Post-rock is a form of experimental rock characterized by a focus on exploring textures and timbre over traditional rock song structures, chords, or riffs. Post-rock artists are instrumental combining rock instrumentation with electronics; the genre emerged within the indie and underground music scene of early 1990s. However, due to its abandonment of rock conventions, it bears little resemblance musically to contemporary indie rock, borrowing instead from diverse sources including ambient music, jazz, krautrock and minimalist classical. Artists such as Talk Talk and Slint have been credited with producing foundational works in the style in the early 1990s; the term post-rock itself was coined by journalist Simon Reynolds in a review of the 1994 Bark Psychosis album Hex. It solidified into a recognizable trend with the release of Tortoise's 1996 album Millions Now Living Will Never Die; the term has since been used to describe bands which differ in style, making the term controversial among listeners and artists alike.

The concept of "post-rock" was coined by critic Simon Reynolds in his review of Bark Psychosis' album Hex, published in the March 1994 issue of Mojo magazine. Reynolds expanded upon the idea in the May 1994 issue of The Wire. Writing about artists like Seefeel, Disco Inferno, Techno Animal, Robert Hampson, Insides, Reynolds used the term to describe music "using rock instrumentation for non-rock purposes, using guitars as facilitators of timbre and textures rather than riffs and power chords", he further expounded on the term, Perhaps the provocative area for future development lies... in cyborg rock. Reynolds, in a July 2005 entry in his blog, claimed he had used the concept of "post-rock" before using it in Mojo referencing it in a feature on the band Insides for music newspaper Melody Maker, he said he found the term itself not to be of his own coinage, saying in his blog, "I discovered many years it had been floating around for over a decade." The term was used by American journalist James Wolcott in a 1975 article about musician Todd Rundgren, although with a different meaning.

It was used in the Rolling Stone Album Guide to name a style corresponding to "avant-rock" or "out-rock". The earliest use of the term dates back as far as September 1967. In a Time cover story feature on the Beatles, writer Christopher Porterfield hails the band and producer George Martin's creative use of the recording studio, declaring that this is "leading an evolution in which the best of current post-rock sounds are becoming something that pop music has never been before: an art form." Another pre-1994 example of the term in use can be found in an April 1992 review of 1990s noise-pop band The Earthmen by Steven Walker in Melbourne music publication Juke, where he describes a "post-rock noisefest". The post-rock sound incorporates characteristics from a variety of musical genres, including krautrock, psychedelia, prog rock, space rock, math rock, tape music, minimalist classical, British IDM, dub reggae, as well as post-punk, free jazz, contemporary classical, avant-garde electronica.

It bears similarities to drone music. Early post-rock groups often exhibited strong influence from the krautrock of the 1970s borrowing elements of "motorik", the characteristic krautrock rhythm. Post-rock compositions make use of repetition of musical motifs and subtle changes with an wide range of dynamics. In some respects, this is similar to the music of Steve Reich, Philip Glass and Brian Eno, pioneers of minimalism. Post-rock pieces are lengthy and instrumental, containing repetitive build-ups of timbre and texture. Vocals are omitted from post-rock; when vocals are included, the use is non-traditional: some post-rock bands employ vocals as purely instrumental efforts and incidental to the sound, rather than a more traditional use where "clean" interpretable vocals are important for poetic and lyrical meaning. When present, post-rock vocals are soft or droning and are infrequent or present in irregular intervals. Sigur Rós, a band known for their distinctive vocals, fabricated a language they called "Hopelandic", which they described as "a form of gibberish vocals that fits to the music and acts as another instrument."In lieu of typical rock structures like the verse-chorus form, post-rock groups make greater use of soundscapes.

Simon Reynolds states in his "Post-Rock" from Audio Culture that "A band's journey through rock to post-rock involves a trajectory from narrative lyrics to stream-of-consciousness to voice-as-texture to purely instrumental music". Reynolds' conclusion defines the sporadic progression from rock, with its field of sound and lyrics to post-rock, where samples are stretched and looped. Wider experimentation and blending of other genres have taken hold in the post-rock scene. Cult of Luna, Russian Circles, Palms and Pelican have fused metal with post-rock styles; the resulting sound has been termed post-metal. More sludge metal has grown and evolved to include some elements of post-rock; this second wave of sludge metal has been pioneered by bands such as Giant Battle of Mice. This new sound is seen on the label of Neurot Recordings. Bands such as Altar of Plagues, Lantlôs and Agalloch blend between post-rock and black metal, incorpora

Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, the results obtained may turn out to be useful for practical applications, but pure mathematicians are not motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles. While pure mathematics has existed as an activity since at least Ancient Greece, the concept was elaborated upon around the year 1900, after the introduction of theories with counter-intuitive properties, the discovery of apparent paradoxes; this introduced the need of renewing the concept of mathematical rigor and rewriting all mathematics accordingly, with a systematic use of axiomatic methods. This led many mathematicians to focus on mathematics for its own sake, that is, pure mathematics. All mathematical theories remained motivated by problems coming from the real world or from less abstract mathematical theories.

Many mathematical theories, which had seemed to be pure mathematics, were used in applied areas physics and computer science. A famous early example is Isaac Newton's demonstration that his law of universal gravitation implied that planets move in orbits that are conic sections, geometrical curves, studied in antiquity by Apollonius. Another example is the problem of factoring large integers, the basis of the RSA cryptosystem used to secure internet communications, it follows that, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference than a rigid subdivision of mathematics. In particular, it is not uncommon that some members of a department of applied mathematics describe themselves as pure mathematicians. Ancient Greek mathematicians were among the earliest to make a distinction between pure and applied mathematics. Plato helped to create the gap between "arithmetic", now called number theory, "logistic", now called arithmetic.

Plato regarded logistic as appropriate for businessmen and men of war who "must learn the art of numbers or will not know how to array troops" and arithmetic as appropriate for philosophers "because to arise out of the sea of change and lay hold of true being." Euclid of Alexandria, when asked by one of his students of what use was the study of geometry, asked his slave to give the student threepence, "since he must make gain of what he learns." The Greek mathematician Apollonius of Perga was asked about the usefulness of some of his theorems in Book IV of Conics to which he proudly asserted, They are worthy of acceptance for the sake of the demonstrations themselves, in the same way as we accept many other things in mathematics for this and for no other reason. And since many of his results were not applicable to the science or engineering of his day, Apollonius further argued in the preface of the fifth book of Conics that the subject is one of those that "...seem worthy of study for their own sake."

The term itself is enshrined in the full title of the Sadleirian Chair, Sadleirian Professor of Pure Mathematics, founded in the mid-nineteenth century. The idea of a separate discipline of pure mathematics may have emerged at that time; the generation of Gauss applied. In the following years and professionalisation started to make a rift more apparent. At the start of the twentieth century mathematicians took up the axiomatic method influenced by David Hilbert's example; the logical formulation of pure mathematics suggested by Bertrand Russell in terms of a quantifier structure of propositions seemed more and more plausible, as large parts of mathematics became axiomatised and thus subject to the simple criteria of rigorous proof. Pure mathematics, according to a view, is what is proved. Pure mathematician achievable through training; the case was made that pure mathematics is useful in engineering education: There is a training in habits of thought, points of view, intellectual comprehension of ordinary engineering problems, which only the study of higher mathematics can give.

One central concept in pure mathematics is the idea of generality. Uses and advantages of generality include the following: Generalizing theorems or mathematical structures can lead to deeper understanding of the original theorems or structures Generality can simplify the presentation of material, resulting in shorter proofs or arguments that are easier to follow. One can use generality to avoid duplication of effort, proving a general result instead of having to prove separate cases independently, or using results from other areas of mathematics. Generality can facilitate connections between different branches of mathematics. Category theory is one area of mathematics dedicated to exploring this commonality of structure as it plays out in some areas of math. Generality's impact on intuition is both dependent on the subject and a matter of personal preference or learning style. Generality is seen as a hindrance to intuition, although it can function as an aid to it when it provides analogies to material for which one has good intuition.

As a prime example of generality, the Erlangen progra

The 2017 LA Galaxy season was the club's twenty-second season of existence, their twenty-second season in Major League Soccer, the top flight of American soccer. 2017 marked a downturn for the club signalling the end of a dynasty for the Galaxy. It was the first season since 2008. Where a player has not declared an international allegiance, nation is determined by place of birth. Squad correct as of September 2, 2017; the LA Galaxy passed on making a selection with the 81st overall pick. The first preseason match was announced on December 9, 2016; the full preseason schedule was released on January 20, 2017. All times in Pacific Time Zone; the pairing for the fourth round was announced on May 18, 2017. The draw for this round was held on June 15, 2017; as of October 22. 2017 in American soccer 2017 LA Galaxy II season Official website