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Topic: Reduction (mathematics)

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	Reduction (mathematics) - Wikipedia
		In linear algebra, reduction is the process of applying rules to a series of equations or matrices to change them into a "simpler" format.
		Often the aim of reduction is to transform a matrix into its "row-reduced echelon form" or "row-echelon form"; this is the process of Gaussian elimination.
		In calculus, reduction refers to the technique of integration by parts to evaluate a whole class of integrals by reducing them to simpler forms.
	en.wikipedia.org /wiki/Reduction_(mathematics) (144 words)

	Reduction - Wikipedia
		In mathematics, reduction is the process of manipulating a series of equations or matrices into a desired 'simpler' format.
		In cooking, reduction is the process of thickening a liquid mixture such as a sauce by evaporation.
		In chemistry, reduction is the reverse of oxidation, i.e.
	en.wikipedia.org /wiki/Reduction (290 words)

	Logic - Open Encyclopedia (Site not responding. Last check: 2007-11-04)
		Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.
		The boldest attempt to apply logic to mathematics was undoubtedly the logicism pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic.
		Brouwer as the correct logic for reasoning about mathematics, based upon his rejection of the law of the excluded middle as part of his intuitionism.
	open-encyclopedia.com /Logic (2307 words)

	CONK! Encyclopedia: Logic (Site not responding. Last check: 2007-11-04)
		The ambiguity is that 'formal logic' is very often used with the alternate meaning of symbolic logic as we have defined it, with informal logic meaning any logical investigation that does not involve symbolic abstraction; it is this sense of 'formal' that is parallel to the received usages coming from "formal languages" or "formal theory".
		Certain conventions have become prevalent in the symbolic analysis of logic: the logic is captured by a formal systems, comprising a formal language, which describes a set of formulas, a set of rules of derivation.
		The analytical generality of the predicate logic allowed the formalisation of mathematics, and drove the investigation of set theory, allowed the development of Alfred Tarski's approach to model theory; it is no exaggeration to say that it is the foundation of modern mathematical logic.
	www.conk.com /search/encyclopedia.cgi?q=Logic (3360 words)

	quinenatepis (Site not responding. Last check: 2007-11-04)
		If in particular the concepts of mathematics were all reducible to the clear terms of logic, then all the truths of mathematics would go over into truths of logic; and surely the truths of logic are all obvious or at least potentially obvious, i.e., derivable from obvious truths by individually obvious steps.
		Reduction in the foundations of mathematics remains mathematically and philosophically fascinating, but it does not do what the epistemologist would like of it: it does not reveal the ground of mathematical knowledge, it does not show how math- ematical certainty is possible.
		To relax the demand for definition, and settle for a kind of reduction that does not eliminate, is to renounce the last remaining advantage that we supposed rational reconstruction to have over straight psychology; namely, the advantage of translational reduction.
	www.loyno.edu /~folse/quinenatepis.html (6177 words)

	6: Origins of Philosophy and Mathematics
		Mathematics began as Geometry, the systematic application of logic to Mensuration, the practical art of measuring distances, areas, volumes, and angles.
		The reduction of an infinite number of instances to a single principle or formula, such as is achieved by a mathematical theorem, profoundly expands the range of questions we can ask as well as answer.
		Another characteristic of mathematics is that a few axioms lead to an endless number of theorems; equivalently, mathematics reduces a endless number of truths to a relatively few basic truths.
	members.cox.net /edremler/Papers/Worldview/Reductions/text.html (5680 words)

	The Mathematics of Hair Restoration Surgery
		Mathematics is prevalent in almost all aspects of life, and so it is with hair restoration surgery.
		Mathematics pervades many of the aspects of hair restoration, from the donor site, to the recipient site, to scalp reduction, to scalp extension, and the list goes on.
		Circumferential scalp reduction: the application of the principles of extensive scalp-lifting for the improvement of scalp reduction surgery.
	www.brandymd.com /restoration_math.cfm (3369 words)

	The Repressed Content-Requirements of Mathematics
		Mathematics, as it is conceived in the twentieth century, has presuppositions about perception, and about the comprehension of lived experience relative to the apprehension of apparitions, which are repressed in professional doctrine.
		Mathematical knowledge is not supposed to depend on the word of a particular authority--on citations which have the character of Biblical verses.
		Moreover, mathematics is obviously not chess because mathematics is infinitary.
	www.henryflynt.org /studies_sci/reqmath.html (6508 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		a reduction of 12 percent in violent crime.
		A decrease in positive valence or an increase in negative valence by the gaining of electrons.
		The converting of an expression or equation to its simplest form.
	www.homoexcelsior.com /omega.db/datum/mathematics/reduction/7594 (77 words)

	Nat' Academies Press, Mathematics Education in the Middle Grades: Teaching to Meet the Needs of Middle Grades Learners ... (Site not responding. Last check: 2007-11-04)
		Mathematics educators for many years have interpreted this stage as one which requires concrete embodiments or manipulatives to promote what are essentially abstract mathematical ideas.
		CONCLUSION Mathematics in the middle grades is still "Mathematics for All," although the move is towards a formalisation of the subject.
		The issue of certifica- tion for teaching mathematics in the middle grades, the nature of preservice programs, and professional develop- ment were repeatedly identified as critical in helping teachers move beyond their comfort with number to other mathematical strands that should be part of the middle grades curriculum.
	books.nap.edu /books/0309067979/html/39.html (6871 words)

	Reduction (Site not responding. Last check: 2007-11-04)
		In mathematics, reduction is the process of manipulating a series of equations or matrix into a desired 'simpler' format.
		In philosophy, reduction is the process of explaining one phenomenon in terms of another.
		In linguistics, reduction is to shorten the pronounciation of a word.
	www.eurofreehost.com /re/Reduction.html (158 words)

	math-cur
		The use of mathematics is no longer restricted to those who know and remember the details of complicated procedures, but this does not mean a reduction in the need for mathematical knowledge.
		Many of the areas of mathematics that are commonly used in both civic and practical contexts are rarely taught in school, while other topics having long since outlived their usefulness remain in the curriculum simply because they are still on tests or in texts.
		The majority of mathematics teachers have a concentration in calculus and related studies and thus are comfortable with the present system and, in fact, may have backgrounds that make teaching extended topics in statistics, probability, matrices, and applied methods in technology or finance difficult.
	educ.queensu.ca /~rouletg/WEB-PPR.htm (12034 words)

	Read about Logic at WorldVillage Encyclopedia. Research Logic and learn about Logic here! (Site not responding. Last check: 2007-11-04)
		Their actions may be a perverse attempt to raise a conversational issue, suspect to the push-pull of dialectic, but perverse only when, unlike Hegel, one doesn't make individual and social will a prime mover.
		The boldest attempt to apply logic to mathematics was undoubtedly the
		Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic.
	encyclopedia.worldvillage.com /s/b/Logic (2596 words)

	Russell’s reduction of mathematics to logic (Site not responding. Last check: 2007-11-04)
		The case we are interested in -- the reduction of arithmetic to logic -- is a case in point.
		As noted earlier in our discussion of reductions of one theory to another, what we want is a proof of the axioms of arithmetic on the basis of the axioms of Russell’s logical system.
		The epistemological and metaphysical aims of the logicist reduction as dependent on the claim to have captured the meaning of arithmetical statements.
	www.arts.mcgill.ca /philo/speaks/370/logicism.html (4343 words)

	Neo-Logicism? An Ontological Reduction of Mathematics to Metaphysics (Site not responding. Last check: 2007-11-04)
		In this paper, we describe "metaphysical reductions", in which the well-defined terms and predicates of arbitrary mathematical theories are uniquely interpreted within an axiomatic, metaphysical theory of abstract objects.
		After the technical details are sketched, the paper concludes with some observations about the approach.
		Though I shall not claim that they are logical axioms, some philosophers have argued that we should accept (something like) them as being logical.
	mally.stanford.edu /abstracts/neologicism1.html (98 words)

	Amazon.ca: Books: Hamiltonian Reduction (Site not responding. Last check: 2007-11-04)
		In some instances, the symmetries in a dynamical system can be used to simplify its kinematical description via an important procedure that has evolved over the years and is known generically as reduction.
		The focus of this work is a comprehensive and self-contained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail.
		This is followed by a discussion of momentum maps and the geometry of conservation laws that are used in the development of symplectic reduction.
	www.amazon.ca /exec/obidos/ASIN/0817643079 (296 words)

	Class Size Reduction - Learning Support (CA Dept of Education)
		Information about federal and state class size reduction (CSR) programs established to improve educational achievement for all students by reducing class size ratios per teacher.
		The Class Size Reduction program, which was established in 1996 to improve education, especially in reading and mathematics, of children in kindergarten and grades one through three.
		The Morgan-Hart Class Size Reduction Act, which reduces class size in ninth-grade English and one other ninth-grade course required for graduation (either mathematics, science, or social studies).
	www.cde.ca.gov /ls/cs (97 words)

	Expression Reduction Systems - Khasidashvili (ResearchIndex)
		Abstract: this paper, the notion of Expression Reduction System (ERS) is introduced, and the strict form of Church-Rosser property and minimal and maximal strategies for S; E ; !; ff; fi (Update)
		0.0: On the Longest Perpetual Reductions in Orthogonal Expression..
		Proceedings of I. Vekua Institute of Applied Mathematics of Tbilisi State University, vol.
	citeseer.ist.psu.edu /khasidashvili90expression.html (372 words)

	Engineering, Computing and Mathematics - 23 November 1999
		However, covering the same subject matter twice is good practice and just because some school mathematics are re-taught at university does not necessarily mean that school mathematics should be changed.
		There is room in the current TEE for reduction in mathematics content provided it is matched by an increase in problem solving skills.
		There was general support for a reduction in prerequisite knowledge, provided that the resulting increased breadth of knowledge and language/reasoning/problem solving skills could be adequately assessed and demonstrated.
	www.ecm.uwa.edu.au /for/staff/mins/utlc/1999/23_november_1999 (961 words)

	Readings: Theory of Computation
		The essence of this book is words, explaining mathematical ideas, but readers who feel so inclined can follow me all the way to LISP programs that pretty much show Gödel's, Turing's and my proofs working on the computer.
		A collection of fundamental papers by Gödel, Church, Post, etc. The papers that have direct bearing on the Miser Project are cited individually in one of the appropriate annotated bibliographies.
		As I have continued to explore mathematical logic as a context for computation theory and the Miser Project, I am now inclined to classify most of these papers as strongly centered in mathematical logic and as less specific to computation, even the seminal work of Turing.
	nfocentrale.net /miser/readings/theory.htm (1816 words)

	EMTeachline mathematics software - problem solving - math test authoring
		The software is suitable for elementary, middle and high school use and for mathematics self-study.
		Based on a unique teaching technology, the EMTeachline mathematics software controls, analyses and grades your performance, detects gaps in your theoretical knowledge and problem-solving skills, and generates an optimal set of tasks to close the revealed gaps.
		The EMTeachline Mathematics Software is a problem-solving learning and teaching tool for students of all ages and skill levels, from elementary school through adult, and for math teachers and tutors.
	www.emteachline.com /eng/index_main.htm (1560 words)

	Mathematics Reduction Theory @ www.ezboard.com (Site not responding. Last check: 2007-11-04)
		Pop in, say hello, and enjoy the new Mathematics Reduction Theory.
		Main forum for discussion of the New Mathematics Reduction Theory by Stephen Salaka.
		Forum for any other mathematical issues not found in other forums.
	p070.ezboard.com /bmathematicsreductiontheory (211 words)

	Amazon.ca: Books: Noise Reduction by Wavelet Thresholding (Site not responding. Last check: 2007-11-04)
		The book also pays attention to fast algorithms, and Matlab code reproducing many of the illustrations is available for free.
		Maarten Jansen received a Ph.D. in applied mathematics from the Katholieke Universiteit Leuven, Belgium, in 2000 and currently he is a postdoctoral fellow with the Belgian Foundation for Scientific Research (FWO).
		The viewpoint of the text lies somewhere between logic and statistics, signal and image processing, and approximation theory.
	www.amazon.ca /exec/obidos/ASIN/0387952446 (467 words)

	Amazon.de: English Books: Reduction of Nonlinear Control Systems: A Differential Geometric Approach (Mathematics & ... (Site not responding. Last check: 2007-11-04)
		Reduction of Nonlinear Control Systems: A Differential Geometric Approach (Mathematics and Its Applications (Numbered Hardcover))
		Within the framework of this category the reduction of control systems becomes a reduction to isomorphic objects, quotient objects, and subobjects.
		The theory of reduction of nonlinear control systems discussed here outlines the elements of the general theory of such systems, which is of necessity purely differential geometric by nature.
	www.amazon.de /exec/obidos/ASIN/0792356233 (269 words)

	MSN Encarta - Search Results - reduction firing
		MSN Encarta - Search Results - reduction firing
		Reduce (mathematics), to simplify an expression or equation without changing its value, usually by dividing by a common factor.
		Search for books about your topic, "reduction firing"
	encarta.msn.com /reduction_firing.html (140 words)

	Dipl. Eng. Pierre Ricco, M.S.E. - PhD student in Applied Mathematics, (Site not responding. Last check: 2007-11-04)
		Quadrio, M. Reduction of turbulent friction by spanwise wall oscillation
		Quadrio, M. and Ricco, P. Reduction of turbulent friction by spanwise wall oscillations
		Mathematics Postgraduate Forum - Physics Common Room - Imperial College, November 28
	www.ma.ic.ac.uk /~par/publications.html (485 words)

	Reduction of Nonlinear Control Systems : A Differential Geometric Approach (Mathematics and Its Applications)
		Reduction of Nonlinear Control Systems : A Differential Geometric Approach (Mathematics and Its Applications)
		This monograph is devoted to methods of reduction of nonlinear control systems to a simpler form: for example, decomposition into systems of lesser dimension.
		Audience: This book will be of interest to graduate students as well as to researchers who wish to gain insight into the modern differential geometric theory of nonlinear control systems.
	www.literacyconnections.com /0_0792356233.html (183 words)

	High School Class Size Reduction - Class Size Reduction (CA Dept of Education)
		The Morgan-Hart Class Size Reduction Act provides funds to school districts for participating schools that reduce class size in Grade 9 English and one other Grade 9 course required for graduation, either Mathematics, Science, or Social Studies.
		The majority of pupils in participating classes must be identified as Grade 9 students.
		Average class size for the school year at each participating school can be no more than 20:1 per certificated teacher and no more than 22 pupils enrolled in any participating class.
	www.cde.ca.gov /ls/cs/mh (222 words)

	UC Berkeley Mathematics (Site not responding. Last check: 2007-11-04)
		Given a Hamiltonian action on a contact manifold one can perform reduction to obtain a new contact manifold (Willett’s reduction).
		However this reduction procedure is not as natural as the usual Marsden-Weinstein reduction.
		We will show how so-called contact groupoids provide a more general and natural setting for contact reduction, and time permitting we will present an application to prequantization of coadjoint orbits.
	math.berkeley.edu /calendar-event140.html (106 words)

	Nat' Academies Press, Mathematics Education in the Middle Grades: Teaching to Meet the Needs of Middle Grades Learners ... (Site not responding. Last check: 2007-11-04)
		In sum, REFLECTIONS ON MIDDLE SCHOOL MATHEMATICS these young people are developmentally ripe for intellectual growth.
		Paper prepared for Middle Grades Mathematics Convocation, September, 24-25,1998.
		REFLECTIONS ON MIDDLE SCHOOL MATHEMATICS Reiff, L. Seeking diversity: Language arts with adolescents.
	www.nap.edu /books/0309067979/html/39.html (6871 words)

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