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In the most commonly used convention (e.g., Apostol 1967, pp. 202-204), the first fundamental theorem of calculus, also termed "the fundamental theorem, part I" (e.g., Sisson ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

Let there be three polynomials a(x), b(x), and c(x) with no common factors such that a(x)+b(x)=c(x). Then the number of distinct roots of the three polynomials is one or more ...

Thâbit ibn Kurrah's rules is a beautiful result of Thâbit ibn Kurrah dating back to the tenth century (Woepcke 1852; Escott 1946; Dickson 2005, pp. 5 and 39; Borho 1972). ...

Grinberg constructed a number of small cubic polyhedral graph that are counterexamples to Tait's Hamiltonian graph conjecture (i.e., that every 3-connected cubic graph is ...

An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

Binet's formula is an equation which gives the nth Fibonacci number as a difference of positive and negative nth powers of the golden ratio phi. It can be written as F_n = ...

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time ...