Search results
Results from the WOW.Com Content Network
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
The Trachtenberg system is a system of rapid mental calculation.The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly.
Local and global maxima and minima for cos(3πx)/x, 0.1≤ x ≤1.1. In mathematical analysis, the maximum and minimum [a] of a function are, respectively, the greatest and least value taken by the function.
Throughout, it is assumed that is a real or complex vector space.. For any ,,, say that lies between [2] and if and there exists a < < such that = + ().. If is a subset of and , then is called an extreme point [2] of if it does not lie between any two distinct points of .
A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. [17] [d] Michael Maestlin, the first to write a decimal approximation of the ratio. The golden ratio was studied peripherally over the next millennium.
The extreme value theorem was originally proven by Bernard Bolzano in the 1830s in a work Function Theory but the work remained unpublished until 1930. Bolzano's proof consisted of showing that a continuous function on a closed interval was bounded, and then showing that the function attained a maximum and a minimum value.
The extreme value theorem states that M is finite and f (c) = M for some c ∈ [a, b]. This can be proved by considering the set S = {s ∈ [a, b] : sup f ([s, b]) = M} . By definition of M, a ∈ S, and by its own definition, S is bounded by b. If c is the least upper bound of S, then it follows from continuity that f (c) = M.