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Topic: Neighborhood (mathematics)

	Mathematics
		Closure (mathematics) In mathematics, the closure C(X) of an object X is defined to be the smallest object that both inc...
		Degeneracy (mathematics) In mathematics, a degenerate case is a limiting case in which a class of object changes its nat...
		Mathematics Mathematics is commonly defined as the study of Philosophy of mathematics.
	www.brainyencyclopedia.com /topics/mathematics.html (2391 words)

	Neighbourhood (mathematics) - Wikipedia, the free encyclopedia
		In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
		Intuitively speaking, a neighbourhood of a point is a set containing the point where you can "wiggle" or "move" the point a bit without leaving the set.
		There is an alternative way to define a topology, by first defining the neighbourhood system, and then open sets as those sets containing a neighbourhood of each of their points.
	en.wikipedia.org /wiki/Neighborhood_(topology) (697 words)

	Reference Details (Site not responding. Last check: 2007-10-10)
		Researchers expected that the neighborhood may influence students and their academic achievement directly, and it may affect students' academic achievement indirectly through its influence on parental practices that lead to positive student outcomes.
		The data analyses supported the researchers' expectation of a dual process of educational influence operating primarily at the neighborhood level; that is, the place of residence may have important consequences for the academic success of adolescents.
		The findings suggested that neighborhoods characterized by concentrated disadvantage and schools characterized by student poverty and absenteeism tend to depress students' achievement in mathematics.
	www.nwrel.org /scpd/re-engineering/rycu/ReferenceDetails.asp?RefID=81 (300 words)

	Neighbourhood - Wikipedia, the free encyclopedia
		Neighbourhood is also a term used in mathematics (see the concepts of neighbourhood in topology and the concepts of neighbour and neighbourhood in graph theory) and a song by Space.
		A neighbourhood (CwE) or neighborhood (AmE) is a geographically localized community located within a larger city or suburb.
		The residents of a given neighbourhood are called neighbours (or neighbors), although this term may also be used across much larger distances in rural areas.
	en.wikipedia.org /wiki/Neighborhood (383 words)

	Aligning and Articulating Standards Across the Curriculum
		The NCTM Standards, which emphasize problem solving and connections between mathematics and other disciplines as well as students' daily lives, also can be used to stimulate the aligning of mathematics standards with schoolwide goals for meaningful and engaged learning and with goals of other disciplines addressed by schools.
		Mathematics should not be isolated from other school subjects or the everyday lives of students.
		Teachers should design mathematics writing projects that are based on issues and questions justifying the mathematics and that will increase student involvement in the classroom.
	www.ncrel.org /sdrs/areas/issues/content/cntareas/math/ma400.htm (2193 words)

	Connection Collection - National Center for Family & Community Connections with Schools
		This study seeks to determine whether neighborhoods and schools make a difference in parental practices in 8th graders' schooling and examine the ways parent practices, neighborhoods, and schools influence students' 8th grade achievement.
		Authors conclude that neighborhoods may influence students' academic achievement by depressing parental practice associated with high math achievement, but that parents may be able to overcome neighborhood disadvantages through communication, monitoring, and providing learning opportunities for their children.
		Researchers suggest the following from their findings: neighborhood and school characteristics may influence students and their mathematics achievement; lower levels of math achievement are associated with school poverty and neighborhood disadvantage; neighborhoods affect parents' abilities to help children succeed in school and; poverty and absenteeism associate with low math achievement.
	www.sedl.org /connections/resources/citations/155.html (316 words)

	Real-World Projects - Vol 15 No 3 - Rethinking Schools Online
		The mathematics included percentages, ratios, and proportions, and students also had to pose their own mathematical problems based on the article.
		They had to write a creative piece about the watch and its price, using mathematics at the level of at least eighth grade, and have their opinion about the watch and ad come through in the piece.
		Students had to define what a "fair ad" was, then had to analyze the advertisement to determine whether the ad was fair, give justifications for their decisions, and if they believed the ad to be unfair, create a new ad that would make it fair.
	www.rethinkingschools.org /archive/15_03/Mside153.shtml (896 words)

	Limits...Taback's Child's Concept of Limit
		The tasks that Taback used to investigate children's understanding are excellent for connecting elementary school mathematics learning activities to those that will be used as they become more mathematically sophisticated in middle and high school and beyond.
		The "Neighborhood" task examines the child's ability to locate an open interval and an open circle given the defining properties of each.
		There was a sharp increase in the number of responses at the highest level going from the eight-year-olds to the ten-year-olds and a small increase going from the ten- to the twelve-year-olds.
	www.unf.edu /~tbratina/mathed/limits/neighborhoodteacherpage.htm (566 words)

	Mathematics
		Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry.
		Students use number sense and numeration to communicate mathematically and use numbers in the development of concrete mathematical ideas.
		Equilibrium is a state of stability due either to a lack of changes (static equilibrium) or a balance between opposing forces (dynamic equilibrium).
	www.vesid.nysed.gov /specialed/publications/learnstand/lrnstd4.htm (2742 words)

	In The Neighborhood of Mathematical Space, by Karen Shenfeld
		A mathematical work, he held, could be judged fairly on the basis of its depth and its breadth -- both of which criteria could be applied to either a discussion of a single theorem or the accumulated achievements of a lifetime.
		The notion of a neighborhood describes the relationship between one of a space's points to a sub-collection of its points; it describes, that is, the state of one point in a topological space being near -- infinitely near, in fact -- to a sub-collection of its points, without the measurement of any distances whatsoever.
		The importance of the notion of neighborhood and its utility in the definition of a topological space was propagated by the German mathematician Felix Hausdorff.
	at.yorku.ca /t/o/p/c/02.dir/6.htm (17907 words)

	University Neighborhood High School - New York, New York / NY - school information
		The state average for Mathematics A was 81% in 2004.
		The state average for Mathematics B was 76% in 2004.
		The state average for Sequential Mathematics, Course III was 50% in 2004.
	www.greatschools.net /modperl/achievement/ny/6268 (266 words)

	Topology
		Which case an event should be subordinated to, in mathematical view, is just that which set the "element" standing for the event should belong to.
		However, in Mathematics, a set A can be equivalently represented by its characteristic function ‑ a mapping XA from the universe X of discourse (region of consideration, i.e., a larger set) containing A to the 2‑value set [0,1): i.e.
		In view of the fact that set theory is the cornerstone of modern mathematics, a new and more general framework of mathematics was established.
	www.wordtrade.com /science/mathematics/topology.htm (2132 words)

	The Role of Reverse Mathematics
		Reverse Mathematics is a highly developed research program whose purpose is to investigate the role of strong set existence axioms in ordinary mathematics.
		Reverse Mathematics is a technique which frequently yields precise answers to special cases of this question.
		This might be called ``forward mathematics.'' But in order to establish that the axioms are needed for a proof of the theorem, one must reverse the process and deduce the axioms from the theorem.
	www.math.psu.edu /simpson/papers/hilbert/node5.html (729 words)

	Crime in the Hood
		The probability of a white being violently attacked is developed as a function of a neighborhood's racial composition.
		As his neighborhood turns fl, John and his family will notice many changes, but none will be more dreaded than the prospect of being violently victimized.
		However, as a neighborhood turns fl, this factor could increase fl-on-white violence at most by a factor of 3, and then only when a neighborhood is virtually all fl.
	www.lagriffedulion.f2s.com /hood.htm (1978 words)

	Penn College Outreach for K-12: Pennsylvania Governor's Institute for Mathematics
		Select and use an appropriate method, materials and strategy to solve problems, including mental mathematics paper and pencil and concrete objects.
		Pick a fact family house out of the neighborhood each day that you would like to live in that day (that will be the house you may take home for homework practice).
		Children can work individually or with a buddy to make a classroom book out of house pattern with math fact families (they may do as high as they are able).
	www.pct.edu /k12/gov-math/2004/k-2-neighborhood-fact-families.html (704 words)

	neighborhood. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
		A district or area with distinctive characteristics: a neighborhood of fine homes; an ethnic neighborhood.
		The surrounding area; vicinity: happened to be in the neighborhood.
		Mathematics The set of points surrounding a specified point, each of which is within a certain, usually small distance from the specified point.
	www.bartleby.com /61/35/N0053500.html (153 words)

	[No title]
		Topological Spaces: From Distance to Neighborhood is a gentle introduction to topological spaces leading the reader to understand the notion of what is important in topology vis-a-vis geometry and analysis.
		The authors have also restricted the mathematical vocabulary in the book to avoid overwhelming the reader with the extensive array of technical terms indicating the properties of topological spaces.
		Additionally, the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology.
	www.aspalliance.com /aspxtreme/shop/product.aspx?asin=0387949941 (573 words)

	Meetings & Conferences
		NCSM is an organization promoting leadership in mathematics education.
		How have you, as a mathematics leader, used research to support current practices that are effective for students in your neighborhood?
		Join other mathematics leaders on an adventure that just gets curiouser and curiouser with each assessment strategy, technique, and tool.
	mathforum.org /ncsm/MeetingsConferences/04conferences.html (669 words)

	[No title]
		This neighborhood includes domains in Mathematics related to the problem under consideration; the relation can be either obvious from start or be discovered during the student’s autonomous work.
		The frame of the author's courses is fixed by the institution where he teaches; the added value of extra tasks, not officially present in the syllabus but given as pilots, is received by most students as a “plus” in their education.
		Consider the cognitive neighborhood of a given mathematical topic as included in a kind of space, which could be called ``Mathematical Knowledge''.
	www.fi.uu.nl /~pauld/CERME4/Papers/Dana-Picard.doc (3379 words)

	Ph.D. Program
		The Ph.D. program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in basic research in a nonacademic setting.
		The mathematics and statistics departments are housed in a comfortable building containing an excellent Mathematics Library, computing facilities, graduate student offices, lounge for tea and conversation, and numerous seminar and lecture rooms.
		Each student admitted to the Ph.D. program is appointed a fellow in the Department of Mathematics for the duration of his or her doctoral candidacy, up to total of five years.
	www.math.columbia.edu /department/PhD.html (603 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		] A bundle for which each point in the base has a neighborhood U whose inverse image under the projection map is isomorphic to a cartesian product of U with a space isomorphic to the fibers of the bundle.
		Procurement of supplies or equipment for its own use in an area outside the United States by a United States military command located in that area.
		] A property of an object (such as a space, function, curve, or surface) whose specification is based on the behavior of the object in the neighborhoods of certain points.
	www.accessscience.com /Dictionary/L/L19/DictL19.html (2606 words)

	TeacherSource . Math . Mathematics of Bicycles I \| PBS
		The mathematics and science of bicycles offers interesting questions.
		From the past when you were limited to a Stingray, a regular bike, or a ten-speed, today you have options including the BMX, road bikes, mountain bikes, and hybrid bikes, which are a cross between a mountain bike and a road bike.
		To develop the mathematics, we will look at the differences among bikes.
	www.pbs.org /teachersource/mathline/concepts/neighborhoodmath/activity3.shtm (434 words)

	John Locke -- Overview [Internet Encyclopedia of Philosophy]
		In the former case, the agreement or disagreement is immediately perceived; in the latter, it is perceived through the mediation of a third idea, but each step in the demonstration is itself an intuition, the agreement or disagreement between the two ideas compared being immediately perceived.
		He thinks also that "morality is capable of demonstration as well as mathematics." But, in spite of the request of his friend Molyneux, he never set out his ethic doctrine in detail.
		Thus, knowledge of mathematics and ethics may be firmly establish, particularly as these subjects involve relations between ideas, and thus make no claims about matters of real existence.
	www.iep.utm.edu /l/locke.htm (7767 words)

	City of Orlando, Neighborhood Services, Mayor's Educational Grants Program, Year 2000 Projects
		Skills in reading, mathematics and problem solving will be practiced and enhanced through a program of cross-curricular activities using computers.
		SECME is a nationwide organization whose mission is to encourage and prepare all students to enter and complete post-secondary studies in science, mathematics, engineering and technology.
		School staff and members of the College Park Neighborhood Association will work together as a team during weekly meetings to excite the students about various fields in science.
	www.cityoforlando.net /executive/nso/mepg2001.htm (1147 words)

	Mathematics is More than Number
		First, reasoning about space is basic to many forms of mathematics that children encounter in their schooling.
		Common experiences such as finding their way about the neighborhood, building with blocks and legos, drawing and looking at pictures, and noticing common shapes in nature lead children to ideas about:
		For homework this week, you can try this activity in your neighborhood, at a park, or anywhere else that is convenient.
	www.wcer.wisc.edu /archive/mims/Parent_Newsletters/Math_is_More_than_Number/newsletter2.html (868 words)

	VITAE
		A Neighborhood Condition Which Implies the Existence of a Complete Multipartite Subgraph, (with R. Faudree) Discrete Mathematics Vol.
		A Neighborhood Condition Which Implies the Existence of a Class of d-Chromatic Subgraphs, Journal of Graph Theory, Vol.
		Neighborhood Unions, Generalized Degrees and Graphical Properties, (With L. Lesniak), Graph Theory, Combinatorics, Algorithms and Applications, Vol.
	www.etsu.edu /math/vita02.htm (988 words)

	Neighborhood (Site not responding. Last check: 2007-10-10)
		Unless otherwise specified, this definition of neighborhood predominantes on this
		At the other extreme, some analysis texts which deal only in metric spaces define a neighborhood to be an open ball around a point
		In fact, almost any argument involving neighborhoods would be unaffected by shrinking a neighborhood to a smaller open set or to an open ball (in the context ot metric spaces).
	www.objectsspace.com /encyclopedia/mathematics/entries/54/Neighborhood/Neighborhood.html (132 words)

	Cub Scout Academics - Mathematics (Site not responding. Last check: 2007-10-10)
		Observe the world around you for at least a week and keep a record of where you see this shape or figure and how it is used.
		Look at different types of buildings-houses, churches, businesses, etc.-and create a presentation (a set of photographs, a collage of pictures from newspapers and magazines, a model) that you can share with your den or pack to show what you have seen and learned about shapes in architecture.
		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).
	www.usscouts.org /advance/cubscout/academics/mathematics.html (766 words)

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