101. Knot Theory RAP knot theory RAP. When, Th 200350 (with a break). http://www.math.uiuc.edu/~brinkman/teaching/rap/

Knot Theory RAP When Th 2:00-3:50 (with a break) Where Altgeld Organizers Peter Brinkmann and Nadya Shirokova Email brinkman@math.uiuc.edu or nadya@math.uiuc.edu This RAP serves two purposes. First, we will discuss some of the basics of knot theory such as knot projections, types of knots, knot groups, etc., loosely based on some introductory texts (such as Adams, 'The Knot Book'; Crowell-Fox, 'Introduction to Knot Theory'; Burde-Zieschang, 'Knots'; Rolfsen, 'Knots and Links'; Kauffman, 'On Knots'). Second, the RAP will serve as a platform for talks about current research (such as Vassiliev invariants, geometric knot theory, and slalom knots). Archive: Fall 01 Spring 02 Peter Brinkmann $Date: 2002-06-03 01:33:18-05 $

102. Knot Theory RAP knot theory RAP. When, Th 200250. 09/06/2001, Peter Brinkmann, Introduction to knot theory. 09/13/2001, Peter Brinkmann, Introduction to knot theory (cont.). http://www.math.uiuc.edu/~brinkman/teaching/rap/fall01.html

Knot Theory RAP When Th 2:00-2:50 Where Altgeld Organizer Peter Brinkmann Office Altgeld Email brinkman@math.uiuc.edu This RAP serves two purposes. First, we will discuss some of the basics of knot theory such as knot projections, types of knots, knot groups, etc., loosely based on some introductory texts (such as Adams, 'The Knot Book'; Crowell-Fox, 'Introduction to Knot Theory'; Burde-Zieschang, 'Knots'; Rolfsen, 'Knots and Links'; Kauffman, 'On Knots'). Second, the RAP will serve as a platform for talks about current research (such as Vassiliev invariants, geometric knot theory, and slalom knots). Please let me know if you would like to give a talk. Date Speaker Title Organizational meeting Peter Brinkmann Introduction to knot theory Peter Brinkmann Introduction to knot theory (cont.) Nadya Shirokova Finite type knot invariants We will discuss the axiomatics for the invariants of finite type, introduced by V.Vassiliev. We will study their properties and show that classical invariants, like Alexander-Conway polynomial can be decomposed over invariants of finite type. Katharine Preedy Types of knots Nadya Shirokova Finite type knot invariants (cont.)

103. Sitebits | Knot Theory welcome to sitebits, knot theory. knot theory. Feb 15 2000 I am a mathematician. Once upon a time these words were guaranteed to bring http://www.sitebits.com/2000/2000-02-15.html

Knot Theory Knot Theory Feb 15 2000 I am a mathematician. Once upon a time these words were guaranteed to bring conversation to a shuddering halt, but no more. People's curiosity about maths (you'll have to humour my Britishisms) seems to have been sparked by something: perhaps by the press coverage of the proof of Fermat's Last Theorem; perhaps by the mushrooming culture of the information age; or maybe just by Jeff Goldblum and Matt Damon trying to convince us that maths was the new rock 'n roll (I'm not ready to give up the old one yet). So what is it that I do then? To answer the first common question: it has nothing to do with computers, statistics, cryptography or finance. I am a pure mathematician, which means that I spend most of my day sitting in a room with pen and paper and thinking. (Of course I do use a computer, but only for emailing, word processing and finding out the current cricket scores.) I study topology, which can be thought of as a qualitative version of geometry: topologists are interested not in distances or angles but in the overall shapes of things. The prime example is knot theory: everybody can understand that these two knotted strings are different, in the sense that without some kind of cutting and rejoining (this Gordian option not being allowed!) you can't turn one of them into the other. We care nothing about physical or quantitative aspects such as length, thickness, material composition, curvature and so on, but only about the different ways in which these loops are entangled in space. The starting point for the knot theorist, then, is to formulate this sentence as a precise mathematical assertion and to prove it. Although there was plenty of interest in knots before 1900 for example, the speculation by Maxwell, Tait and Kelvin that perhaps atomic, knotted loops of magnetic flux might explain the existence and behaviour of the chemical elements this was on the whole educated hand-waving, and it was not until the 20th century that any really rigorous framework was worked out.

104. Alexa Web Search - Subjects > Science > Math > Topology > Knot Theory knot theory Subjects Science Math Topology knot theory. Browse, Sites in knot theory (28). Research Oriented (8). Best Selling Products in knot theory. http://www.alexa.com/browse/categories?catid=26948

105. Knot Theory -- From Eric Weisstein's Encyclopedia Of Scientific Books knot theory. see also knot theory. Adams, Colin Conrad. 329358, 1970. Crowell, RH and Fox, RH Introduction to knot theory. New York Springer-Verlag, 1977. $?. http://www.ericweisstein.com/encyclopedias/books/KnotTheory.html

Knot Theory see also Knot Theory Adams, Colin Conrad. The Knot Book: An Elementary Introduction to Mathematical Theory of Knots. New York: W.H. Freeman, 1994. 306 p. $32.95. Aneziris, Charilaos N. The Mystery of Knots: Computer Programming for Knot Tabulation. Singapore: World Scientific, 1999. 396 p. $?. Artin, E. ``The Theory of Braids.''American Scientist 38, 112-119, 1950. Ashley, Clifford W. The Ashley Book of Knots. New York: Doubleday, 1993. 610 p. $62.50. Atiyah, Michael Francis. The Geometry and Physics of Knots. Cambridge, England: Cambridge University Press, 1990. Difficult to extract useful information from. $19.95. Belash, Constantine A. Braiding and Knotting. Birman, Joan S. Braids, Links, and Mapping Class Groups. Princeton, NJ: Princeton University Press, 1974. 228 p. $49.50. Budsworth, Geoffrey. The Knot Book. Burde, Gerhard and Zieschang, Heiner. Knots. Berlin: W. De Gruyter, 1985. $?. Conway, J.H. ``An Enumeration of Knots and Links.''In Leech, John (Ed.). Computational Problems in Abstract Algebra. Oxford, England: Pergamon Press, pp. 329-358, 1970.

106. Knot Theory And 3-Manifolds (Summer Graduate Program) Calendar. knot theory and 3Manifolds (Summer Graduate Program). July 7, 2004 to July 20, 2004 at the University of British Columbia, Vancouver http://www.msri.org/calendar/programs/ProgramInfo/125/show_program

Calendar Knot Theory and 3-Manifolds (Summer Graduate Program) July 7, 2004 to July 20, 2004 at the University of British Columbia, Vancouver Organized by: S. Boyer (UQAM), R. Fenn (Sussex), D. Rolfsen, Chair (UBC), D. Sjerve (UBC) Open only to graduate students nominated by MSRI's Academic Sponsors Co-sponsored by MSRI and the Pacific Institute for the Mathematical Sciences. The mathematical theory of knots has become one of the most active areas of mathematics in the last few decades. Two important reasons for this are that many fields of mathematics (and physics) converge in the study of knots, and secondly there are applications to the study of manifolds as well as fields such as stereochemistry and molecular biology. This course will begin with an introduction to the subject, covering classical subjects such as the knot group, Seifert surfaces, Dehn surgery, branched coverings, Alexander polynomial as well as more recent work such as knot polynomials, skein theory, etc. The second week will be devoted to more specialized subjects such as hyperbolic goemetry in knot theory

107. Divisibility Criteria A theory of divisibility with examples. Divisibility by 3, 7, 9, 11, 19. http://www.cut-the-knot.org/blue/divisibility.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Divisibility Criteria Divisibility criteria are ways of telling whether one number divides another without actually carrying the division through. Implicit in this definition is the assumption that the criteria in question affords a simpler way than the straight division to answer the question of divisibility. Divisibility criteria re constructed in terms of the digits that compose a given number. To fix the notation, A will be the number whose divisibility by another number d we are going to investigate on this page. In the decimal system, A = 10 n a n n-1 a n-1 a + a a n 0. We readily have several examples: Divisibility by 3 . Let s (A) = a n + a n-1 + ... + a . Then A is divisible by 3 iff s (A) is. Divisibility by 9 . With the same function s , A is divisible by 9 iff s (A) is. Divisibility by 11 . Let s (A) = a - a n a n . Then A is divisible by 11 iff s (A) is. They all follow from the two basic properties of the modulo arithmetic [A] d + [B] d = [A + B] d [A] d d d and the fact that 10 = 1 (mod 9) and 10 = -1 (mod 11), from which we successively get 10

108. Writhe -- From MathWorld search. Adams, C. C. The knot Book An Elementary Introduction to the Mathematical theory of knots. New York W. H. Freeman, pp. 152153 and 185, 1994. http://mathworld.wolfram.com/Writhe.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Topology Knot Theory Knot Invariants Writhe A knot property, also called the twist number, defined as the sum of crossings p of a link L where C L ) is the set of crossings of an oriented link The writhe of a minimal knot diagram is not a knot invariant , as exemplified by the Perko pair , which have differing writhes (Hoste et al. 1998). This is because while the writhe is invariant under Reidemeister moves If a knot K is amphichiral , then (Thistlethwaite). A formula for the writhe is given by where K is parameterized by for along the length of the knot by parameter s , and the frame associated with K is where is a small parameter, is a unit vector field normal to the curve at s , and the vector field is given by (Kaul 1999). Letting Lk be the linking number of the two components of a ribbon, Tw be the

109. Patrick Bangert Braidlink is software for knot and braid theory computations. It performs both analytic and numerical manipulations of knots and braids. http://www.knot-theory.org/

Patrick Bangert Patrick Bangert

110. The Khipu: String, And Knot, Theory Of Inca Writing String, and knot, theory of Inca Writing. by John Noble Wilford. This article appeared in the New York Times on August 12, 2003. Of http://www.ee.ryerson.ca:8080/~elf/abacus/inca-khipu.html

String, and Knot, Theory of Inca Writing by John Noble Wilford This article appeared in the New York Times on August 12, 2003. Of all the major Bronze Age civilizations, only the Inca of South America appeared to lack a written language, an exception embarrassing to anthropologists who habitually include writing as a defining attribute of a vibrant, complex culture deserving to be ranked a civilization. Inca Khipu: An Inca khipu, top, and a khipu at the American Museum of Natural History. The only possible Incan example of encoding and recording information could have been cryptic knotted strings, which are unlike anything that sailors or Eagle Scouts tie. The Inca left ample evidence of the other attributes: monumental architecture, technology, urbanization and political and social structures to mobilize people and resources. Mesopotamia, Egypt, China and the Maya of Mexico and Central America had all these and writing too. The only possible Incan example of encoding and recording information could have been cryptic knotted strings known as khipu. The knots are unlike anything sailors or Eagle Scouts tie. In the conventional view of scholars, most khipu (or quipu, in the Hispanic spelling) were arranged as knotted strings hanging from horizontal cords in such a way as to represent numbers for bookkeeping and census purposes. The khipu were presumably textile abacuses, hardly written documents.

111. Untangling The Mathematics Of Knots One of the most peculiar things which emerges as you study knots is how a category of objects as simple as a knot could be so rich in profound mathematical http://www.c3.lanl.gov/mega-math/workbk/knot/knot.html

Untangling the Mathematics of Knots Overview Knots have been studied extensively by mathematicians for the last hundred years. Recently the study of knots has proved to be of great interest to theoretical physicists and molecular biologists. One of the most peculiar things which emerges as you study knots is how a category of objects as simple as a knot could be so rich in profound mathematical connections. Here are a variety of activities for exploring knots made from pieces of rope. Students can make and verify observations about knots, classify them, combine them, and find ways to determine if two knots are alike. The activities outlined here can be combined to form a single lesson about mathematical knots, or a larger investigative unit that extends over a longer period of time. The sequence in which the activities are listed is roughly in order of increasing difficulty and challenge, but all of the earlier activities are not strict prerequisites for the later ones. Finding ways to make precise spoken or written statements about an inherently spatial and manipulative experience is a meaningful and interesting challenge for all students. Teachers can help students learn to do this by helping them develop classroom conventions for naming knots, parts of knots, groups of knots, or for labeling parts of knots to make them easier to talk about. Although presentations and discussions are appropriate as a whole-class activity when studying knots, most of these activities will work best when students work individually, in pairs and small groups. It is important for each stu dent to be able touch and twist the knots that they are thinking about.

112. Research Group On Topological Quantum Field Theory And Knots Research Group on Topological Quantum Field Theories in any dimension and their relation to topological invariants. Particular attention is given to BF theories and knots in any dimension. http://wwwteor.mi.infn.it/users/cotta/tqft.html

Research Group on Topological Quantum Field Theories and Knots Goals To study topological field theories in any dimension and their relation to topological invariants. Particular attention is given to BF theories. Topological invariants include 3-manifold invariants and invariants of ordinary links and knots and, at the higher dimensional level, the homology and cohomology of the spaces of imbedded and immersed loops and spheres. Participants Alberto Cattaneo Assistant Professor of Mathematics, University of Zurich, Switzerland asc@math.unizh.ch Paolo Cotta-Ramusino paolo.cotta@mi.infn.it Riccardo Longoni ... riccardo.longoni@mi.infn.it Maurizio Rinaldi rinaldi@univ.trieste.it Carlo Rossi PhD Student in Mathematics, University of Zurich, Switzerland carossi@math.unizh.ch Preprints and recent publications A. S. Cattaneo, Juerg Froehlich, Bill Pedrini Topological Field Theory Interpretation of String Topology [abs] [ps] math.GT/0202176 A. S. Cattaneo G. Felder, L. Tommasini Fedosov connections on jet bundles and deformation quantization [abs] [ps] math.QA/0111290

113. Differential Geometry The extension of the theory to higher dimensions leads to the study of nmanifolds, 1-manifolds being curves and 2 Some animations of curves, surfaces and knots http://www.ma.umist.ac.uk/kd/ma351/ma351.html

Next: Geometry, topology and homotopy Differential Geometry C.T.J. Dodson General description: Differential geometry begins with the study of curves and surfaces in three-dimensional Euclidean space. Using vector calculus and moving frames of reference on curves embedded in surfaces we can define quantities such as Gaussian curvature that allow us to distinguish among surfaces. The extension of the theory to higher dimensions leads to the study of n-manifolds, 1-manifolds being curves and 2-manifolds being surfaces. A distance structure was provided by Riemann and so we study Riemannian n-manifolds, their curvature and curves in them. We consider geodesic (literally, `divide the Earth') curves, which give extremal paths in n-manifolds, generalizing lines in the plane and great circles on a sphere. Some animations of curves, surfaces and knots Notes On Making Mathematical Notes For Your Course (PDF format). Course description: Tangent vectors, vector fields, differentiable maps; curves, Frenet frames; surfaces, shape operator, Gaussian and mean curvature; n-manifolds, metric, Riemann curvature and geodesics. See the online documents relating to this course: 351 Background Notes Curves Surfaces Manifolds ... Tutorial Problems 4 Mathematica Notebooks on curves and surfaces from 117To use, download and open in Mathematica

114. Athens Users Login Athens Users Login. EBSCOhost Support. User ID, Password, Minimum browser requirements Internet Explorer 5.0 and Netscape 4.7. Important http://search.epnet.com/direct.asp?db=aph&jid=8KL&scope=site

115. Page Personnelle : Christine Lescop Translate this page Christine Lescop . Chargée de recherches Institut Fourier, UMR 5582 du CNRS Université de Grenoble I BP 74, 38402 http://www-fourier.ujf-grenoble.fr/~lescop/

Christine Lescop Institut Fourier , UMR 5582 du CNRS Bureau 334 Fax : 04.76.51.44.78 E-mail : lescop@fourier.ujf-grenoble.fr lettre postscript lettre html source latex ... English homepage Recherche Mes principaux champs d'investigation sont la et la et dans le survol On the Casson invariant. et je vous conseille l'excellente page personnelle de Dror Bar-Natan programme survol introductif et dans la de Sylvain Poirier (et son introduction About the uniqueness and the denominators of the Kontsevich integral Notes de cours de DEA 2001 Quelques liens ... Ronan prise le mardi-gras 7 mars 2000.

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