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Topic: Trivial (mathematics)

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	Trivial (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, the term trivial is frequently used for objects (for examples, groups or topological spaces) that have a very simple structure.
		Also, trivial refers to solutions (to an equation) that have a very simple structure, but for the sake of completeness cannot be ignored.
		For instance, proofs by mathematical induction usually have two parts: a part that shows that if the theorem is true for a certain value of n, it is also true for the value n+1, and a so-called "base case" that shows that the theorem is true for the particular value n=0.
	en.wikipedia.org /wiki/Trivial_(mathematics) (450 words)

	Riemann hypothesis - Wikipedia, the free encyclopedia
		In mathematics, the Riemann hypothesis (also called the Riemann zeta-hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous unsolved problems.
		The Riemann hypothesis is one of the most important open problems of contemporary mathematics; a $1,000,000 prize has been offered by the Clay Mathematics Institute for a proof.
		In other words, the importance of 'the Riemann hypothesis' in mathematics today really stems from the importance of the generalized Riemann hypothesis, but it is simpler to refer to the Riemann hypothesis only in its original special case when describing the problem to people outside of mathematics.
	en.wikipedia.org /wiki/Riemann_hypothesis (2305 words)

	A mathematician's apology
		The trivial mathematics may be justified by arguments which would appeal to Hogben, or other writers of his school, but there is no such defence for the real mathematics, which must be justified as art if it can be justified at all.
		We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not; that the trivial mathematics does, and that the real mathematics does not, ‘do good’ in a certain sense; but we have still to ask whether either sort of mathematics does harm.
		It is true that there are branches of applied mathematics, such as ballistics and aerodynamics, which have been developed deliberately for war and demand a quite elaborate technique: it is perhaps hard to call them ‘trivial’, but none of them has any claim to rank as ‘real’.
	mywebpage.netscape.com /jaimecarvalho/485/Hardy.htm (605 words)

	String Figures and Knot Theory: Part I
		Yet no mathematical result that applies equally to all string figures (two dimensional and three dimensional, symmetric and asymmetric) appears ever to have been published.
		With the exception only of the ethnographical figures and the use made in one paragraph of knot theory, the contents are due solely to the present author.
		Limp designs, such as those formed by arranging a loop of string on a horizontal surface, while examples of trivial knots, are not here considered as examples of string figures.
	website.lineone.net /~m.p/sf/motifs.html (1652 words)

	Feedback on 57 of Doron Zeilberger
		But I do not consider the answer to a chess problem (however general it would be regarding the chosen rules of chess) of any importance in itself for mathematics (and of any general intellectual interest to speak like Dr Friedmann and Dr Simpson) and this is not by a kind of infinitarian bigotry.
		In fact the trivialization of the original question would be the necessary mark of the mathematical interest of the ensuing theory.
		And his not considering chess to be mathematics, but only the 'trivial' chess problems, is perhaps as amazing, or more, than saying it is trivial mathematics.
	www.math.rutgers.edu /~zeilberg/fb57.html (1170 words)

	Islamic mathematics
		Islamic mathematics and Arabic mathematics are modern historical terms for the mathematical sciences in Islamic civilization from the beginning of Islam (A.D. 622) until the 17th century.
		The Islamic mathematical tradition was a continuation of the traditions of ancient Greece, India and pre-Islamic Iran.
		On mathematics education in Islamic India, with emphasis on the transmission of Euclid's Elements and Arabic and Persian commentaries.
	www.math.uu.nl /people/hogend/Islamath.html (7938 words)

	NOVA \| Infinite Secrets \| Working with Infinity \| PBS
		In mathematics nowadays, when we think about infinity, we think about a set whose properties are different from those of ordinary sets.
		There are philosophers who think that because of the rigorous establishment of the calculus in the 19th century, and because of the rigorous treatment of the concept of infinity in set theory from Cantor onward, the philosophical problem of infinity has been solved.
		In fact, mathematics has shown us during the 20th century that you can have all sorts of mathematical theories out there that are compatible with all sorts of possible universes.
	www.pbs.org /wgbh/nova/archimedes/infinity.html (2989 words)

	Non trivial applications of Maple in Teaching Mathematics
		For instance, while teaching mathematics, we have to explore algorithms, use recursive functions, or build complex constructions in 2D or 3D geometry.
		If you are going to use Maple for teaching mathematics in high school or university, the book by Cheung [1] can serve as a great and compact tutorial of Maple features.
		While teaching discrete mathematics, I often use the Euclid algorithm to calculate the greatest common divisor of two integers.
	www.adeptscience.co.uk /maplearticles/f391.html (2039 words)

	sci.crypt: Re: SF: Areas of confusion, infinity
		It's a mathematical theorem which allows you to choose factors and in
		In mathematics there has to be a reason for a theorem to make a choice.
		If it does there has to be a mathematical reason.
	www.derkeiler.com /Newsgroups/sci.crypt/2005-04/0900.html (1711 words)

	Doron Zeilberger's 57th Opinion
		Most mathematicians think that whatever is `finite' is trivial, and reducing a problem to `checking finitely many cases' renders it trivial, and makes the actual checking unnecessary.
		Part of the reason that humans were so successful is that in their research they `cheated' and used pseudo-algorithms, that usually did not work (and then, of course, they never reported their failure), but sometimes did work (and then they had a publication).
		Hence "Blessed is the 'Trivial' for it shall inherit the Non-Trivial Land", and, analogously, "Damned is the (so-called) `Non-Trivial' since it is really Trivially TRIVIAL".
	www.math.rutgers.edu /~zeilberg/Opinion57.html (1116 words)

	[No title]
		candidates in mathematics and applied mathematics were dropped an average of 7.2 times before their 13th birthdays, which undoubtedly did untold damage to their psyches.
		Of course, several concepts (such as rigid rods and deformation of solids) actually encompass mathematics as applied to various engineering and scientific disciplines, but applied mathematicians are in a truly unique position, as they are familiar with more of this language than anybody who studies only one or two scientific areas in depth.
		Another oddity endemic to mathematicians is their fascination with the word "trivial." Things are not "difficult"; instead, they are "non-trivial." As a service to any engineers reading the present essay, I will now provide a brief glossary of various notions of difficulty in the language of mathematics.
	www.its.caltech.edu /~mason/writing/compare.txt (968 words)

	MATHEMATICS & STATISTICS: A Brief Guide to Reference Resources
		Beginning with a thorough overview that chronicles the transition of mathematics scholarly communications from paper to electronic, the bulk of this guide describes the most important resources for mathematics and statistics.
		There are twelve chapters in the second part that focus on resources for specific sub-fields of mathematics.
		Issued annually by the American Statistical Association and the Institute for Mathematical Statistics, it is a comprehensive index to journal articles and monographs for mathematical statistics from 1974 forward.
	library.albany.edu /subject/guides/mathguid.htm (771 words)

	. . . . VU Math Weekly Events . . . .
		Most scientists and engineers use mathematics; that is, functions and equations developed earlier by mathematicians who had no purpose other than to develop mathematics.
		The physical sciences and engineering, throughout most of their history, have progressed by the interaction of new observations, experiments, technology, with theory and new mathematics.
		("Trivial" is also not too well defined but in this instance illuminates my prejudice.) The talk will attempt to explain why this is so and will attempt to predict where "new" mathematics might furnish insights into problems arising in biology.
	www.math.vanderbilt.edu /~calendar/archive/1998/98_11_30.html (749 words)

	Computers and Mathematics with Applications
		Subject: Computers and Mathematics with Applications Date: Sun, 13 Jun 1999 19:55:28 -0400 (EDT) Computers and Mathematics with Applications http://www.elsevier.com/locate/camwa Content available at: http://www.sciencedirect.com/science/journal/08981221 ISSN: 0898-1221 AIMS AND SCOPE Computers and Mathematics with Applications provides a medium of exchange for those engaged in fields where there exists a non-trivial interplay between mathematics and computers.
		Interactive applications - essentially the utilization of a (non-trivial) combination of classical mathematics and of computer science in the solution of problems arising in other fields.
		The journal pays particular attention to applications in "non-classified" fields, such as environmental science, ecology, biology, urban systems and also to appropriate papers in applied mathematics.
	gort.ucsd.edu /newjour/c/msg02902.html (119 words)

	Factoring and rationals (Site not responding. Last check: 2007-10-23)
		In that set, every number but 0 is trivially a factor of every other
		The reality of mathematics which you can see in mathematical history is
		Yes, that is correct, every rational number but 0 is trivially a factor of
	www.newsbackup.com /about673985.html (2263 words)

	Penn State Logic Seminar (Site not responding. Last check: 2007-10-23)
		Participants are largely from Mathematics but also from Computer Science, Philosophy, Linguistics, Physics, Electrical Engineering, and other departments.
		The Reverse Mathematics of Ramsey's Theorem, part 2.
		Fernando Ferreira (University of Lisbon, Mathematics and Philosophy).
	www.math.psu.edu /simpson/logic/seminar (1395 words)

	The Survival, Origin and Mathematics of String Figures
		The Survival, Origin and Mathematics of String Figures
		A knowledge of the set of all look-alikes ('similar-looking string figures') is a considerable aid in attempting to reconstruct such a figure.
		Any publisher interested in publishing the collection is invited to contact the author.
	website.lineone.net /~m.p/sf/menu.html (465 words)

	Einstein,Newton,Dirac..are they really genious?..
		In fact why are they considered genious?..the fotoelectric efect, and the formula F=m.a are in most cases trivial to discover as it is the gravitation formula F=GMm/r2 trivial** from Kepler,s second law.
		Seems very unlikely to me, as I have said before, to think outside of the box, you need to know where the box is. People with no formal education in math and physics have no idea what is known or not known.
		Just because you figure something out for yourself, does not mean that it is made trivial by another well established bit of knowledge which you do not possess.
	www.physicsforums.com /showthread.php?threadid=2758 (1744 words)

	SF: Two Az's (Site not responding. Last check: 2007-10-23)
		For every trivial Az value there is a second non-trivial value.
		This is trivial to show: Let d_1 be the denominator of b_1 and d_2 the
		mathematically as trivial factors, more often than not.
	www.newsbackup.com /about761482.html (1699 words)

	Discrete Mathematics & Discrete Applied Mathematics: Editors' Choice 2003
		In this paper we introduce the concept of a boundary class, which is a helpful tool for classification of hereditary classes of graphs according to the complexity of the independent set problem.
		The problem of simultaneously locating obnoxious facilities and routing obnoxious materials between a set of built-up areas and the facilities is addressed.
		Two important branches of graph connectivity problems are connectivity augmentation, which consists of augmenting a graph by adding new edges so as to meet a specified target connectivity, and connectivity orientation, where the goal is to find an orientation of an undirected or mixed graph that satisfies some specified edge-connection property.
	www.elsevier.com /framework_products/promis_misc/505610editchoice.htm (3429 words)

	Department of Mathematics Preprint 1999-10 (Site not responding. Last check: 2007-10-23)
		Przytycki proved that some classes of links, including 11 crossing links, are 3-equivalent to trivial links.
		Based on this result we prove that all closed 4-braids are 3-equivalent to trivial links.
		Then we show that all links with no more than 12 crossings are 3-equivalent to trivial links.
	www.gwu.edu /~math/preprints/ma9910.html (97 words)

	Joint Mathematics Colloquium (Site not responding. Last check: 2007-10-23)
		Abstract: We consider the stable category of kG-modules modulo projectives, where G is a finite group and k is a field of characteristic p> 0.
		The thick subcategory K generated by the trivial module k consists of all modules that can be pieced together by extension from k and from O
		In this lecture I will try to survey some of the recent results in the area and present some examples to illustrate the points.
	www.math.neu.edu /bhmn/carlson.html (151 words)

	SIAM: Non-Trivial Pursuits
		I buried myself in the study of all that was good and pure, and I emerged four years later with a doctorate and a serious case of burnout.
		He has used his mathematical expertise to write software for amateur astronomers, programming a computer to get the most information out of the intermittent stream of photons recorded by a charge-coupled device, or CCD.
		Meanwhile, mathematics has definitely taken a back seat; she says she needs "time to reevaluate and regroup." When she does get started on research again, she may move into a field with closer ties to her hobby, such as image processing.
	www.siam.org /news/news.php?id=279 (2532 words)

	Frequently Asked Questions in Mathematics (Site not responding. Last check: 2007-10-23)
		This is a compilation of Frequently Asked Questions (and their answers) about Mathematics.
		Topics range from trivia and the trivial to advanced subjects such as Wiles recent proof of Fermat's Last Theorem.
		There are several formats available for the table of contents, mostly because HTML does not handle math symbols well.
	www.cs.uwaterloo.ca /~alopez-o/math-faq/math-faq.html (364 words)

	math lessons - Riemann hypothesis
		In mathematics, the Riemann hypothesis, first formulated by Bernhard Riemann in 1859, is one of the most famous of all unsolved problems.
		It has certain so-called "trivial" zeros for s = −2, s = −4, s = −6,...
		Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire.
	www.mathdaily.com /lessons/RH (1391 words)

	Introduction to Meet-Continuous Topological Lattices (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		Preliminaries Let S be a finite 1-sorted structure.
		423 Journal of Formalized Mathematics (context) - Trybulec, subsets - 1989
		281 Journal of Formalized Mathematics (context) - Bancerek, nets et al.
	citeseer.ist.psu.edu /471069.html (534 words)

	sci.crypt: SF: Areas of confusion, infinity
		I've been looking at that question as I want to know the actual answer,
		So they just pick an area where this work would be dramatic, and say
		However, the theorem is enough to explain the link.
	www.derkeiler.com /Newsgroups/sci.crypt/2005-04/0882.html (1356 words)

	[No title]
		> In mathematics there has to be a reason for a theorem to make a choice.
		There, I think what you mean is, "The people who know mathematics try to
		Your question is, as usual, so vague as to be unanswerable.
	mathforum.org /kb/plaintext.jspa?messageID=3731926 (1704 words)

	DiscreteApplet Mathematics 137 (2004) 97 -- 107 www.el5-S[[][5-l-l][5-l Trivial two-stage group testing forcompl5] ... (Site not responding. Last check: 2007-10-23)
		DiscreteApplet Mathematics 137 (2004) 97 - 107 www.el5-S[[][5-l-l][5-l Trivial two-stage group testing forcompl5] using alng- disjunct matrices
		A pool is said to be positive if itcompl5-SO contains acomplWotherwise thepool is said to be negative.
		Incl;]O#Ngroup testing, each member of # is asingl-SON In this paper, we exhibit andanalO5 aprobabilINII trivial two-stage...
	citeseer.ist.psu.edu /711285.html (337 words)

	Mathematics
		My research at New Mexico State University focusses on the ring of invariants of locally trivial and of proper (C,+)-actions.
		The ultimate hope is to show (or disprove) that every proper (C,+)-action on C
		Technical Report 0202, Department of Mathematics, University of Nijmegen.
	www.cs.ru.nl /~petervr/math.html (378 words)

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