Crazy (Seal song)

"Crazy" is a song originated by English soul artist Seal, who wrote its lyrics and jointly composed its music in collaboration with producer Guy Sigsworth. The song was produced by Trevor Horn for Seal's debut album Seal (1991). Released as his debut single, "Crazy" became one of Seal's biggest hits, reaching the top five in the United Kingdom while becoming his first top ten single in the United States. It has since been interpreted by several artists, including Alanis Morissette, whose version was released as a single from her album The Collection (2005).

Background and composition

Seal wrote "Crazy" in 1990 inspired by the fall of the Berlin Wall in 1990 and the Tiananmen Square Massacre in 1989. In 2015, Seal said of the song's conception in 1990: "I felt the cycle had reached its apex. I felt the world changing and I felt profound things happening."

According to the song's producer Trevor Horn, "Crazy" was made over the course of two months: "Crazy wasn't an easy record to make, because we were aiming high".

Crazy (Ricki-Lee Coulter song)

"Crazy" is a song by Australian recording artist Ricki-Lee Coulter, taken from her third studio album Fear & Freedom (2012). It was written by Coulter, Brian London and Johnny Jam, while the production was also handled by the latter two. The song was released digitally on 13 July 2012, as the third single from the album.

Lyrically, Coulter stated that "Crazy" is about "encouraging you [to] let go of your inhibitions, go crazy and let the music take over". Following its release, "Crazy" peaked at number four on the ARIA Dance Chart and number 46 on the ARIA Singles Chart. The accompanying music video was directed by Melvin J. Montalban and filmed in the Callan Park Hospital for the Insane in Sydney. The video features Coulter playing three characters – a nurse, patient and psychologist.

Background and release

"Crazy" was written by Ricki-Lee Coulter, Brian London and Johnny Jam, while the production was also handled by the latter two. During an interview with The Daily Telegraph, Coulter said she wrote the song "as if I was actually singing it directly to the people on the dance floor". She went on to describe it as "sensual and erotic, encouraging you let go of your inhibitions, go crazy and let the music take over". "Crazy" was released digitally on 13 July 2012. On 23 July 2012, it debuted at number 52 on the ARIA Singles Chart and number four on the ARIA Dance Chart. The following week, "Crazy" fell out of the top 100 of the ARIA Singles Chart. On 6 August 2012, the song re-entered the chart at number 46, where it peaked.

Because of You (Ne-Yo album)

Because of You is the second studio album by American recording artist Ne-Yo, released on April 25, 2007 by Def Jam Recordings in the United States. It features guest contributions from rapper Jay-Z on "Crazy" and singer Jennifer Hudson on "Leaving Tonight". Because of You debuted at number one on the Billboard 200 and Top R&B/Hip-Hop Albums charts, selling over 250,000 copies in its first week. Upon its release, the album received generally positive reviews from most music critics, based on an aggregate score of 74/100 from Metacritic. It won a Grammy Award for Best Contemporary R&B Album at the 2008 Grammy Awards.

Critical reception

The album has drawn mainly positive reviews, with Entertainment Weekly magazine noting, "Indeed, the album is an unmistakable attempt to channel [Michael Jackson's early work such as "Off the Wall"]...and the effort often pays off beautifully...Ne-Yo's lithe falsetto puts the many others who've been labeled Jackson-esque to shame." PopMatters.com called the album "a masterpiece of a record" and praised the title track's blend of "upbeat modern-day funk tempo, beautifully melodic backdrop and love-sick (in a good way) vocals...[it's] the perfect lead single off an album that is filled with number-one hits".Slant Magazine also compared the album's sensual ballads to Janet Jackson.

Degree

Degree may refer to:

As a unit of measurement

Field extension

In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 | a, b ∈ Q} is the smallest extension of Q that includes every real solution to the equation x² = 2.

Definitions

Let L be a field. A subfield of L is a subset K of L that is closed under the field operations of L and under taking inverses in L. In other words, K is a field with respect to the field operations inherited from L. The larger field L is then said to be an extension field of K. To simplify notation and terminology, one says that L / K (read as "L over K") is a field extension to signify that L is an extension field of K.

If L is an extension of F which is in turn an extension of K, then F is said to be an intermediate field (or intermediate extension or subextension) of the field extension L / K.

Degree of an algebraic variety

The degree of an algebraic variety in mathematics is defined, for a projective variety V, by an elementary use of intersection theory.

Definition

For V embedded in a projective space Pⁿ and defined over some algebraically closed field K, the degree d of V is the number of points of intersection of V, defined over K, with a linear subspace L in general position, when

Here dim(V) is the dimension of V, and the codimension of L will be equal to that dimension. The degree d is an extrinsic quantity, and not intrinsic as a property of V. For example the projective line has an (essentially unique) embedding of degree n in Pⁿ.

Properties

The degree of a hypersurface F = 0 is the same as the total degree of the homogeneous polynomial F defining it (granted, in case F has repeated factors, that intersection theory is used to count intersections with multiplicity, as in Bézout's theorem).

Other approaches

For a more sophisticated approach, the linear system of divisors defining the embedding of V can be related to the line bundle or invertible sheaf defining the embedding by its space of sections. The tautological line bundle on Pⁿ pulls back to V. The degree determines the first Chern class. The degree can also be computed in the cohomology ring of Pⁿ, or Chow ring, with the class of a hyperplane intersecting the class of V an appropriate number of times.