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Topic: Composition (number theory)

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Integer partition

Composition

Number theory

Mathematics

	HR - Automatic Theory Formation In Pure Mathematics
		The fact that HR only re-invented tau numbers shouldn't detract from its achievement, as these integers are clearly interesting and despite having a very simple definition, they have only recently been introduced to number theory, and have rarely been discussed.
		A047727]Average divisor is an integer and the number is refactorable.
		Tau numbers are congruent to 0,1,2 or 4 mod 8.
	www.dai.ed.ac.uk /homes/simonco/research/hr/number_theory.html (2020 words)

	Galois theory Summary
		Galois theory depends on the concept of a group since it is the mathematical interpretation of group theory.
		The central idea of Galois theory is to consider those permutations (or rearrangements) of the roots having the property that any algebraic equation satisfied by the roots is still satisfied after the roots have been permuted.
		If a factor group in the composition series is cyclic of order n, then the corresponding field extension is a radical extension, and the elements of L can then be expressed using the nth root of some element of K.
	www.bookrags.com /Galois_theory (2469 words)

	Perfect numbers
		It is not known when perfect numbers were first studied and indeed the first studies may go back to the earliest times when numbers first aroused curiosity.
		Today the usual definition of a perfect number is in terms of its divisors, but early definitions were in terms of the 'aliquot parts' of a number.
		Among simple even numbers, some are superabundant, others are deficient: these two classes are as two extremes opposed to one another; as for those that occupy the middle position between the two, they are said to be perfect.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Perfect_numbers.html (4360 words)

	ENGLISH 401: COMPOSITION IV: THEORY & RESEARCH Composition Studies - Find Articles (Site not responding. Last check: 2007-10-08)
		The first goal necessarily engages students in the exploration of composition theory by requiring extensive reading and discussion of composition theory and current research.
		Since I believe that theory is best presented at this level as a "work in progress" with a myriad of dissenting factions, I selected the Villanueva anthology that, while organized around salient topics, also notably offers conflicting views regarding those topics.
		Her ultimate argument that two factors-dialogue and the rejection of mastery-are the essence of the relevance of post-process theory to pedagogy were especially relevant to this course.
	www.findarticles.com /p/articles/mi_qa3986/is_200504/ai_n13637618 (610 words)

	FGC, Inc. - Theory (Site not responding. Last check: 2007-10-08)
		The composition, temperature and pressure of the gas govern the basic particle charging capability of the precipitator while particle size, particle concentration, and electrical resistivity of the ash affect both the charging and collecting capability of the precipitator.
		The chemical composition of the flyash varies widely.
		Flyash resistivity depends upon a number of factors, including not only the chemical composition, but the flue gas temperature, the moisture content, and the SO3 content in the flue gas.
	www.peco-fgc.com /fgc/theory.php (877 words)

	ThinkQuest : Library Search
		The Theory of Relativity is the most groundbreaking scientific theory of this century (along with Quantum Mechanics), reshaping our ideas of space and time.
		Our aim is to introduce quantum theory in a easily understandable form with the idea to interest other young people in science and more spesific in the quantum theory.
		Theories of famous scientists are explained and questions regarding the nature of the universe are asked.
	www.thinkquest.org /library/search.html?search_text=theory (1025 words)

	UM School of Music, Theatre & Dance - Department of Music Theory - Degree Programs
		In addition to the necessary transcripts and recommendations, each applicant for the Ph.D. in music composition and theory must demonstrate by scores and recordings of original music and by interview, when requested, the qualities of mind, the gift, the technical resources, and the musical maturity requisite to graduate study in composition.
		A sample of his or her writing related to music theory must be submitted; the applicant's master's thesis or a major term paper are particularly recommended.
		Composition exam: During the first year of doctoral study, each student in the program will be given a list of 60 to 75 works from which to choose or be assigned ten works on which to be examined during a general oral preliminary examination.
	www.music.umich.edu /departments/mustheory/phd_comp_theory.htm (1963 words)

	UM School of Music, Theatre & Dance - Department of Music Theory - Degree Programs
		The faculty in music theory, numbering ten, are distinguished for their nationally and internationally recognized achievement in research, composition, and performance.
		Students entering without the master's degree in music theory should normally achieve candidacy by the end of the sixth term; those entering with a master's degree in music theory should achieve candidacy by the end of the fourth term.
		The examination is administered by three members of the Music Theory department chosen by the student in consultation with the Graduate Committee; one of these three faculty members serves as the major preliminary examination advisor.
	www.music.umich.edu /departments/mustheory/phd.htm (2178 words)

	Music Theory Dictionary - The Method Behind the Music
		One unit of meter, consisting of a number of accented and unaccented beats.
		Meter signatures usually consist of two numbers, the lower indicating the note of value, and the upper the number of these notes per measure.
		A melodic figure or phrase that is the basis for a composition or a section of a composition.
	www.numbera.com /musictheory/theory/dictionary.aspx (1596 words)

	Bio. 315 _515@ Towson: Germ theory of disease (Site not responding. Last check: 2007-10-08)
		Kochs postulates not only proved the germ theory but also gave a tremendous boost to the development of microbiology by stressing a laboratory culture and identification of microorganisms.
		The number and composition of chromosomes and the number of genes on each chromosome are characteristic of the each species.
		The composition of capsule is useful in differentiating between different types of bacteria.
	www.towson.edu /~wubah/medmicro/Germ_theory.htm (1323 words)

	Apogee Photo Magazine: Gestalt Theory and Photographic Composition
		The result was a theory of principles, supposedly free from subjective aesthetic bias, that artists have been able to use to present visual information - whether it be the printed page, painting or photography.
		This theory is called "Gestalt theory" and although it may use unfamiliar names or titles, these principles should be familiar to most photographers.
		Portrait artists often do this in their "bullseye" style of composition, because they want you, as the viewer, to be drawn into the face and eyes of their subjects.
	www.apogeephoto.com /mag1-6/mag2-3mf.shtml (953 words)

	VARIOUS NUMBER THEORY ANNOUNCEMENTS (Site not responding. Last check: 2007-10-08)
		All of these conferences have been acclaimed by the international number theory community for the high quality of the scientific program, as evidenced by the excellence of the speakers and the diversity of topics presented.
		Neumann: The impact of Gauss's DA on the theory of solvability of equations by radicals.
		Haubrich: Gaussian number theory and algebraic number theory.
	www.numbertheory.org /ntw/announcements.html (8704 words)

	The Math Forum - Math Library - Group Theory (Site not responding. Last check: 2007-10-08)
		Group Theory is a branch of algebra, but has strong connections with almost all parts of mathematics.
		Group theory can be considered the study of symmetry: the collection of symmetries of some object preserving some of its structure forms a group; in some sense all groups arise this way.
		A paper that presents an integrally generalized theory or conceptualization of life that includes elements of an axiomatic approach and is physically interpretable, formulated as the result of attempts to invent a holistic system of creative synthetic...more>>
	mathforum.org /library/topics/group_theory (2240 words)

	Fasset.org -. threads, fass fuel pump, painting, textiles, composition, realism, designs, colour, monet, pottery (Site not responding. Last check: 2007-10-08)
		The food composition of the nationalrat is determined every four years by a free general election in which every citizen is allowed to vote to fill its 183 seats.
		Completed in 1972 in panama city, it is perched on a high cliff overlooking the canal, and is constructed of local stone laid in a pattern reminiscent of native american fabric designs.
		This allowed the dj to chose the colourful and shape of the beam and, by moving the mirror, where in the room it would be projected.
	www.fasset.org /Threads.html (854 words)

	Algorithmic Composition as a Model of Creativity
		The explicit message is that algorithmic composition is invalid as a methodology, but the implicit message is that the music produced is in some sense unlike what the composer would have produced without help.
		In other words, music produced by algorithmic composition is considered somehow inferior not because it was produced by an algorithm, but because it is someone else's music--it belongs to the designer of the algorithm, and not to the user of the algorithm.
		The composition process described in the previous section is not specific to a computer program; the process is quite similar to the creative processes of a human.
	www.ee.umd.edu /~blj/algorithmic_composition/algorithmicmodel.html (3643 words)

	PAINTING THEORY of Peter Hubbard
		While I handle composition with the element I term GRID, the fact that this GRID is also a visible element in my paintings makes it an especially important part of my system, and so I have more to say about the theory behind it.
		Composition has to do with the shape of the canvas (ratio of length to width), where the IMAGE occurs on it, and how other elements of the painting are positioned relative to each other.
		Then I will attempt to explain some of the theory behind this process, which is especially important to make clear, as I feel it is the way my system applies the colors repeatedly that the chief benefit of the system is derived.
	www.petehubbard.com /theory.php (7511 words)

	The History of Algorithmic Composition
		Cage also delegated the compositional process to natural phenomena, as in his Atlas Eclipticalis (1961), which was composed by laying score paper on top of astronomical charts and placing notes simply where the stars occurred, again delegating the compositional process to indeterminacy (Schwartz, 1993).
		The earliest instance of computer generated composition is that of Lejaren Hiller and Leonard Isaacson at the University of Illinois in 1955-56.
		These new techniques could also potentially improve algorithmic composition, it would seem, since the "critic" functions that we have seen in examples of genetic programming could gain much improvement from their insights into how humans listen to music: the computer could, then, better judge itself as to the quality of its output.
	ccrma-www.stanford.edu /~blackrse/algorithm.html (3211 words)

	Bibliography - Music Theory and Composition (Site not responding. Last check: 2007-10-08)
		There are also general music theory and orchestration/composition topics covered, lending the book to be a good supplemental reading for anyone interested in music theory or composition, in my opinion.
		This is the official website of Larry Solomon, a widely respected professor of music theory, with many unconventional elements and contemporary theories built in, to provide his students with a broader palate of musical tools to express themselves.
		It is a means of teaching music theory, while allowing users to self-test and self-diagnose problem areas in their comprehension (or lack thereof) in the realm of theory and composition.
	www.rit.edu /~cjm1367/imm/project1/biblio.html (2379 words)

	UH Music Department - COMPOSITION & THEORY PROGRAMS and DEGREES
		All composition students are strongly encouraged to study with each of the faculty composers, thus receiving a variety of perspectives and feedback on their music.
		There is no language requirement for the Master of Music in Composition, but a 30-45 minute public recital of original works composed during the master's studies is required in addition to the thesis composition and detailed analysis.
		The PhD in Music with emphasis in Composition also has no language requirement, but a full 60-75 minute public recital of original works composed during the course of study is required in addition to the thesis composition and detailed analysis.
	www.hawaii.edu /uhmmusic/ptheory.htm (1466 words)

	Compositon-Theory at UIUC: Salvatore Martirano Award
		Professor Martirano studied composition with Herbert Elwell at Oberlin College (1947-51), Bernard Rodgers at The Eastman School of Music (1952), and with Luigi Dallapiccola at the Cherubini Conservatory in Florence, Italy (1952-4).
		He was professor of composition at the University of Illinois from 1963 till his retirement in 1995.
		His compositions have been performed by the New York Philharmonic, Chicago Symphony, Los Angeles Philharmonic, Vienna Philharmonic Orchestra, and the Cleveland Orchestra, and by radio orchestras and choral ensembles throughout the United States, Europe and Asia.
	www-camil.music.uiuc.edu:16080 /comptheory/Awards/Martirano.html (666 words)

	Moores School of Music: Music Theory Curriculum
		Students, transfer or native, who fail to achieve a score of 70 on any proficiency exam are not required to repeat theory courses in which they received grade of C- or better but must, however, correct their deficiencies.
		All theory and aural skills proficiency exams will be offered on audition days, during the week of final exams and again the week before classes begin in August and January.
		Study of compositional practices of the twentieth century and later, through analysis and composition exercises.
	www.music.uh.edu /comp-theory/theory_curriculum.html (780 words)

	Lawrence Conservatory of Music Theory/Composition (Site not responding. Last check: 2007-10-08)
		Intensive coursework in tonal harmony, twentieth-century techniques, counterpoint, form, and analysis complements private lessons in composition, small seminars in orchestration, and frequent colloquia which provide opportunities to share ideas, present works in progress, and discuss a range of technical and aesthetic issues in contemporary music.
		Stephen Rodgers, BA '98, was awarded a prestigious Mellon Fellowship to pursue the Ph.D. in Music Theory at Yale University, where he is currently completing his dissertation, a study of the metaphorical relationship between musical form and literary program in the music of Berlioz.
		In addition to private and class instruction in composition and music theory for non-majors, the department oversees the core music theory curriculum required of all music majors (First- and Second-year Theory and Analysis) and offers a number of upper-level theory and composition electives.
	www.lawrence.edu /conservatory/theory_comp (801 words)

	B-W: Music Theory / History and Literature / Composition
		Jennifer Conner also teaches theory and composition at the Cleveland Institute of Music and is head of the Suzuki music theory program there.
		Her Foundations in Music curriculum for teaching music theory to the young is currently used by both the Institute of Music and the Pittsburgh Academy.
		Feldman is a Pianist, accompanist, and composer whose compositions have been published by Shawnee Press and Mark Foster; he has been awarded the Louis Lane Prize for Composition.
	www.bw.edu /academics/conservatory/people/theory (982 words)

	University of the Incarnate Word
		He received his MM in Music Theory and Composition from the University of Nevada, Las Vegas and a Ph.D. in Fine Arts with an emphasis in Composition from Texas Tech University, where he also served as a full-time instructor of music theory and jazz.
		His main research interest is in the relationship of number theory to music theory.
		He is active as a composer and his music has been performed at music festivals and concerts across the country.
	www.uiw.edu /music/metz.html (125 words)

	Courses in Theory and Composition
		In fact, all of the dialogues that follow assumed that the student understands the difference between any two such enharmonically equivalent pitches, and is able to notate music accordingly.
		Thus, the first reading and its associated exercises establish the rules of naming and notating that will be followed throughout all the lessons of the various theory and composition courses.
		You may pay for each lesson individually, or in advance for a specified number of lessons.
	www.wholarts.com /music/ed/theory.htm (452 words)

	Function composition in Number Theory: symmetries -n, 1/n and FLT
		Function composition in Number Theory: symmetries -n, 1/n and FLT
		on Number Theory and Arithmetic --- : in arithmetic ring Z(+,.) both (+) and (.) are associative and commutative.
		Number theory without fundamental use of function composition algebra [semigroups, like Z(.) analysed additively, including non-cmt, finite, with divisors of zero,..&c] I would dare to call not quite complete, missing an essential concept.
	home.iae.nl /users/benschop/func.htm (1792 words)

	Moores School Theory and Composition Faculty
		Hear a composition by Michael Horvit: The Moores School Symphony Orchestra: Daughters of Jerusalem.
		B.M. and M.M., University of Houston; D.M.A. in composition from Rice University; has served in capacities as performer, conductor, producer and orchestrator for commercials, jingles, recordings, television projects and motion pictures; commissions include works for Houston Symphony and Paragon Brass Ensemble.
		Hear a composition by Rob Smith: The Moores School Wind Ensemble: Whirl.
	www.music.uh.edu /people/theory_comp.html (453 words)

	BERKLEE \| Composition Major
		The student majoring in Composition will study tonal harmony, counterpoint and fugue, tonal composition, twentieth-century compositional techniques, instrumentation, and orchestration.
		The Composition major will develop sufficient skills and knowledge to function as a composer of concert music, to gain entry to a graduate program in music theory or composition, and hence to pursue a career as a teacher, scholar, and practitioner of music theory and composition.
		Students are strongly encouraged to verify their course requirements with the Office of the Registrar.
	www.berklee.edu /majors/composition.html (203 words)

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