In additive combinatorics, the Ruzsa triangle inequality, also known as the Ruzsa difference triangle inequality to differentiate it from some of its variants, bounds the size of the difference of two sets in terms of the sizes of both their differences with a third set. It was proven by Imre Ruzsa (1996), and is so named for its resemblance to the triangle inequality. It is an important lemma in the proof of the Plünnecke-Ruzsa inequality. (Wikipedia).
21. Structure of set addition I: introduction to Freiman's theorem
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX What can we say about sets A of integers whose sumset A +
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
This video states and investigates the triangle inequality theorem. Complete Video List: http://www.mathispower4u.yolasite.com
From playlist Relationships with Triangles
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Summary for solving one variable inequalities
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About
What do you need to know to solve one variable inequalities
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About
The Quasi-Polynomial Freiman-Ruzsa Theorem of Sanders - Shachar Lovett
Shachar Lovett Institute for Advanced Study March 20, 2012 The polynomial Freiman-Ruzsa conjecture is one of the important open problems in additive combinatorics. In computer science, it already has several diverse applications: explicit constructions of two-source extractors; improved bo
From playlist Mathematics
Why do we have to flip the sign when we divide or multiply by negative one - Cool Math
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About
Introduction to additive combinatorics lecture 9.5 --- Freiman's theorem for subsets of F_p^N.
Freiman's theorem for subsets of F_p^N states that if A is a subset of F_p^N and |A + A| is at most C|A|, then there is a subspace X of F_p^N of size at most C'|A| that contains A, where C' depends only on C. The result is actually due to Imre Ruzsa. Here I give not Ruzsa's original proof,
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
How to solve and graph one variable inequalities
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About
Introduction to additive combinatorics lecture 6.6 --- Ruzsa's embedding lemma for subsets of Z
Ruzsa's embedding lemma for subsets of Z says that if A is a finite set of integers and the set kA - kA has size at most C|A|, then it is possible to find a subset A' of A of size at least |A|/k that is Freiman isomorphic of order k to a subset of Z/NZ, where N is a prime between 2C|A| and
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
How to graph and shade a system of linear inequalities
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of Inequalities by Graphing
How to graph a system of linear inequalities in slope intercept form
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of Inequalities by Graphing
Graphing a system of inequalities when one inequality is a vertical boundary line
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of Inequalities by Graphing
An Additive Combinatorics Approach to the Log-Rank Conjecture in... Complexity - Noga Zewi
Noga Zewi Technion February 27, 2012 For a (0,1}-valued matrix M let CC(M) denote he deterministic communication complexity of the boolean function associated with M. The log-rank conjecture of Lovasz and Saks [FOCS 1988] states that CC(M) less than =logc(rank(M))CC(M) less than=logc(rank(
From playlist Mathematics
22. Structure of set addition II: groups of bounded exponent and modeling lemma
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao explains the Ruzsa covering lemma and uses it
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Graphing a system of linear inequalities
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of Inequalities by Graphing
17. Graph limits IV: inequalities between subgraph densities
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Among all graphs with a given edge density, which graph h
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
24. Structure of set addition IV: proof of Freiman's theorem
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX This lecture concludes the proof of Freiman's theorem on
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Max/Min Value of |z| (2 of 2: Triangle inequality)
More resources available at www.misterwootube.com
From playlist Using Complex Numbers
How to determine the solution of a system of linear inequalities by graphing
👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of
From playlist Solve a System of inequalities by Graphing | Standard Form