Map (mathematics)

In mathematics, the term mapping, usually shortened to map, refers to either

There are also a few, less common uses in logic and graph theory.

Maps as functions

In many branches of mathematics, the term map is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a continuous function in topology, a linear transformation in linear algebra, etc.

Some authors, such as Serge Lang, use "function" only to refer to maps in which the codomain is a set of numbers, i.e., a subset of the fields R or C, and the term mapping for more general functions.

Sets of maps of special kinds are the subjects of many important theories: see for instance Lie group, mapping class group, permutation group.

In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. See also Poincaré map.

Map

A map is a symbolic depiction highlighting relationships between elements of some space, such as objects, regions, and themes.

Many maps are static two-dimensional, geometrically accurate (or approximately accurate) representations of three-dimensional space, while others are dynamic or interactive, even three-dimensional. Although most commonly used to depict geography, maps may represent any space, real or imagined, without regard to context or scale; e.g. brain mapping, DNA mapping and extraterrestrial mapping.

Although the earliest maps known are of the heavens, geographic maps of territory have a very long tradition and exist from ancient times. The word "map" comes from the medieval Latin Mappa mundi, wherein mappa meant napkin or cloth and mundi the world. Thus, "map" became the shortened term referring to a two-dimensional representation of the surface of the world.

Geographic maps

Cartography or map-making is the study and practice of crafting representations of the Earth upon a flat surface (see History of cartography), and one who makes maps is called a cartographer.

Maap

Maap (Yapese: Maap′) is an island and village and municipality in the state of Yap, Federated States of Micronesia. It lies on the north east of the archipelago of Yap.

Climate

References

Coordinates: 9°36′04″N 138°09′54″E / 9.601°N 138.165°E / 9.601; 138.165

Map (band)

Map is an indie pop band from Riverside, CA that consists of Josh Dooley (guitar, Voice, Harmonica), Paul Akers (Keyboards) and Trevor Monks (drums).

Biography

Josh Dooley formed Map in 2000, recording two EPs, Teaching Turtles to Fly, and Eastern Skies, Western Eyes.

Map released their first full length record, Secrets By The Highway, in 2003.

In the summer of 2004, Map released their second full length record, Think Like An Owner. This album was his first record backed by his current band line-up, consisting of Loop (bass), Heather Bray (guitar, voice) and Ben Heywood (drums).

Map released their third EP, San Francisco in the 90s, with more additions to their band line-up, consisting of Paul Akers (keyboards) and Trevor Monks (drums). This album gives tribute to late-80s Brit pop and mid-60s American jangle rock.

Discography

Full-length albums

Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Mathematics (song)

"Mathematics" is a b-side single from Mos Def's solo debut album, Black on Both Sides. It contains lyrics about various social issues and asks the listener to add them up and come to conclusions about them. Many references to numbers are found in this song and at times, Mos Def rhymes statistics in numerical order. The song highlights the differences between the White and African-American citizens of the US and uses the lyrics "Do your math..." (from Erykah Badu's "On & On") telling young African-American's to 'do their maths' so they can avoid being part of the numerous degrading statistics he raps about in the opening and third verses of the song. The song is produced by DJ Premier whose famous scratch samples make up the song's bridge. Premier has called it one of his favorite beats.

It can be found on the soundtrack of Madden NFL 2002. The song is also played briefly in the CSI: Crime Scene Investigation episode "Crate 'n' Burial".

Samples

The bridge of "Mathematics" contains DJ Premier's signature scratched vocals from various hip hop songs. The lyrics of those samples as well as information about their origin can be found below:

Mathematics (Cherry Ghost song)

"Mathematics" is the debut single from Manchester band Cherry Ghost. It was released as a digital download on March 26, 2007 and on CD and 7" vinyl on April 9, 2007. It went to #57 on the UK singles chart. "Mathematics" acquired the title "song of the week" on BBC Radio 2 in early 2007, and Zane Lowe of BBC Radio 1 declared the song "the hottest record in the world" in February 2007. Jimi Goodwin of Doves plays bass and drums on the single. The B-side "Junebug" is a Sparklehorse cover.

The song is also coincidentally appropriate for the band, as songwriter Simon Aldred has a B.Sc. in Pure Mathematics from the University of Leeds.

Two music videos were made for the song. The first, a self-produced video featuring a man in a bird costume, was posted in late 2006. The second, featuring Simon Aldred's family home movies, appeared on Heavenly Records' website in early 2008.

Track listings

All songs written by Simon Aldred except where noted.

Promo CD (HVN167CDRP):