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...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...Sperner, which uses concepts called '''shadows''' and '''shades''' of set systems. ...

...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...Sperner, which uses concepts called '''shadows''' and '''shades''' of set systems. ...

...s and Rado, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...

...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...Sperner, which uses concepts called '''shadows''' and '''shades''' of set systems. ...

'''Special relativity''' (or '''the special theory of relativity''') is a theory in [[physics]] that was developed and explained by [[Albert Einstein]] in 1 ...ved in [[luminiferous aether]]. Various tiny effects were expected if this theory were true. Gradually it seemed these predictions were not going to work out ...

...s and Rado, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...

...s and Rado, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...

...s and Rado, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...

...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...Sperner, which uses concepts called '''shadows''' and '''shades''' of set systems. ...

*[[set theory]] *[[Banach space]] theory ...

...olecular orbital]]s. This is used in the [[Hückel method]], [[ligand field theory]], and the [[Woodward–Hoffmann rules]]. Another idea on a larger scale is t ...ic point groups was published in 1936 by Rosenthal and Murphy.<ref>''Group Theory and the Vibrations of Polyatomic Molecules'' Jenny E. Rosenthal and G. M. M ...

...s and Rado, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...

...s and Rado, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...ult, called Sperner's theorem today, initiated the studies of extremal set theory. ...

| title = Schaum's outline of theory and problems of linear algebra | title = Cauchy and the spectral theory of matrices ...

...en.wikipedia.org/wiki/Computational_learning_theory computational learning theory]. ...on is found by Vapnik and Chervonenkis, who use the framework to develop a theory of classifications. ...

...en.wikipedia.org/wiki/Computational_learning_theory computational learning theory]. ...on is found by Vapnik and Chervonenkis, who use the framework to develop a theory of classifications. ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

...4mhz.de/cook.html|title = Proceedings of the Third Annual ACM Symposium on Theory of Computing|pages = 151–158}}</ref> ...able to check <math>1,000,000</math> combinations per second using current systems.<!--How to remove the need for annual editorial review of this eventually o ...

*The letters ''m'' and ''b'' are constants.<ref>{{cite book|title=Theory and Problems of Beginning Finite Mathematics|last1=Lipschutz|first1=Seymour ...his form is often used in [[geometry]] and in [[system of linear equations|systems of linear equations]]. ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

In probability theory class we have learned the basic concepts of '''events''' and '''random vari ...f events and random variables are related to the foundation of probability theory, which is not the topic of this class. Here we only give an informal descri ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

== Systems of Distinct Representatives (SDR)== {{Theorem|Hall's Theorem (graph theory form)| ...

Note that (*) and (**) are both linear systems with unique solution, thus <math>\tau_{u,v}=\phi_{u,v}</math>. Since electrical networks are linear systems, we can super-pose <math>A</math> and <math>C</math> (summing up the voltag ...

Note that (*) and (**) are both linear systems with unique solution, thus <math>\tau_{u,v}=\phi_{u,v}</math>. Since electrical networks are linear systems, we can super-pose <math>A</math> and <math>C</math> (summing up the voltag ...

Note that (*) and (**) are both linear systems with unique solution, thus <math>\tau_{u,v}=\phi_{u,v}</math>. Since electrical networks are linear systems, we can super-pose <math>A</math> and <math>C</math> (summing up the voltag ...

...non-linear approach, the orbital approaches at a slightly off angle. The π-systems ability to rotate as the small molecule approaches is crucial in forming ne ...curs through a non-linear approach (see figure 2 at right). However, while theory clearly favors a non-linear approach, there are no obvious experimental imp ...