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Gauge group (mathematics) A gauge group is a group of gauge symmetries of the Yang–Mills gauge theory of principal connections on a principal bundle. Given a principal bundle with a structure Lie group , a gauge group is defined to be a group of its vertical automorphisms. This group is isomorphic to the group of global sections of the ...
Limit (mathematics) In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. [1] Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals . In formulas, a limit of a function is usually written as.
The Principles of Mathematics (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical. [1] The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference.
Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
Principles of Mathematical Analysis. Principles of Mathematical Analysis, colloquially known as " PMA " or " Baby Rudin ," [1] is an undergraduate real analysis textbook written by Walter Rudin. Initially published by McGraw Hill in 1953, it is one of the most famous mathematics textbooks ever written.
The principal part at of a function. is the portion of the Laurent series consisting of terms with negative degree. [1] That is, is the principal part of at . If the Laurent series has an inner radius of convergence of , then has an essential singularity at if and only if the principal part is an infinite sum.
Ideal (ring theory) In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3.
In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus is Latin for "small pebble" (the diminutive of calx, meaning "stone"), a meaning which still persists in medicine. Because such pebbles were used for counting out distances, [5 ...