- Duration: 29:59
- Uploaded Date: 18 Apr 2017
- views: 520
Date: April 13, 2017
Speaker: Aaron Robertson, Colgate University
Title: Probability and Ramsey Theory
Abstract:
We will find a threshold function...
Date: April 13, 2017
Speaker: Aaron Robertson, Colgate University
Title: Probability and Ramsey Theory
Abstract:
We will find a threshold function f(k;r) such that almost all r-colorings of more than f(k;r) consecutive integers admit a monochromatic k-term arithmetic progression while almost no r-colorings do if we have less than f(k;r) consecutive integers. We will then move on to investigate the distribution of the random variable X = number of monochromatic k-term arithmetic progressions in [1,n] under random coloring of each integer. It is known that X tends to a Poisson distribution as k tends to infinity. We investigate what X is for small k.
https://wn.com/Probability_And_Ramsey_Theory_Part_1
Date: April 13, 2017
Speaker: Aaron Robertson, Colgate University
Title: Probability and Ramsey Theory
Abstract:
We will find a threshold function f(k;r) such that almost all r-colorings of more than f(k;r) consecutive integers admit a monochromatic k-term arithmetic progression while almost no r-colorings do if we have less than f(k;r) consecutive integers. We will then move on to investigate the distribution of the random variable X = number of monochromatic k-term arithmetic progressions in [1,n] under random coloring of each integer. It is known that X tends to a Poisson distribution as k tends to infinity. We investigate what X is for small k.
- published: 18 Apr 2017
- views: 520
1:24:37
Natasha Dobrinen - Ramsey theory on trees and applications to big Ramsey degrees
Mini-course “Infinitary Ramsey Theory”, part II: Ramsey theory on trees and applications t...
published: 09 Jan 2019
Natasha Dobrinen - Ramsey theory on trees and applications to big Ramsey degrees
Natasha Dobrinen - Ramsey theory on trees and applications to big Ramsey degrees
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- published: 09 Jan 2019
- views: 287
Mini-course “Infinitary Ramsey Theory”, part II: Ramsey theory on trees and applications to big Ramsey degrees
Natasha Dobrinen (University of Denver, Colorado, USA)
This is part II of a two-part mini-course given at the Kurt Gödel Research Center, Universität Wien on January 9, 2019. Part I has been given on January 8, 2019.
The slides for part II (this part) are available at https://drive.google.com/open?id=1I7h8Cwxhk2Or-F_tWaiuiFmimsQg2GDX
(The slides for part I (the previous part) are available at https://drive.google.com/open?id=1TSzT6D9n8W0UtXVLFz6JKWkMTlPgW5dl)
Abstract
The Infinite Ramsey Theorem states that given $n,r\ge 1$ and a coloring of all $n$-sized subsets of $\mathbb{N}$ into $r$ colors, there is an infinite subset of $\mathbb{N}$ in which all $n$-sized subsets have the same color. There are several natural ways of extending Ramsey's Theorem. One extension is to color infinite sets rather than finite sets. In this case, the Axiom of Choice precludes a full-fledged generalization, but upon restricting to definable colorings, much can still be said. Another way to extend Ramsey's Theorem is to color finite sub-objects of an infinite structure, requiring an infinite substructure isomorphic to the original one. While it is not possible in general to obtain substructures on which the coloring is monochromatic, sometimes one can find bounds on the number of colors, and this can have implications in topological dynamics.
In Part I, we traced the development of Ramsey theory on the Baire space, from the Nash-Williams Theorem for colorings of clopen sets to the Galvin-Prikry Theorem for Borel colorings, culminating in Ellentuck's Theorem correlating the Ramsey property with the property of Baire in a topology refining the metric topology on the Baire space. This refinement is called the Ellentuck topology and is closely connected with Mathias forcing. Several classical spaces with similar properties will be presented, including the Carlson-Simpson space and the Milliken space of block sequences. From these we derived the key properties of topological Ramsey spaces, first abstracted by Carlson and Simpson and more recently given a refined presentation by Todorcevic in his book {\em Introduction to Ramsey spaces}. As the Mathias forcing is closely connected with Ramsey ultrafilters, via forcing mod finite initial segments, so too any Ramsey space has a $\sigma$-closed version which forces an ultrafilter with partition properties. Part I showed how Ramsey spaces can be used to find general schemata into which disparate results on ultrafilters can be seen as special cases, as well as obtain fine-tuned results for structures involving ultrafilters.
Part II (the part you are watching) will focus on Ramsey theory on trees and their applications to Ramsey theory of homogeneous structures. An infinite structure is {\em homogeneous} if each isomorphism between two finite substructures can be extended to an automorphism of the infinite structure. The rationals as a linearly ordered structure and the Rado graph are prime examples of homogeneous structures. Given a coloring of singletons in the rationals, one can find a subset isomorphic to the rationals in which all singletons have the same color. However, when one colors pairs of rationals, there is a coloring due to Sierpinski for which any subset isomorphic to the rationals has more than one color on its pairsets. This is the origin of the theory of {\em big Ramsey degrees}, a term coined by Kechris, Pestov and Todorcevic, which investigates bounds on colorings of finite structures inside infinite structures. Somewhat surprisingly, a theorem of Halpern and Läuchli involves colorings of products of trees, discovered en route to a proof that the Boolean Prime Ideal Theorem is strictly weaker than the Axiom of Choice, is the heart of most results on big Ramsey degrees. We will survey big Ramsey degree results on countable and uncountable structures and related Ramsey theorems on trees, including various results of Dobrinen, Devlin, Džamonja, Hathaway, Larson, Laver, Mitchell, Shelah, and Zhang.
19:12
Biggest Breakthroughs in Math: 2023
Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory ...
published: 23 Dec 2023
Biggest Breakthroughs in Math: 2023
Biggest Breakthroughs in Math: 2023
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- published: 23 Dec 2023
- views: 1847135
Quanta Magazine’s mathematics coverage in 2023 included landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.
Read about more math breakthroughs from this year at Quanta Magazine: https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/
00:05 Ramsey Numbers
One of the biggest mathematical discoveries of the past year was in graph theory where the proof of a new, tighter upper bound to Ramsey numbers. These numbers measure the size that graphs must reach before inevitably containing structures called cliques. The discovery, announced in March, was the first advance of its type since 1935.
- Original story with links to research papers can be found here: https://www.quantamagazine.org/after-nearly-a-century-a-new-limit-for-patterns-in-graphs-20230502/
06:21 Aperiodic Monotile
The most attention-getting result of the year was the discovery of a new kind of tile that covers the plane but only in a pattern that never repeats. A two-tile combination that does this has been known since the 1970s, but the single tile, discovered by a hobbyist named David Smith and announced in March, has been a sensation.
CORRECTION: In the video, the image presented as the 'turtle' tile is in fact a rotated 'spectre' tile. To see the correct version of the turtle tile, you can visit Dave Smith's webpage: https://hedraweb.wordpress.com/2023/03/23/its-a-shape-jim-but-not-as-we-know-it/
- Original story with links to research papers can be found here: https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/
- Build your own aperiodic tiling patterns with Kaplan's online tool: https://cs.uwaterloo.ca/~csk/hat/h7h8.html
14:20 Three Arithmetic Progressions
Two computer scientists, Zander Kelley and Raghu Meka, stunned mathematicians with news of an out-of-left-field breakthrough on an old combinatorics question: How many integers can you throw into a bucket while making sure that no three of them form an evenly spaced progression? Kelley and Meka smashed a long-standing upper bound on the number of integers smaller than some cap N that could be put in the bucket without creating such a pattern.
- Original story with links to research papers can be found here: https://www.quantamagazine.org/surprise-computer-science-proof-stuns-mathematicians-20230321/
- VISIT our Website: https://www.quantamagazine.org
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Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/
51:15
Alexander Clifton: "Ramsey Theory for Diffsequences"
Abstract: Van der Waerden's theorem states that any coloring of the natural numbers with a...
published: 26 Feb 2022
Alexander Clifton: "Ramsey Theory for Diffsequences"
Alexander Clifton: "Ramsey Theory for Diffsequences"
- Report rights infringement
- published: 26 Feb 2022
- views: 76
Abstract: Van der Waerden's theorem states that any coloring of the natural numbers with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number W(r,k)$which is the smallest $n$ such that any $r$-coloring of {1,2,...,n} guarantees the presence of a monochromatic arithmetic progression of length k.
It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a D-diffsequence, which is an increasing sequence a_1,a_2...,a_k in which the consecutive differences a_i-a_{i-1} all lie in some given set D. For each D that exhibits a van der Waerden-type result, we let Delta(D,k;r) represent the analogue of the van der Waerden number W(r,k). One question of interest is to determine the possible behaviors of Delta as a function of k. In this talk, we will demonstrate that it is possible for Delta(D,k;r) to grow faster than polynomial in k. Time permitting, we will also discuss a class of D's for which no van der Waerden-type result is possible.
57:21
Ramsey Theory: Lecture 2 - Finite Ramsey's Theorem and Ramsey's Theorem for r-sets
This is the second lecture in my course on Ramsey Theory.
Email for queries: fransucic...
published: 01 Sep 2021
Ramsey Theory: Lecture 2 - Finite Ramsey's Theorem and Ramsey's Theorem for r-sets
Ramsey Theory: Lecture 2 - Finite Ramsey's Theorem and Ramsey's Theorem for r-sets
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- published: 01 Sep 2021
- views: 189
This is the second lecture in my course on Ramsey Theory.
Email for queries: [email protected]
23:00
Why complete chaos is impossible || Ramsey Theory
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days —...
published: 27 Aug 2023
Why complete chaos is impossible || Ramsey Theory
Why complete chaos is impossible || Ramsey Theory
- Report rights infringement
- published: 27 Aug 2023
- views: 48139
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!
Normal tic-tac-toe can always be drawn. But what if it lives in high dimensions? It turns out that no matter how large a tic-tac-toe board you have or how many players want to play, there always is a dimension long enough that guarantees the 1st player will always win. The theorem behind this, Hales-Jewett, is part of a family of theorems in Ramsey theory that show how lower level structures (like straight lines of the same colour) are always going to occur if the dimension is large enough. That is, you can't have a system that is totally without order. In this video we explore these tic-tac-toe generalizations, the Van Der Waerden theorem and sketch it's proof.
Reference: This undergrad level book introducing Ramsey Theory has lots more detail on all the theorems and more: https://www.sfu.ca/~vjungic/RamseyNotes/sec_Intro.html
0:00 Friends and Strangers Theorem
2:56 What is Ramsey Theory?
3:36 High dimensional Tic-Tac-Toe
7:58 Hales-Jewett Theorem
10:37 Van der Waerden's theorem
14:42 Proof sketch of Van der Waerden's theorem
21:23 Summary
21:57 Brilliant.org/TreforBazett
Check out my MATH MERCH line in collaboration with Beautiful Equations
►https://beautifulequations.net/pages/trefor
COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
► Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Cool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS I LOVE (affilliate link):
► https://www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): http://twitter.com/treforbazett
►Instagram (photography based): http://instagram.com/treforphotography
32:53
Graph Theory 9-2: Ramsey's Theorem
In this second video of Week 9, we prove Ramsey's theorem and some of its generalizations;...
published: 04 Feb 2021
Graph Theory 9-2: Ramsey's Theorem
Graph Theory 9-2: Ramsey's Theorem
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- published: 04 Feb 2021
- views: 730
In this second video of Week 9, we prove Ramsey's theorem and some of its generalizations; in particular, this involves finding order in the midst of chaos.
59:19
Advances on Ramsey numbers - Jacob Fox
https://www.math.ias.edu/seminars/abstract?event=83564
published: 23 Nov 2015
Advances on Ramsey numbers - Jacob Fox
Advances on Ramsey numbers - Jacob Fox
- Report rights infringement
- published: 23 Nov 2015
- views: 4502
https://www.math.ias.edu/seminars/abstract?event=83564
3:58
Ramsey Theory: An Introduction
This video is created as a study project by Class Math 303 Group 1B from Simon Fraser Univ...
published: 06 Apr 2014
Ramsey Theory: An Introduction
Ramsey Theory: An Introduction
- Report rights infringement
- published: 06 Apr 2014
- views: 85546
This video is created as a study project by Class Math 303 Group 1B from Simon Fraser University. The purpose of this video is to create a gentle introduction about Ramsey Theory.
Credits:
Director: Naiyuan Guo
Animation: Naiyuan Guo,Rose (Rong) Luo
Design: Biying Xu
Sound: Chrisitine Yang
Academic Proof: Nicole Cossey
Editing: Zen So
Production Supervisor: Rose (Rong) Luo
1:07:57
2022.09.27, Alexander Clifton, Ramsey Theory for Diffsequences
Alexander Clifton, Ramsey Theory for Diffsequences
September 27 2022, Tuesday @ 4:30 PM ~ ...
published: 27 Sep 2022
2022.09.27, Alexander Clifton, Ramsey Theory for Diffsequences
2022.09.27, Alexander Clifton, Ramsey Theory for Diffsequences
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- published: 27 Sep 2022
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Alexander Clifton, Ramsey Theory for Diffsequences
September 27 2022, Tuesday @ 4:30 PM ~ 5:30 PM
Room B332, IBS (기초과학연구원)
Speaker
Alexander Clifton
IBS Discrete Mathematics Group
https://sites.google.com/view/alexander-clifton/home
Van der Waerden's theorem states that any coloring of $\mathbb{N}$ with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number $W(r,k)$ which is the smallest $n$ such that any $r$-coloring of $\{1,2,\cdots,n\}$ guarantees the presence of a monochromatic arithmetic progression of length $k$.
It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a $D$-diffsequence, which is an increasing sequence $a_1, a_2, \cdots, a_k$ ($a_i$ is smaller than $a_{i+1}$) in which the consecutive differences $a_i-a_{i-1}$ all lie in some given set $D$. We say that $D$ is $r$-accessible if every $r$-coloring of $\mathbb{N}$ contains arbitrarily long monochromatic $D$-diffsequences. When $D$ is $r$-accessible, we define $\Delta(D,k;r)$ as the smallest $n$ such that any $r$-coloring of $\{1,2,\cdots,n\}$ guarantees the presence of a monochromatic $D$-diffsequence of length $k$.
One question of interest is to determine the possible behaviors of $\Delta$ as a function of $k$. In this talk, we will demonstrate that is possible for $\Delta(D,k;r)$ to grow faster than polynomial in $k$. We will also discuss a broad class of $D$'s which are not $2$-accessible.
29:59
Probability and Ramsey Theory part 1
Date: April 13, 2017
Speaker: Aaron Robertson, Colgate University
Title: Probability and...
published: 18 Apr 2017
Probability and Ramsey Theory part 1
Probability and Ramsey Theory part 1
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- published: 18 Apr 2017
- views: 520
Date: April 13, 2017
Speaker: Aaron Robertson, Colgate University
Title: Probability and Ramsey Theory
Abstract:
We will find a threshold function f(k;r) such that almost all r-colorings of more than f(k;r) consecutive integers admit a monochromatic k-term arithmetic progression while almost no r-colorings do if we have less than f(k;r) consecutive integers. We will then move on to investigate the distribution of the random variable X = number of monochromatic k-term arithmetic progressions in [1,n] under random coloring of each integer. It is known that X tends to a Poisson distribution as k tends to infinity. We investigate what X is for small k.
Large (film)
Large is a 2001 feature film directed by Justin Edgar for FilmFour.
Plot
Large is a gross-out teen comedy which centres on Jason, the son of a fading rock star, and his comic attempts to fulfill the conditions of his father's will in order to inherit a fortune.
Cast
Luke de Woolfson as Jason Mouseley
Simon Lowe as Rob
Phil Cornwell as Barry Blaze Mouseley
Melanie Gutteridge as Sophie
Morwenna Banks as Lorraine
Lee Oakes as Ian
Andrew Grainger as Norman Gates
Production
Large was produced by Alex Usburne.The pre-production period was relatively long, with writers Mike Dent and Justin Edgar draughting 20 versions of the script.Large was filmed and edited at Pebble Mill Studios and on location in Birmingham, UK, for six weeks in March and April 2000 on a budget of £1.4 million. The line producer was Paul Ritchie (Slumdog Millionaire, Bend It Like Beckham). It was the first film of Director of Photography Robbie Ryan (Fish Tank, Wuthering Heights) and Editor Eddie Hamilton (Kick Ass, X-Men: First Class). It was also Edgar's feature film debut.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Large_(film)
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