intermediate value theorem
51Approximation theory — In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by best and simpler will depend on …
52Polynomial function theorems for zeros — are a set of theorems aiming to find (or determine the nature) of the complex zeros of a polynomial function.Found in most precalculus textbooks, these theorems include: * Remainder theorem * Factor theorem * Descartes rule of signs * Rational… …
53Brent's method — In numerical analysis, Brent s method is a complicated but popular root finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some of …
54Smooth infinitesimal analysis — is a mathematically rigorous reformulation of the calculus in terms of infinitesimals. Based on the ideas of F. W. Lawvere and employing the methods of category theory, it views all functions as being continuous and incapable of being expressed… …
55Irrational number — In mathematics, an irrational number is any real number that is not a rational number that is, it is a number which cannot be expressed as a fraction m / n , where m and n are integers, with n non zero. Informally, this means numbers that cannot… …
56Karl Weierstrass — Infobox Scientist name = Karl Weierstrass |300px caption = Karl Theodor Wilhelm Weierstrass (Weierstraß) birth date = birth date|1815|10|31|mf=y birth place = Ostenfelde, Westphalia death date = death date and age|1897|2|19|1815|10|31|mf=y death… …
57Chebyshev polynomials — Not to be confused with discrete Chebyshev polynomials. In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev,[1] are a sequence of orthogonal polynomials which are related to de Moivre s formula and which can be defined… …
58Bisection method — A few steps of the bisection method applied over the starting range [a1;b1]. The bigger red dot is the root of the function. The bisection method in mathematics is a root finding method which repeatedly bisects an interval and then selects a… …
59Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …
60Atom (measure theory) — In mathematics, more precisely in measure theory, an atom is a measurable set which has positive measure and contains no set of smaller but positive measure. A measure which has no atoms is called non atomic or atomless. Contents 1 Definition 2… …
