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Topic: Metric (mathematics)

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	Metric (mathematics) - Wikipedia, the free encyclopedia
		In mathematics a metric or distance is a function which assigns a distance to elements of a set.
		A metric induces a topology on a set but not all topologies can be generated by a metric.
		On manifolds, the metric is commonly expressed as a metric tensor.
	en.wikipedia.org /wiki/Metric_(mathematics) (803 words)

	Metric - Wikipedia, the free encyclopedia
		Metric and metrical refer to the topic treated in meter (music) or to that treated in meter (poetry).
		a metric (mathematics) is an abstraction of the notion of distance in a metric space.
		a norm (mathematics) is an abstraction of the notion of size in a normed vector space.
	en.wikipedia.org /wiki/Metric (129 words)

	Encyclopedia: Metric space
		In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.
		In any metric space M we can define the open balls as the sets of the form A synonym for ball (in geometry or topology, and in any dimension) is disk (or disc Geometry In metric geometry, a ball is a set containing all points within a specified distance of a given point.
		In mathematics, the closure of a set S consists of all points which are intuitively close to S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
	www.nationmaster.com /encyclopedia/metric-space (4121 words)

	Metric space (Site not responding. Last check: 2007-11-05)
		In mathematics, a metric space is a set (or "space") where a distance between points is defined.
		In metric spaces, one can talk about limits of sequences ; a metric space in which every Cauchy sequence has a limit is said to be complete.
		Other embedding constructions show that every metric space is isometrically isomorphic to a closed subset of some normed vector space and that every complete metric space is isometrically isomorphic to a closed subset of some Banach space.
	www.sciencedaily.com /encyclopedia/metric_space (1768 words)

	Metric Space [Definition] (Site not responding. Last check: 2007-11-05)
		In mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of "figures and numbers".
		If X is a topological (or metric) space and M is a metric space, then the set of all bounded continuous In mathematics, a continuous function is one in which arbitrarily small changes in the input produce arbitrarily small changes in the output.
		Metric geometry In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.
	www.wikimirror.com /Metric_space (5760 words)

	METRIC Research in Mathematics Education (Site not responding. Last check: 2007-11-05)
		We are working with colleagues in the Chemistry Department on the development of Mathematica -based materials which attempt to "embed" mathematical concepts in the context of physical chemistry.
		This is discussed in Section 4 of Mathematics Laboratories for Science Undergraduates and in A new approach to mathematical training for chemists.
		We have collaborated with Professor Richard Noss and Dr Ian Stevenson, Mathematical Sciences group, Institute of Education.
	metric.ma.ic.ac.uk /research.html (87 words)

	Ball (mathematics) - Enpsychlopedia (Site not responding. Last check: 2007-11-05)
		In metric geometry, a ball is a set containing all points within a specified distance of a given point.
		With the ordinary (Euclidean) metric, if the space is the line, the ball is an interval, and if the space is the plane, the ball is the disc inside a circle.
		With other metrics the shape of a ball can be different; for example, in taxicab geometry a ball is diamond-shaped.
	www.grohol.com /wiki/Disk_(mathematics) (521 words)

	Edinburgh Mathematics Programme
		In this module, two of the fundamental tools of modern mathematical analysis are developed: the basic theory of the Lebesgue integral and metric spaces.
		We link metric spaces and integration together in the context of L^p spaces, which are fundamental examples of the function spaces that provide the language for much of modern analysis.
		The metric space part of the course is intended to be fairly similar to the old Mathematics 3 presentation.
	www.maths.ed.ac.uk /~carbery/AaI.html (913 words)

	Saltire Software - A readability metric for computer-generated mathematics
		Mathematical expressions can be written in different forms and although the forms are mathematically equivalent, they are not necessarily equally understandable.
		The one with the highest correlation was obtained by using the best metric for single expressions, applying this metric to each expression in the system in turn, taking the largest value and adding the number of intermediate expressions.
		This metric, the worst individual expression metric plus the number of intermediate expressions, had a Pearson's correlation of 0.96 with our human data in terms of which expressions were preferred.
	www.saltire.com /equation.html (1013 words)

	Edinburgh Mathematics Programme
		The uniform metric on C[a,b] and the notion of uniform convergence.
		In this module, metrics provide a language for discussing convergence and completeness, and so the emphasis is on the definition of a metric space and giving plenty of useful examples of metrics.
		Section 9 introduces the idea that the language of metrics is the appropriate one for concrete problems in analysis such as that of convergence of Fourier series.
	www.maths.ed.ac.uk /~carbery/FoA.html (932 words)

	MA222 Metric spaces
		Or the set might be the set of real valued continuous functions on the unit interval, in which case we could take as a measure of the distance between two functions either the maximum of their difference, or alternatively its ``root mean square''.
		For example, a continuous real-valued function on a compact metric space must be bounded.
		Continuity is readily described in terms of open subsets, which leads us naturally to study the above concepts also in the more general context of a topological space, where, instead of a distance, it is declared which subsets are open.
	www.maths.warwick.ac.uk /pydc/green/green-MA222.html (530 words)

	Mathematics 328
		A handout treating the Hausdorff metric on the space of closed and bounded subsets of a Euclidean space.
		From Chapter 2 in the textbook, and now (as in the book) in the context of metric spaces: sequences, convergence, Cauchy sequences, completeness, brief dicsussion of series (on normed linear spaces), Banach spaces, absolute convergence, completeness of the space of continuous functions on a closed interval (uniform convergence).
		From Chapter 5 in the textbook: integration and differentiation of series, the space of bounded continuous maps as a metric space, and as a normed vector space if the image space is a normed vector space, with completeness if the image space is complete; equicontinuity and the Arzela-Ascoli Theorem.
	www.mast.queensu.ca /~leo/more.html (1261 words)

	Amazon.com: Books: Metric Spaces (Site not responding. Last check: 2007-11-05)
		Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory.
		Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory.
		Metric Spaces is an especiallywell-written introduction to analysis.
	www.amazon.com /exec/obidos/tg/detail/-/0521318971?v=glance (1221 words)

	Thomson Nelson - Elementary Mathematics - Mathematics 3
		Metric Quiz lets students answer interactive questions about metric length.
		Converting Metric Measurements lets students relate kilometres to other metric units of measure.
		To use Converting Metric Measurements, type a number into the text field beside the metric unit to convert.
	www.nelsonk8math.com /math3/teachercentre/teachsurf_ch05_lesson03.html (204 words)

	pseudometric (Site not responding. Last check: 2007-11-05)
		If this latter condition is dropped, then g(x,y) is called a pseudometric instead of a metric.A set possessing a metric is called a metric space.
		The only diÂ¤erence between a metric and pseudometric is that for a pseudometric d it could be that d ( x;y)= 0 but x 6 = y.
		The pseudometric topology on X is deâ¦ned in the same way as the metric...
	pseudometric.networklive.org (246 words)

	Appointments (Site not responding. Last check: 2007-11-05)
		The METRIC team has been writing Web-based educational resources in Mathematics at Imperial College London for several years.
		METRIC has now joined a consortium to make our Question Test elements interoperable with other systems and compliant with emerging standards, and to create an authoring tool for mathematics questions.
		You will work mostly on the development of wholly fresh code for the authoring tool and its associated web service interface, leaving the process of porting to the new formats to the existing members of the team.
	www.ma.ic.ac.uk /showparticularsURL.php?rowid=25 (249 words)

	family problemsoct2003 (Site not responding. Last check: 2007-11-05)
		The Somerville Mathematics Fund was founded in 2000 to celebrate and encourage mathematics achievement in the city of Somerville.
		When the metric system was officially adopted by the Republic of France, the system’s motto was “For all people, for all time.” Thirty-eight years later, it was made the only system of measurement in France.
		The Metric Conversion Act was passed requiring all federal agencies in the United States to have converted to the metric system of measurement.
	members.aol.com /mathfund/familymathps/oct03familymathps.html (917 words)

	Clinical Mathematics
		My overall objective is a collection of mathematical tools useful in clinical anesthesia practice.
		The NIST Metric System Teaching Site has a wealth of information on every aspect of the metric system, very clearly presented.
		Metric pressure units (based on the Pascal) are less familiar to most than metric measures of weight.
	www.udmercy.edu /crna/agm/mathweb.htm (1926 words)

	Mathematics
		Graded Exercises in Advanced Mathematics - Secondary Education...
		Mathematics is the science of size, structure, order, and shapes, and other relationships among quantities.
		Conversion calculators : metric to English and English to metric
	www.101science.com /math.htm (1686 words)

	Mathematics
		Math anxiety, the fear of mathematics, is extremely stressful to individuals and can be devastating to their careers.
		In addition, the lack of basic mathematics skills is a drain on their organization's productivity.It is a limiting factor in the growth and development of both the individuals and the organization for which they work.
		You'll meet and become familiar with the metric mathematics of your field of expertise.
	www.reaengrs.com /page7.html (432 words)

	IC Reporter, Imperial goes METRIC (Site not responding. Last check: 2007-11-05)
		The transitional mathematics project (TMP) was established in the Department of Mathematics in early 1993.
		For three years it was externally funded by the Teaching and Learning Technology Programme, an initiative of the four UK higher education funding councils, to develop mathematics learning modules based on the computer mathematics system Mathematica.
		These modules are pitched at a level roughly corresponding to A level, and are designed to be used as revision materials by students beginning studies in science and engineering.
	www.ic.ac.uk /publications/reporterarchive/0027/news08.htm (318 words)

	Metric Spaces as Topological Spaces --- Fundamental Concepts
		Some notions connected with metric spaces and the relationship between metric spaces and topological spaces.
		Compactness of topological spaces is transferred for the case of metric spaces [ 13 ].
		Some basic theorems about translations of topological notions for metric spaces are proved.
	mizar.uwb.edu.pl /JFM/Vol3/topmetr.html (99 words)

	Amazon.de: English Books: Fixed Point Theory in Probabilistic Metric Spaces (Mathematics and Its Applications) (Site not responding. Last check: 2007-11-05)
		The text is self-contained for a reader with a modest knowledge of the metric fixed point theory.
		The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces.
		Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces.
	www.amazon.de /exec/obidos/ASIN/1402001290/ww2afvportalinpa (314 words)

	Frank Potter's Science Gems - Mathematics
		In middle school mathematics a regular tessellation is a tiling of the plane using a triangle, a square, or a hexagon..."
		Favorite Mathematical Constants - S. Finch at MathSoft, Inc. All numbers are not created equal; that certain constants appear at all and then echo throughout mathematics, in seemingly independent ways, is a source of fascination.
		Unsolved Mathematics Problems - S. Finch at Wolfram Research "This evolving collection of unsolved mathematics problems is not systematic or complete; it is only an eclectic gathering of questions and partial answers which have come to my attention over the years.
	www.sciencegems.com /math.html (2999 words)

	Mathematics 446 / 646: Introduction to Topology (Site not responding. Last check: 2007-11-05)
		The emphasis will be on the definition of metric space, a large number of examples, and detailed discussions of convergent sequences, open and closed sets, continuous functions and compactness.
		A special emphasis willl be placed on the usual (absolute value) metric for the real line but additionally we will explore some rather esoteric metrics.
		The main goal of the course is to acquaint the beginning mathematics student with the spirit of modern abstract mathematics (in which theorems, their proof and examples play an approximately equal role) by involving him/her with the basic of point-set topology.
	www.math.ndsu.nodak.edu /courses/446.html (241 words)

	Mathematics (US pub. Before 1999)
		Mathematics Education in Hong Kong : From the 1960s to the 1990s, a Festschrift for K. Leung 1995 /Hong Kong University Press PP.
		Mathematics Workbook for SAT I / Samuel C. Brownstein 1994 Ed.# 7 /Barron's Educational Series, Incorporated PP.
		Mathematical Curiosities II / Gerald Jenkins / Anne Wild 1982 /Prentice Hall PP.
	www.find-out-of-print-books-online.info /mathematics_B-b499.htm (15167 words)

	Cub Scout Academics - Mathematics
		Do five activities within your home or school that require the use of mathematics.
		Explain to your den how a meteorologist or insurance company (or someone else) might use the mathematics of probability to predict what might happen in the future (i.e., the chance that it might rain, or the chance that someone might be in a car accident).
		The IRS has not recognized the USSSP as a 501(c)(3) organization, so donations may not be tax deductible.
	www.usscouts.org /advance/cubscout/academics/mathematics.html (766 words)

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