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What (who) is residue class - definition

SYSTEM OF ALGEBRAIC OPERATIONS DEFINED FOR REMAINDERS UNDER DIVISION BY A FIXED POSITIVE INTEGER; SYSTEM OF ARITHMETIC FOR INTEGERS, WHERE NUMBERS "WRAP AROUND" UPON REACHING A CERTAIN VALUE—THE MODULUS

ModularArithmetic; Modulo arithmetic; Clock arithmetic; Residue class; Mod out; Integers mod n; Advanced modular arithmetic theory; Modular arithmetic theory; Common residue; Modular multiplication; Modular Math; Modular arithmatic; Complete set of residues; Congruence arithmetic; Modular arithmetics; Congruence class; Modulo Arithmetic; Modular Arithmetic; Clock Arithmetic; Modular division; Z/nZ; Mod division; Modular math; Modulus arithmetic; Integers modulo n; Congruence modulo n; Least residue system modulo m; Complete residue system modulo m; Mod 12; Congruence modulo m; Z/n; Applications of modular arithmetic; Ring of integers modulo n; Modulus (modular arithmetic); Congruent (integers); Congruence (integers); Modulo 24

Residue (complex analysis)

COEFFICIENT OF THE TERM OF ORDER −1 IN THE LAURENT EXPANSION OF A FUNCTION HOLOMORPHIC OUTSIDE A POINT, WHOSE VALUE CAN BE EXTRACTED BY A CONTOUR INTEGRAL

Residue of an analytic function; Residue at a pole; Complex residue; Residue (mathematics)

In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f\colon \mathbb{C} \setminus \{a_k\}_k \rightarrow \mathbb{C} that is holomorphic except at the discrete points {ak}k, even if some of them are essential singularities.

https://en.wikipedia.org/wiki/Residue_(complex_analysis)

Residue theorem

THE THEOREM THAT COMPLEX CONTOUR INTEGRALS ARE SIMPLY THE SUMS OF RESIDUES OF SINGULARITIES CONTAINED WITHIN THE CONTOUR

Cauchy residue theorem; Cauchy residue formula; Residue theory; Residue Theorem; Cauchy's Residue Theorem; Cauchys Residue Theorem; Cauchy Residue Theorem; Residue formula; Residue theorem of Cauchy; Cauchy's residue theorem

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula.

https://en.wikipedia.org/wiki/Residue_theorem

Poincaré residue

GENERALIZATION OF THE CONCEPT OF RESIDUE OF A HOLOMORPHIC FUNCTION TO HIGHER DIMENSIONS

Poincare residue; Draft:Residue in several complex variables; Residue (complex geometry); Draft:Residue (Complex Geometry); Draft:Residue (complex geometry)

In mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory. It is just one of a number of such possible extensions.

https://en.wikipedia.org/wiki/Poincaré_residue

Wikipedia

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.

A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in 7 + 8 = 15, but clocks "wrap around" every 12 hours. Because the hour number starts over at zero when it reaches 12, this is arithmetic modulo 12. In terms of the definition below, 15 is congruent to 3 modulo 12, so "15:00" on a 24-hour clock is displayed "3:00" on a 12-hour clock.

https://en.wikipedia.org/wiki/Modular arithmetic