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Topic: Connection (mathematics)

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	The Human Connection: Physical and Metaphysical Connections to the Cosmos
		One can only suppose that their strong evolutionary heritage of animal intuitive feelings of connection carried them through this terrible time, and resulted in the first religions, a means of social comfort and solace, celebrating their connections with the spirits of the dead and with the spirits of nature and the animals.
		The connectivity of all life is demonstrated by the DNA "field"; the "particle" field extends this principle to all matter; spacetime and gravitation are examples of metric fields which bind together all forms of energy at the Cosmic scale.
		Both art and science have physical, external "outputs" as intended consequences of their modes of connection; the truly religious mode is nonphysical, completely mental or spiritual, although it may have a behavioral output and social expression, and hoped-for physical outcomes (as a consequence of prayer).
	people.cornell.edu /pages/jag8/human.html (5371 words)

	Connection (mathematics) - Wikipedia, the free encyclopedia
		Connections are of central importance in modern geometry in large part because they allow a comparison between the local geometry at one point to the local geometry at another point.
		An Ehresmann connection is a connection in a fibre bundle or a principal bundle using osculating spaces of the derivative of a field.
		A Koszul connection is a connection generalizing the derivative in a vector bundle.
	en.wikipedia.org /wiki/Connection_(mathematics) (1716 words)

	Math and Music
		Mathematics is the only science where the methods and the subject are the same.
		Mathematics is the study of mathematics using mathematics.
		Thus, there is a natural connection between mathematics and music: Both are experienced as pure objects of the brain, and both have meaning outside of the brain only by artificial connections.
	members.cox.net /mathmistakes/music.htm (1842 words)

	On Mathematical Reasoning in School Mathematics
		Mathematics is the oldest and most universal part of our culture, in fact, for we share it with all the world, and it has its roots in the most ancient of times and the most distant of lands.
		This distinguishing feature of mathematics is called mathematical reasoning, reasoning that makes use of the structural organization by which the parts of mathematics are connected to each other, and not just to the real world objects of our experience, as when we employ mathematics to calculate some practical result.
		Any program of mathematics teaching that slights these interconnections doesn't just deprive the student of the beauty of the subject, or his appreciation of its philosophic import in the universal culture of humanity, but even at the practical level it burdens that child with the apparent need for memorizing large numbers of disconnected facts.
	www.nychold.com /raimi-reason02.html (3199 words)

	Untitled
		Mathematical skills must extend beyond the ability to calculate into the use of mathematics to investigate, analyze, and interpret.
		A math classroom should provide practical experience in mathematical skills that are a bridge to the real world, as well as explorations which develop an appreciation of the beauty and value of mathematics.
		Taught within the context of mathematical and practical applications, the concept of functions is a unifying theme for algebraic concepts.
	www.state.me.us /education/lres/math.htm (3654 words)

	Mathematics and Narrative - Main 1
		Mathematical affinity necessarily follows from universal properties of the entities involved and this may be easily taken to suggest a certain historical scenario that "might be".
		Like poetry, also mathematics tries to uncover the behavior of such and such kind of universal entity by virtue of being what it is. History on the contrary, has the much less glamorous task of indicating what actually happened, not what might have happened.
		Authors of narrative fiction, and in particular mathematics in fiction, may try to remain as close as possible to what they consider to be the historical truth, but it is not inherent in the genre that this should be the case.
	www.tau.ac.il /~corry/publications/articles/Narrative/main1.html (2420 words)

	LD OnLine :: Learning Disabilities in Mathematics
		One type of learning disability affecting mathematics can stem from an individual's difficulty processing language, another might be related to visual spatial confusion, while yet another could include trouble retaining math facts and keeping procedures in the proper order.
		The fundamental principle in helping a child with a disability in mathematics is to work with the child to define his or her strengths.
		When learners have lost (or never had) the connection between mathematics and meaning, it is helpful to encourage them to estimate their answers before they begin computing.
	www.ldonline.org /articles/5947 (1568 words)

	Connection - Wikipedia, the free encyclopedia
		Connected space, a topological space which cannot be written as the disjoint union of two or more nonempty spaces
		Connection (dance), the primary means of communication between the lead and follow
		Connection (mathematics), a way of specifying a derivative of a vector field along another vector field on a manifold
	en.wikipedia.org /wiki/Connection (298 words)

	The Relevance of An Introduction to Mathematics to Whitehead’s Philosophy
		Thus the insights into the remaining areas of mathematics that were dealt with (the theory of numbers, algebra, geometry, the differential calculus, and topology) had to be reduced to the most basic points of these various branches.
		This analysis of mathematics seems to be the reason for Whitehead to attach e attribute of a "particular individuality" (SMW 229) to eternal objects in his later philosophy.
		For if mathematics holds in any way, and if it is at all applicable to nature, then it is, by its very existence, a guarantee for the reality and significance of eternal objects and their ingression into nature.
	www.religion-online.org /showarticle.asp?title=2753 (4961 words)

	Site Entrance (Site not responding. Last check: 2007-09-17)
		Mathematics mastery in particular further requires numerical and geometry drawing experience from examples and practice to put theory in context.
		Site innovations for mathematics and logic education were initially developed to fill skill and concept gaps and flaws sensed in the high school exposition of modern mathematics curricula prevalent from mid-1950s to the 1980s in schools and colleges.
		Mathematics from the Birth of Numbers, 1996, 950+, by the late Jan Gullberg, is an excellence resource forpupils and instructor in college and the upper years of secondary schools.
	www.whyslopes.com (6446 words)

	The Utility of Mathematics
		Mathematics is the model of a-priori knowledge in the Aristotelian tradition of rationalism.
		The Greek awe of mathematical knowledge is still with us; it's behind the traditional metaphor of mathematics as "Queen of the Sciences". It's been reinforced by the spectacular successes of mathematical models in science, successes the Greeks (lacking even simple algebra) could never have foreseen.
		The majority of mathematicians quickly became "Formalists", holding that pure mathematics could not be philosophically considered more than a sort of elaborate game played with marks on paper (this is the theory behind Robert Heinlein's pithy characterization of mathematics as "a zero-content system").
	catb.org /~esr/writings/utility-of-math (1198 words)

	CSMEE Digest 95-6
		Of all of the reform recommendations being made by the National Council of Teachers of Mathematics, making mathematical connections is among the more difficult to achieve, yet is so helpful in motivating students in the early grades.
		Mathematical connections can relate mathematical topics to students' daily lives and to other mathematical topics but are probably most important in relating mathematics to other curriculum areas.
		Activities in this booklet (1) combine important mathematics and science in a single lesson; (2) have been tried out by classroom teachers and elementary school children; (3) involve "hands-on" activities; (4) use readily available, everyday materials; and (5) can be used as the basis for further activities.
	www.stemworks.org /digests/dse95-6.html (1545 words)

	NCTM Math Standards 9-12
		A mathematician or a student who is doing mathematics often makes a conjecture by generalizing from a pattern of observations made in particular cases (inductive reasoning) and then tests the conjecture by constructing either a logical verification or a counterexample (deductive reasoning).
		Two general types of connections are important: (1) modeling connections between problem situations that may arise in the real world or in disciplines other than mathematics and their mathematical representation(s); and (2) mathematical connections between two equivalent representations and between corresponding processes in each
		Historically, mathematics took a great stride forward in the seventeenth century when the geometric ideas of the ancients were expressed in the language of coordinate geometry, thus providing new tools for the solution of a wide range of problems.
	www.allstar.fiu.edu /aerojava/NCTM_9-12.htm (2563 words)

	Math Journals
		Its use as a tool for the teaching and learning of mathematics is a recent development, springing in part from the NCTM Standards on Communication.
		Through the use of writing in the mathematics classroom, students can clarify their thinking, recognize and appreciate the connection between mathematics and other disciplines, and communicate their thoughts, ideas, and understanding about the subject with other students.
		Mathematics is a way to understand the world and writing is a way to understand mathematics.
	www.geocities.com /kaferico/writemat.htm (1061 words)

	Getsmarter.org - Math & Science Television
		In addition to the obvious connection of mathematics to the musical score, music is linked to ratios, exponential curves, periodic functions and computer science.
		They discovered the connection between musical harmony and whole numbers by recognizing that the sound caused by a plucked string depended upon the length of the string.
		Mathematical discoveries, namely periodic functions, were essential in the modern design of musical instruments and in the design of voice activated computers.
	www.getsmarter.org /mstv/L2_a.cfm (734 words)

	[No title]
		Mathematics seeks to describe and reason about things in a precise and generalized way.
		Mathematical discourse trains you to understand the structure of another person's ideas independent of whether you share their presuppositions, and it equips you to understand the fundamental patterns of reality and apply them in the physical world.
		Mathematics is a rich source of analogies that reflect fundamental relational patterns.
	www.math.wisc.edu /~ejohnson/mathmission/christianMathPhilosophy.html (605 words)

	Doing Mathematics with Your Child (Site not responding. Last check: 2007-09-17)
		More than that, mathematics is a subject that should be more enjoyable than it sometimes is. The National Council of Teachers of Mathematics (NCTM) has identified the appreciation and enjoyment of mathematics as one of the national goals for mathematics education.
		Besides the mathematics learning that takes place at the parent's initiative, there are many opportunities for parents and teachers to work cooperatively in enriching children's experience with mathematics.
		Second, extending mathematical concepts from the classroom to home will establish the idea that mathematics is not just a school subject, but an everyday subject that makes life more interesting and understandable.
	www.math.com /parents/articles/domath.html (1724 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-09-17)
		The equations for the components of the connection form are called the structure equations for the connection in
		is the connection form of a certain affine connection on
		The last two equations for the components of the connection form are called the structure equations for the affine connection on
	eom.springer.de /C/c025150.htm (211 words)

	Welcome to Florida Virtual School
		Mathematics 3 uses the connection between mathematics and music to develop and reinforce mathematical skills and processes.
		The mathematical content addresses the National Council of Teachers of Mathematics (NCTM) principals and standards and is organized by Number and Operation, Algebra, Geometry, Measurement, and Data Analysis and Probability.
		To continue the development of mathematical concepts and processes that can be used to solve real world and mathematical problems.
	www.flvs.net /students_parents/course_descr/cd_middle_math3.php (291 words)

	PROJECT NINE: RESULTS OF RESEARCH ON GENDER IN MATHEMATICS
		Thus, females have problems with self-esteem and learning mathematics just when they are beginning to study algebra, the foundation of most high school and college mathematics courses.
		As examples of the attitudes studied, males were found to be more confident in their ability to learn mathematics than females and males perceived mathematics to be more useful to them than females.
		Because advanced mathematics is often viewed as a "gateway" to high-paying careers, females' attitudes towards mathematics can lock them out of careers in science, law, medicine, and data processing.
	www.prenhall.com /divisions/esm/app/ph-elem/multicult/html/chap9.html (746 words)

	Bernard Morin and Tactile Mathematics
		So, I must posit the proposal that there is a necessary connection between mathematics and the body, which physical, tactical mathematics necessarily triggers.
		She was escorting a blind man. I showed her the Braille-Annotated Hyperbolic Paraboloid and some other mathematical surfaces I was carrying.
		I know that there is a path from 3-D digitizing of the body to a generalized mathematical description of the shape of the body.
	emsh.calarts.edu /~mathart/figure/Morin_Objects.html (949 words)

	Mathematical Imagery Presented by the American Mathematical Society - Home
		Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings.
		In this sense, I like to feel that theory (mathematics), art (outcome), software (algorithms) and engineering (hardware) are integrated and interdependent and that no part survives without the others.
		Viewpoints: Mathematics and Art, by Annalisa Crannell (Franklin and Marshall College) and Marc Frantz (Indiana University)
	www.ams.org /mathimagery (430 words)

	Mathematics and Chess Page
		Though one might think at first that this type of thinking is unrelated to mathematics, in fact, chess also teaches a type of "calculation" (see Soltis's book [4] for the exact idea).
		A paraphrase from the entry under Mathematics and Chess in [5]: In 1893, a Professor Binet (of Stanford-Binet IQ test fame) made a study of the connection between mathematics and chess.
		One characteristic which was missing from mathematics was the combat, in which two individuals contend for mastery, with all the qualities required of generals in the field of battle.
	web.usna.navy.mil /~wdj/math_chess.htm (2039 words)

	cmcmath : Welcome
		The California Mathematics Council believes that all students have the capacity to become mathematically competent and confident when provided a rigorous and challenging mathematical program supported by high expectations.
		CMC has developed new Mathematics Festival Programs which can be taken to your school for parent outreach as well as teacher professional development and student involvement.
		Mathematics and science educators are also invited to collaborate with the Math Forum by reviewing and contributing to a revision of the OMG and by contributing mentoring resources to the Guide (e.g., research articles and Web resources).
	www.cmc-math.org (903 words)

	Interactive Mathematics
		Students are actively involved with other students and the instructor in their learning of mathematics.
		Through this experience students acquire confidence in using mathematics meaningfully and are able to formulate problems from situations within and outside of mathematics.
		The connection of mathematics to the real world is seen as students apply mathematical thinking and modeling to solve problems that arise in disciplines, such as art, music, psychology, science, and business.
	www.mhcc.edu /pages/2053.asp (349 words)

	NCTM: About: MET: Edward G. Begle Grant for Classroom-Based Research (Site not responding. Last check: 2007-09-17)
		The purpose of this grant is support and encourage classroom-based research in precollege mathematics education in collaboration with college or university mathematics educators.
		The research must be a collaborative effort involving a college or university mathematics educator (a mathematics education researcher or a teacher of mathematics learning, teaching, or curriculum) and one or more grades K–12 classroom teachers.
		The college or university mathematics educator must be a member of the NCTM.
	www.nctm.org /about/met/begle.htm (734 words)

	Origami & Math
		The connection with geometry is clear and yet multifaceted; a folded model is both a piece of art and a geometric figure.
		The connection with topology is less clear than the connection with geometry, probably because most people are far less familiar with this field.
		Thomas Hull, an assistant professor of mathematics at Merrimack College in North Andover, Massachusetts, is the expert in the field of origami and topology.
	www.paperfolding.com /math (2393 words)

	Adam, J.A.: Mathematics in Nature: Modeling Patterns in the Natural World.
		Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling.
		Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks.
		"Mathematics in Nature is an excellent resource for bringing a greater variety of patterns into the mathematical study of nature, as well as for teaching students to think about describing natural phenomena mathematically.
	press.princeton.edu /titles/7686.html (557 words)

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