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Topic: Pathological mathematics

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	PlanetMath: pathological
		In mathematics, a pathological object is mathematical object that has a highly unexpected property.
		A very famous pathological function is the Weierstrass function, which is a continuous function that is nowhere differentiable.
		This is version 6 of pathological, born on 2004-10-06, modified 2005-03-03.
	www.planetmath.org /encyclopedia/Pathological.html (167 words)

	Pathology - Wikipedia, the free encyclopedia
		The related term pathological is sometimes used by clinicians, or casually, to signify some abberrant process underlying such a dysfunction, thus a "pathological growth", or casually, a "pathological attitude" or a "pathological woman hater".
		Pathological can also be used in data sets in mathematics or statistics to reference an exceptionally (or awkwardly, or inconveniently) atypical example or set of data, often one which does not abide by rules or succumb to treatment that other similar cases usually do:
		Here, an input (or set of inputs) is said to be pathological if it causes atypical behavior from the algorithm, such as a violation of its average case complexity, or even its correctness.
	en.wikipedia.org /wiki/Pathology (415 words)

	PlanetMath: pathological
		Pathological objects are typically percieved to, in some sense, be badly behaving.
		A very famous pathological function is the Weierstrass function, which is a continuous function that is nowhere differentiable.
		This is version 6 of pathological, born on 2004-10-06, modified 2005-03-03.
	planetmath.org /encyclopedia/Pathological.html (162 words)

	Pathological (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, a pathological example is one whose properties are (or should be considered) atypically bad.
		This highlights the fact that the term pathological is subjective, and its meaning in any particular case resides in the community of mathematicians, not within the subject matter of mathematics itself.
		One can therefore say that (particularly in mathematical analysis and set theory) those searching for the "pathological" are like experimentalists, interested in knocking down potential theorems, in contrast to finding general statements widely applicable.
	en.wikipedia.org /wiki/Pathological_(mathematics) (665 words)

	The Fractal Geometry of Nature - Benoit B. Mandelbrot (1977) (Site not responding. Last check: 2007-10-09)
		A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th.
		Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton.
		Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton.
	www.mountainman.com.au /fractal_00.htm (327 words)

	Pathological (mathematics) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, a pathological example is one whose properties are (or should be considered) untypically (That which is below standard or expectations as of ethics or decency) bad.
		The discovery of the ((mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry) fractals and other "rough" geometric objects.
		Here, an input (or set of inputs) is said to be pathological if it causes atypical behavior from the algorithm, such as a violation of its average case (The quality of being intricate and compounded) complexity, or even its correctness.
	www.absoluteastronomy.com /encyclopedia/P/Pa/Pathological_(mathematics).htm (727 words)

	Encyclopedia: Pathological (mathematics)
		Mathematics, often abbreviated maths in Commonwealth English and math in American English, is the study of abstraction.
		In mathematics, the Weierstrass function was the first example found of a kind of function with the property that it is continuous everywhere but differentiable nowhere.
		In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule, i.
	www.nationmaster.com /encyclopedia/Pathological-(mathematics) (1413 words)

	Is Mathematics a Scientific Discipline?
		In pure mathematics, the equivalent to this stance is that nobody wants to change the decision for the infinity of primes or the irrationality of [root]2 which was made at the outset of rational mathematics.
		Correlatively, mathematics is a fanaticism of mechanistic objectivity and objectification.
		Modern mathematical logic has its origins precisely as a reaction to the philosophic discussion of the truth of such propositions as 7+5 = 12 in Hume and Kant; and to the views on elementary mathematics of the philosopher Husserl, whose university degree was in mathematics.
	www.henryflynt.org /studies_sci/mathsci.html (9178 words)

	On Gödel's Philosophy of Mathematics, Chapter I
		Where it was hoped that subjecting mathematics to restricted methods would cause the unclear concepts and paradoxes to precipitate, leaving a transparent, consistent mathematics in its purest form, it was found that too much of mathematics was lost as well in the process.
		Mathematics has a propensity for employing physical or "thing" language, and this does have considerable heuristic value because the metaphors chosen are usually clever and appropriate.
		Mathematics for Gödel is boundless, having its beginning in the rudiments of logic, extending up to classical analysis, the higher axioms of infinity, and beyond to bolder, richer but as yet undiscovered theories.
	www.friesian.com /goedel/chap-1.htm (4807 words)

	Pure mathematics -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		Broadly speaking, pure mathematics is (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics motivated entirely for reasons other than application.
		Pure mathematics, according to a view that continued to and through the (Click link for more info and facts about Bourbaki) Bourbaki group, is what is proved.
		The question is now more about the roots of mathematical progress — whether they are internal and generated by (Click link for more info and facts about problem-solving) problem-solving suggested by the shape of the subject itself, or external.
	www.absoluteastronomy.com /encyclopedia/p/pu/pure_mathematics.htm (421 words)

	Science Fair Projects - Well-behaved
		In pure mathematics, "well-behaved" objects are those that can be proved or analyzed by elegant means to have elegant properties.
		In both pure and applied mathematics, (optimization, numerical integration, or mathematical physics, for example,) well-behaved also means not violating any assumptions needed to successful apply whatever analysis is being discussed.
		It is not unusual to have situations in which most cases (in terms of cardinality) are pathological, but the pathological cases will not arise in practice unless constructed deliberately.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Well-behaved (447 words)

	Clearing up the market cycle... best Pathological (Site not responding. Last check: 2007-10-09)
		Periodia in one's mathematical form appeals to this function, but it is fold form from value of price row, values of time, characteristic for given row, function sine and parameter of optimization called as Chimerical price.
		Pathological liars may have structural abnormalities in their brains, a new study suggests.
		Pathological -- from MathWorld Pathological -- from MathWorld The term "pathological" is used in mathematics to refer to an example specifically cooked up to violate certain almost universally valid properties.
	ascot.pl /th/Fourier5/Pathological.htm (874 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-09)
		In mathematics, a path in a graph is a sequence of vertices such that from each of its vertices there is an edge to the successor vertex.
		In mathematics, a path in a topological space X is a continuous map f from the unit interval I = [0,1] to X f : I → X. The initial point of the path is f(0) and the terminal point is f(1).
		In mathematics, a path integral (also known as a line integral) is an integral where the function to be integrated is evaluated along a pa..
	pardus.info /browse.php?title=P/PA/PAT (11267 words)

	HAF: Preface
		Every idea in mathematics can be made more general and more abstract by making the hypotheses weaker and more complicated and by introducing more definitions, but I have tried to avoid the weakly upper hemisemidemicontinuous quasipseudospaces of baroque mathematics.
		It is unavoidable that the beginning graduate student of mathematics must wade through a large collection of new definitions, but that collection should not be made larger than necessary.
		Students with sufficient mathematical maturity may not even need to refer to their college calculus textbooks; Chapters 24 and 25 reintroduce calculus in the more general setting of Banach spaces.
	www.math.vanderbilt.edu /~schectex/ccc/excerpts/preface.html (4201 words)

	Alzheimer's Disease
		Alzheimer's disease, osteoporosis, and cancer are three pathological states the incidence of which seems to increase rapidly with age.
		It is a set of symptoms found in a variety of pathological conditions.
		It is characterized by a diffuse atrophy throughout the cerebral cortex with attendant, highly distinctive pathological changes.
	www.csa.com /discoveryguides/archives/alzheimers.php (594 words)

	Ball-Stick-Bird - Article - Music, Mathematics, Dyslexia: The other Ways of Organizing Information.
		They knew that on their triple planets the new testing and neuroscience discoveries had demonstrated that children with high test scores in music, mathematics, and content organization, frequently were school failures.
		However, that does not mean that the differences in brain organization that produce the variations of abilities are themselves either a disability or pathological.
		Rather than being cursed by the variation in our abilities - on which, in a vain attempt to correct, we have spent millions of man-hours, billions of the national treasury, and trillions of hours in misery - these differences should be regarded as our blessing, to be utilized to their fullest potential.
	www.ballstickbird.com /articles/a8_music.html (1856 words)

	Good Math, Bad Math : Conservapedia and Math
		The term "elementary proof" or "elementary techniques" in mathematics means use of only real numbers rather than complex numbers, which relies on manipulation of the imaginary square root of (-1).
		It's an important number, and it does exist in mathematics - as I've explained in the linked post, there are a lot of very important and very real phenomena that we experience in the real world that mathematically require i to be described.
		To be fair, some mathematical philosophers object to defining relations as sets; they claim that they are primitive objects in themselves.
	scienceblogs.com /goodmath/2007/02/conservapedia_and_math_1.php (6710 words)

	Harvard Medical School Division on Addictions - Research and Education (Site not responding. Last check: 2007-10-09)
		The Institute for Research on Pathological Gambling and Related Disorders was established in 2000 as a program of Harvard Medical School's Division on Addictions.
		This curriculum aims to make mathematics more meaningful to students and more relevant to their daily lives by introducing concepts of probability and statistics through the use of gambling- and media-related topics (click here for more information).
		This curriculum aims to make mathematics more meaningful to students and more relevant to their daily lives by introducing concepts of probability and statistics through the use of gambling- and media-related topics.
	www.hms.harvard.edu /doa/research_education.htm (1820 words)

	Pathological (mathematics) - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-10-09)
		Pathological (mathematics) - Encyclopedia, History, Geography and Biography
		Pathological Structures and Fractals (http://www.mountainman.com.au/fractal_00.htm) - Extract of an article by Freeman Dyson, "Characterising Irregularity", Science, May 1978
		The article about Pathological (mathematics) contains information related to Pathological (mathematics) and External links.
	www.arikah.net /encyclopedia/Pathological_%28mathematics%29 (644 words)

	Math Summary (Site not responding. Last check: 2007-10-09)
		Also, the subfields of mathematics are very tightly connected, especially when you move up to the level of modern, research level mathematics.
		There is no one in mathematics, even the most intelligent and accomplished mathematicians the world has know, that understand all of mathematics.
		The Mathematical Atlas has a great overview of the major fields in mathematics.
	www.math.lsa.umich.edu /~aww/mathphys/math_summary.html (1232 words)

	Pathological science (Site not responding. Last check: 2007-10-09)
		Pathological science is a term created by the Nobel Prize-winning chemist Irving Langmuir during a colloquium at the Knolls Research Laboratory, December 18, 1953.
		Langmuir used the term to describe ideas that would simply not "go away", long after they were given up on as wrong by the majority of scientists in the field.
		2 Scientific theories that are not pathological science
	www.kiwipedia.com /en/pathological-science.html (167 words)

	Human Differences
		Instead it was his preference for numbers and his budding fascination for higher mathematics to the exclusion of "appropriate socialization," i.e.
		Their various articles dealt with how the perception of ubiquitous pathological disorders, which of course have to be treated with medication, is a grand moneymaker.
		And yet the successful children I have described belie their presumed pathological diagnoses and raise questions about the treatment they were to receive.
	www.homeeducator.com /FamilyTimes/articles/12-2article11.htm (2615 words)

	Topological Equivalents of the Axiom of Choice and of Weak Forms of Choice, by Eric Schechter
		Although the term ``constructive'' is used in different fashion by different mathematicians, the Axiom of Dependent Choice is the strongest form of choice that is widely held to be constructive.
		A couple of very weak consequences of the Axiom of Choice are the existence of (i) subsets of R which are not Lebesgue measurable, and (ii) subsets of R which lack the Baire property.
		The existence of those two kinds of pathological objects can be proved using other assumptions instead of the Axiom of Choice; in particular, the existence of those pathological objects follows from the existence of many other pathological objects which are classical in the literature.
	at.yorku.ca /z/a/a/b/18.htm (848 words)

	Taking on 'Rational Man': Dissident economists fight for a niche in the discipline
		Their efforts to open the field to diverse views are smothered, they say, by an orthodoxy -- neoclassical economics and its derivatives -- that is indulgently theoretical and mathematical in its aspiration to be more "scientific" than any other social science.
		At the time, the government "embraced the work of these cutting-edge economists, saying, This work can help us wage war." New ideas about the application of mathematical models and modern statistics were used to meet government goals, so economics, like the nuclear arm of physics, benefited from enormous infusions of funds.
		But don't be fooled, he says, by the mainstream's fancy mathematics and claims that it is a predictive science, not just a descriptive social science.
	www.paecon.net /PAEarticles/ChronicleJan03.htm (3122 words)

	Post Autistic Economics
		Most critics say mathematics is not the issue.
		The issue may not be how much mathematics to use, and when, but what kind.
		regarded as an architect of the mathematization of modern economics.
	transmet.org /aj/misc/postautistic.htm (2831 words)

	Pathological (mathematics) (Site not responding. Last check: 2007-10-09)
		In mathematics, a pathological example is one whoseproperties are (or should be considered) untypically bad.
		In that case, the Baire category theorem was later used to show, quite to thecontrary, that such behaviour was typical and even generic.
		One can therefore say that (particularly in mathematicalanalysis) those searching for the 'pathological' are like experimentalists, interested in knocking down potential theoremsproposed (by 'theorists'); this should all take place within mathematics.
	www.therfcc.org /pathological-mathematics--32821.html (231 words)

	Math 130, Spring 2001, Lab 5
		(a) Use more standard mathematical notation to write the amount of tax as a function of the income.
		Mathematicians call examples like this one, which have behaviors that seem bizarre, pathological examples.
		In mathematics, pathological examples are an important tool for understanding, since they show ways in which ``common-sense'' expectations can go wrong in the world of mathematics.)
	math.hws.edu /eck/math130/lab5 (549 words)

	A Numerical Study of a Pathological Example of p-System
		A Numerical Study of a Pathological Example of p-System: SIAM Journal on Numerical Analysis Vol.
		In this paper, we consider several high-order schemes in one space dimension.
		This comparison is made first on a Sod shock tube and then on a very pathological example of a p-system constructed by Greenberg and Rascle [ Arch.
	epubs.siam.org /sam-bin/dbq/article/32318 (195 words)

	Baire Category Theorem (Site not responding. Last check: 2007-10-09)
		Abelian Group Theory papers of Andreas R. Blass...
		Measure and Category by John C. Oxtoby - Mathematical Books - Apronus.com...
		What to study for the Midterm on March 30, 2004...
	www.scienceoxygen.com /math/633.html (159 words)

	Clearing up the market cycle... best Pincherle Derivative (Site not responding. Last check: 2007-10-09)
		Pathological (mathematics) -- Partial derivative -- Partial differential equation -- Partial...
		In mathematics, the Pincherle derivative of a linear operator T on the space of polynomials in x is another linear...
		The derivative of a function represents an infinitesimal change in the function with respect to whatever parameters it may have.
	ascot.pl /th/Fourier5/Pincherle-Derivative.htm (492 words)

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