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Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

...ntifier. Therefore, the sentence "every natural number has another natural number larger than it" is a quantified expression. Quantifiers and quantified expr : For each [[natural number]] ''n'', ''n'' · 2 = ''n'' + ''n''. ...

...ath> satisfying the condition in the Ramsey theory is called the '''Ramsey number'''. Prove that: ...no red triangles and no blue <math>4</math>-cliques. Try to determine the number of red and blue edges adjacent to each vertex.) ...

Note that in probability theory, the "mutual independence" is <font color="red">not</font> equivalent with ...<math>p</math>. Flipping the coin for n times, what is the expectation of number of HEADs? ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

...of samples of various distributions. <ref>Gumbel, E.J. 1954. "Statistical theory of extreme values and some practical applications". ''Applied Mathematics S ...

=== Ramsey number === ...ath> satisfying the condition in the Ramsey theory is called the '''Ramsey number'''. ...

...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 ...

...ny equations and many variables, not just two or three. In many cases, the number of equations and variables in the system are the same. In some cases, ther ...ds on the properties of the field. In many cases there will be an infinite number of solutions. ...

* [<strong>Random number of random variables</strong>] Let <math>\{X_n\}_{n \ge 1}</math> be identic ...rom the <strong>second</strong> round of tosses, and <math>Y</math> be the number of heads resulting from <strong>all</strong> tosses, which includes the fir ...

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

...be found by mathematically manipulating the wave function to return [[real number|real]] values relating to physical properties such as [[position]], [[momen The wave function can be in a number of different states at once, and so a particle may have many different posi ...