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Topic: Chain mathematics

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	Chain (mathematics)
		The boundary of a chain is the linear combination of boundaries of the simplices in the chain.
		Boundaries are cycles, so chains form a chain complex, whose homology groups (cycles modulo boundaries) are called simplicial homology groups.
		In differential geometry, the duality between the boundary operator on chains and the exterior derivative is expressed by the general Stokes' theorem.
	www.ebroadcast.com.au /lookup/encyclopedia/ch/Chain_(mathematics).html (261 words)

	Catenary - LoveToKnow 1911 (Site not responding. Last check: 2007-10-12)
		catena, a chain), in mathematics, the curve assumed by a uniform chain or string hanging freely between two supports.
		It was investigated by Galileo, who erroneously determined it to be a parabola; Jungius detected Galileo's error, but the true form was not discovered until 1691, when James Bernoulli published it as a problem in the Aeta Eruditorum.
		Bernoulli also considered the cases when (I) the chain was of variable density, (2) extensible, (3) acted upon at each point by a force directed to a fixed centre.
	90.1911encyclopedia.org /Catenary (326 words)

	Mathematics
		Mathematics 3 and 8 cover the basic calculus of functions of a single variable, as well as vector geometry and calculus of scalar-valued functions of several variables.
		Prerequisite Courses: Mathematics 3; 8; 13; 22 or 24
		Prerequisite: Mathematics 8, or Mathematics 3 and 6.
	www.dartmouth.edu /~reg/courses/desc/math.html (7962 words)

	TEACHERS’ USES OF SEMIOTIC CHAINING TO LINK HOME AND MIDDLE SCHOOL MATHEMATICS IN CLASSROOMS
		We believe that mathematics is “the science of detachable relational insights” (Thomas, 1996), or, resonating with this conception of the nature of mathematics, “the systematization of relationships” (Ada Lovelace, in Noss, 1997).
		These chains were designed by the first author to develop a mathematical topic that was specified by the teachers from an activity of the students.
		Before each semiotic chain was used in the mathematics classrooms, the teachers and the researcher met to discuss the instructional process that was to be undertaken.
	www.west.asu.edu /cmw/pme/resrepweb/PME-rr-hall.htm (1998 words)

	Is mathematics a science?
		Mathematics is certainly a science in the broad sense of "systematic and formulated knowledge", but most people use "science" to refer only to the natural sciences.
		Since mathematics provides the language in which the natural sciences aspire to describe and analyse the universe, there is a natural link between mathematics and the natural sciences.
		There is also the argument that mathematics is "not really accessible enough to be an art and not immediately useful enough to be a science" [1], but this assumes that art is accessible and science is useful.
	euclid.trentu.ca /math/sb/misc/mathsci.html (1478 words)

	Mathematics
		Simultaneous enrollment in Mathematics 100 and Mathematics 202 is not permitted.
		Principles of Mathematics II Prerequisite: Mathematics 215 with a satisfactory grade or equivalent.
		Interwoven in this course are: mathematical reasoning (logic and mathematical proofs), algorithm (use of pseudocode), combinatorial analysis (ability to count), and discrete structures and their basic applications.
	catalog.lacitycollege.edu /pages/mathematics.htm (1743 words)

	Camp Internet GIS & Mapping Center
		The first tools, invented thousands of years ago, were simple gadgets: the level, the sight, the measuring chain.
		Mathematics developed geometry to describe shapes and relationships of objects in space.
		The magnetic compass, the sextant, the telescope, the theodolite, the planetable, and the marine chronometer, used in combination with mathematics, have greatly increased mapping accuracy.
	www.rain.org /campinternet/gis/topo/maps-reading-location.html (535 words)

	Course of Study - Math
		The mathematics curriculum is built around a core sequence of eight trimester courses: three of elementary algebra, two of geometry, one of intermediate algebra, and two of precalculus topics.
		Placement of new students in the appropriate first course is made by the department, which considers the record in previous schools, the results of a self-administered placement test in elementary algebra that is sent to newly admitted students in the spring, and the course program chosen by the entering student.
		Mathematics 360 is the final course in the precalculus sequence.
	www.andover.edu /academics/studies/cos_math.htm (2655 words)

	QUANTITATIVE AND MATHEMATICS (Site not responding. Last check: 2007-10-12)
		Introduces to the students to basic mathematical concepts and their usage as a useful problem-solving tool in real-life problems and business situations.
		The course is intended to introduce students to the elementary mathematical reasoning and contemporary philosophy of science.
		Covers mathematical logic, theorem proving techniques, number theory, set theory, generating functions, counting techniques, recurrence and recursion, theory of algorithm, and combinatorics.
	www.pafkiet.edu.pk /CS_Quantitative.htm (1264 words)

	University of Calgary: Calendar: Courses: Applied Mathematics
		Prerequisites: One of Applied Mathematics 311 or 307, and one of Mathematics 331, 353, Applied Mathematics 309, or consent of the Division.
		Prerequisites: Mathematics 311 or Applied Mathematics 311; and Mathematics 353 or Applied Mathematics 309 or Mathematics 331; or consent of the Division.
		Prerequisites: Pure Mathematics 445; and one of Applied Mathematics 311 or 307; or consent of the Division.
	www.ucalgary.ca /pubs/calendar/current/what/courses/AMAT.htm (1092 words)

	The Catenary (Site not responding. Last check: 2007-10-12)
		Let one end of the chain be supported at x = L/2 and y = h, and let w be the weight per unit length of the chain.
		The tension T in the chain is in the direction of the derivative dy/dx.
		We have assumed that the chain is supported at equal heights on the two sides, but this is not necessary, and the equations can be modified to suit any case.
	www.du.edu /~jcalvert/math/catenary.htm (617 words)

	[No title] (Site not responding. Last check: 2007-10-12)
		] A method of searching for a data item in a chained list in which an initial key is used to obtain the location of either the item sought or another item in the list, and the search then progresses through the chain until the required item is obtained or the chain is completed.
		The forming of two lines of intermittent fillet welds in a T joint or lap joint so that the increments of welding in one line are approximately opposite those in the other line.
		] A short chain with a hook attached to a ship's forecastle, used to secure the anchor chain when the anchor is raised or lowered, thus relieving the windlass from strain, or to quickly release the anchor.
	www.accessscience.com /Dictionary/C/C17/DictC17.html (1883 words)

	Operations Research Management Science - Value Chain Optimization
		Traditional value chain management systems are based on static, structured information within a rigid planning cycle, while SAR Blue Enterprise orchestrates dynamic, structured and unstructured information within a continuous, adaptive event-based planning process.
		The goal is to create a digital brain with sensors reaching all the way from a company's global value chain to the Internet world, identifying, monitoring, organizing and analyzing critical business information with intelligent decision-making capabilities in order to generate and activate proper business rules, policies and processes.
		The SAR Blue Enterprise addresses the full spectrum of supply chain event management (SCEM), which is an attempt to integrate event monitoring, simulation and optimization capabilities to improve the supply chain control [3].
	www.lionhrtpub.com /orms/orms-4-02/frvaluechain.html (2684 words)


		The tools are used to analyze problems at relatively low levels, specific to an individual plant or at very high levels including the entire supply/value chain.
		Computerized process control systems have had this type of architecture for more than a decade and would be a good model of how to effectively design and implement a real-time portal system.
		SCS specializes in supply chain modeling technologies, optimization systems and implementing processes/systems that automate business strategies. MIND is a non-profit ISP promoting educational use of the Internet.
	supply-chain-systems.com /articles/portals.htm (2281 words)

	MATHEMATICS
		An introduction to basic applications of descriptive and inferential statistics: organizing data, mean, median and mode, and standard deviation, boxplots, probability and discrete random variables, the binomial distribution, the normal distribution, sampling distribution of the mean, confidence intervals and hypothesis tests for one population mean, the chi-square distribution.
		Emphasis will be placed on knowledge, skills, and techniques needed in higher level mathematics courses such as Calculus I. Prerequisite: “C” or better in MA 113 or three years of high school mathematics which include two years of algebra.
		Brief history of mathematics, objectives of the teaching of mathematics, consideration of topics that are or should be included in mathematics courses for junior and senior high school, a survey of instruction and technology in mathematics, and the use of these teaching techniques in specific teaching-learning activities.
	www.muw.edu /registrar/MA02.html (1038 words)

	MATHEMATICS
		MATH 318 Linear Algebra (3) NW Introduction to the mathematical concepts, arguments, and proofs that occur in linear algebra.
		MATH 420 History of Mathematics (3) NW Survey of the development of mathematics from its earliest beginnings through the first half of the twentieth century.
		Issues in the teaching and learning of college mathematics, such as discovering and working with student background and expectations, increasing student engagement with course material, and evaluating student achievement.
	www.washington.edu /students/crscat/math.html (5102 words)

	University of Pittsburgh: Department of Mathematics (Site not responding. Last check: 2007-10-12)
		This theorem was first proved by Aldous for large n, and then for more general n by David Bayer and Persi Diaconis in their very readable article ''Trailing the dovetail shuffle to its lair'', in Annals of Applied Probability, Volume 2, 1992, pages 294-313.
		A Markov chain on a finite state space X can be though of as a matrix K(x,y) where x,y are elements in X, and K(x,y) gives the probability of moving from x to y.
		A tremendous amount of mathematics is related to this question-especially linear algebra and the study of eigenvalues of symmetric matrices.
	www.math.pitt.edu /fall2004-shuffling.html (1286 words)

	MATHEMATICS (Site not responding. Last check: 2007-10-12)
		Emphasising its formal character and its applicability to all conceivable worlds, mathematics has been likened to a language whose semantics is supplied by other sciences or by particular applications.
		However, it is a characteristic of mathematics that the problems giving rise to its constructions are soon forgotten and the constructions develop a life of their own, checked only by such validity criteria as internal consistency, decidability and completeness.
		Empirical data from an existing world do not threaten the products of mathematics.
	pespmc1.vub.ac.be /ASC/MATHEMATICS.html (81 words)

	Trinity Christian College
		We use mathematical experience and developed intuition to judge whether an image is flawed or deceptive.
		In the mathematical contexts, we accept results that are "sufficiently close," results that are in an epsilon-neighborhood of the desired quantity.
		Once students have seen the chain rule for differentiation of composed functions, it is natural to extend the chain rule to nested functions, where there is more than two functions that are composed.
	www.trnty.edu /faculty/robbert/SRobbertWebFolder/ChristianityMath/Calculus.html (2609 words)

	[No title]
		] A hand-operated device for withdrawing supports from the waste or old workings in a mine by means of a long chain which allows the device to be positioned at a safe distance from the support to be extracted.
		] The formal study of symbolism and its use in the foundations of mathematical logic.
		] The manipulation of symbols, representing variables, functions, and other mathematical objects, and combinations of these symbols, representing formulas, equations, and expressions, according to mathematical rules, for example, the rules of algebra or calculus.
	www.accessscience.com /Dictionary/S/S68/DictS68.html (1613 words)

	Chain Rule : Examples for Calculus I at the Library of Math (Site not responding. Last check: 2007-10-12)
		With a lot of work, we can find derivatives without using the chain rule either by expanding a polynomial, by using another differentation rule, or maybe by using a trigonometric identity.
		The derivative would be the same in either approach; however, the chain rule allows us to find derivatives that would otherwise be very difficult to handle.
		Anglin, W.S. Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.
	www.libraryofmath.com /Calculus_I_Example_Chain_Rule.html (275 words)

	Visual Calculus - Chain Rule (Site not responding. Last check: 2007-10-12)
		Objectives: In this tutorial, we derive the Chain Rule.
		After working through these materials, the student should be able to use the Chain Rule to differentiate certain functions.
		LiveMath notebook which illustrates the use of the chain rule.
	archives.math.utk.edu /visual.calculus/2/chain_rule.4 (62 words)

	Chain Rule
		It is used in implicit differentiation, finding rates of changes, as well as parametric differentiation.
		Here we introduce the chain rule, but it is hard to give examples without going into its various applications, which have yet to be explained.
		We have listed an example of the chain rule in this section so far, in the first section, Differentiation.
	library.thinkquest.org /C0110248/calculus/difnchain.htm (106 words)

	What is infinity in mathematics
		For example the question of whether a species will have an infinite chain of descendant species can be defined in a way that requires quantification over the reals .
		We know mathematics that requires quantification over infinite sets is useful because it can make it easier to decide practical questions.
		As long as the number of paths of evolution that you follow increases without limit, there is nothing to prevent one particular path from ultimately solving the halting problem for every TM using a chain of mathematical systems each of which proves the consistency of the previous one.
	www.mtnmath.com /book/node20.html (963 words)

	Department of Mathematics and Statistics
		The Department of Mathematics and Statistics at the University of New Mexico is seeking applications for the following positions:
		This award is sponsored by the Bernoulli society for mathematical statistics and Probability.
		The internships are salaried positions typically 10 weeks long at one of three IBM research locations (San Jose, CA, Austin, TX, or Yorktown Heights, NY), and include in addition a $2,500 grant, plus the opportunity to work with an IBM mentor.
	www.math.unm.edu (449 words)

	Markov Chains and Mixing Times (Site not responding. Last check: 2007-10-12)
		We are writing a textbook, Markov Chains and Mixing Times, on the modern theory of Markov chains and their applications.
		Yuval Peres, Departments of Mathematics and Statistics, University of California, Berkeley.
		In June, 2006, the authors organized Mathematics of Markov Chain Monte Carlo, an MAA PREP workshop held at the Mathematical Sciences Research Institute.
	www.oberlin.edu /markov (132 words)

	chain - OneLook Dictionary Search
		Chain, -chain, chain, chain, chain : Dictionary.com [home, info]
		Chain, chain : Dorland's Illustrated Medical Dictionary [home, info]
		Words similar to chain: chained, chaining, concatenation, iron, irons, range, strand, string, catena, chain of mountains, chemical chain, fetter, mountain chain, mountain range, range of mountains, sequence, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=chain (529 words)

	Finding the Derivative Using Shortcut Techniques
		Now, let’s evaluate the Chain Rule using the formal definition.
		The Chain Rule is the technique used most in calculus to find the derivatives of functions.
		I strive to provide accurate and error-free documentation concerning all aspects of mathematics.
	www.mathematicshelpcentral.com /lecture_notes/calculus_1_folder/finding_the_derivative_using_shortcut_techniques.htm (323 words)

	[No title]
		Moves in Monopoly are (almost) a Markov chain.
		The reference is: Ash & Bishop, "Monopoly as a Markov chain", Mathematics Magazine, vol 45 (1972) pp.
		Gerald A. Edgar edgar@math.ohio-state.edu Department of Mathematics The Ohio State University telephone: 614-292-0395(Office) Columbus, OH 43210 614-292-4975 (Math.
	www.math.niu.edu /~rusin/uses-math/games/other/monop (755 words)

	The Chain Rule
		The answer is given by the Chain Rule.
		This second formulation (due to Leibniz) is easier to remember and is the formulation used almost exclusively by physicists.
		Then the Chain rule implies that f'(x) exists, which we knew since it is a polynomial function, and
	www.sosmath.com /calculus/diff/der04/der04.html (312 words)

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