41. Menasco's Home Page Menasco s knot theory Hot List. Check out the following knot theory web sites. KnotPlot A Circular History of knot theory. Knot Table courtesy of KnotPlot. http://www.math.buffalo.edu/~menasco/knot-theory.html

Menasco's Knot Theory Hot List Check out the following knot theory web sites. KnotPlot Knot Theory version 3.6 Snappea A Circular History of Knot Theory Knot Table courtesy of KnotPlot

42. Prof. W.B.R. Lickorish University of Cambridge. Topology, threedimensional manifolds, knot theory. http://www.dpmms.cam.ac.uk/site2002/People/lickorish_wbr.html

Department of Pure Mathematics and Mathematical Statistics DPMMS People Prof. W.B.R. Lickorish Prof. W.B.R. Lickorish Title: Professor of Geometric Topology College: Pembroke College Room: E1.18 Tel: +44 1223 764283 Research Interests: Topology, three-dimensional manifolds, knot theory Information provided by

43. Liverpool Pure Maths: Knot Theory knot theory Research Group. http://www.liv.ac.uk/~su14/knotgroup.html

Pure Mathematics Knot Theory Dept. Home Page Find someone? Pure home page Knot Theory at Liverpool Members of the Research Group Hugh Morton (e-mail: morton@liv.ac.uk Peter Cromwell (e-mail: spmr02@liv.ac.uk Victor Goryunov (e-mail: goryunov@liv.ac.uk Elisabetta Beltrami (e-mail: elisa@liv.ac.uk Research Students Nathan Ryder (e-mail: rydern@liv.ac.uk Previous Members Anna Aiston Yongju Bae (e-mail: ybae@knu.ac.kr Richard Hadji (e-mail: rhadji@liv.ac.uk Jonny Hill Sascha Lukac (e-mail: sl@wip.tu-berlin.de Pedro Manchon (e-mail: pmanchon@ma.upm.es Ian Nutt (e-mail: iann@wrox.com Marta Rampichini (e-mail: rampichini@mat.unimi.it Hayley Ryder Paul Strickland (e-mail: p.m.strickland@livjm.ac.uk Publications We maintain a list of our publications , which includes PostScript copies of some recent preprints. There are also some braid programs , mainly in Pascal, for calculating a number of knot invariants. Areas of Interest Hugh's interests include: Fibred knots and links.

44. Math Applications, Resources, Tutorials And More - Maple Application Center - Ma Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations. http://www.mapleapps.com/categories/mathematics/Knot theory/html/Knots.htm

Maple MapleNet Maple T.A. Toolboxes ... Contact Maple Application Center Research PowerTools Education PowerTools Browse Applications Advanced Search ... Submit Your Work Other Resources Maple 10 Online Training Maplesoft Books Maple Reporter More Information Contact Maplesoft Home Maple Application Center Browse by Category: Engineering Science Finance Operations Research ... Research PowerTools Application Search conduct an advanced search Keyword or phrase: Application type: Any Type Maple Worksheet Maplet Maple Animation Maple Graphic Maple Tutorial Maple Package Maple TA Question Bank Maple TA Course Module Maple TA Tutorial MapleNet Application MapleNet Tutorial Education PowerTool Research PowerTool Book White Paper Color Plate Products Industry Academic Support ... Login Language: English Deutsch Privacy Trademarks

45. String Figures And Knot Theory: Part I String Figure Mathematics (or Trivial knot theory) theorems and examples. http://website.lineone.net/~m.p/sf/sfmaths1.html

String Figures and Knot Theory - mathematics of the unknot under tension by Martin Probert First posted February 2001. Last revised December 2002. Abstract Many ethnographical string figures have come down to us only in the form of an ambiguous photograph in which, at the crossings, it is impossible to determine by eye which string lies over which. A knowledge of the set of all look-alikes ('similar-looking string figures') is a considerable aid in attempting to reconstruct such a figure. Part I shows how the set of all look-alikes may be determined mathematically : certain subsets of string contacts are labelled, the figure is then projected onto two dimensions, and finally the techniques of KNOT THEORY can be applied to identify the look-alikes. Part II contains examples illustrating the results. Part III shows how members of the set of look-alikes may be obtained manipulatively : a process of 'unravelling by motifs' is introduced which transforms one look-alike into another. Part IV contains an analysis of a number of string figures. Part V contains several conjectures concerning the unravelling process on the set of all look-alikes.

46. Links To Low-dimensional Topology: Knot Theory The page of the knot theory Group at the Univ. of Liverpool. Picture of a link An introduction to knot theory which seems to be aimed at teachers of http://www.math.unl.edu/~mbritten/ldt/knots.html

General Conferences Pages of Links 3-manifolds ... Home pages Knot Theory Joe Christy has put together www.computop.org , to serve as a source for the computational 3-dimensional topology community. The site includes links to downloadable software, and a set of mailing lists. The page of the Knot Theory Group at the Univ. of Liverpool. An introduction to knot theory which seems to be aimed at teachers of mathematics can be found at Los Alamos National Laboratory There is also another knot theory page at the University of British Columbia. Another page , developed from a course for liberal arts students, is at York Univ. A discussion, and several lists, concerning the classification of knots, may be found in Charilaos Aneziris' home page. This table of knots up to nine crossings came from Sean Collom 's home page at Oxford. A collection of pages on Mathematics and Knots at the University of Wales. A huge page of links to pages on knots and knot theory of all kinds. An on knot theory appears in the November 1997 issue of American Scientist A page at the Univ. of Liverpool for accessing preprints on knot theory.

47. Knot Theory - Wikipedia, The Free Encyclopedia knot theory is a branch of topology that was inspired by observations, knot theory concerns itself with abstract properties of theoretical knots — the http://en.wikipedia.org/wiki/Knot_theory

Knot theory From Wikipedia, the free encyclopedia. Trefoil knot, the simplest non-trivial knot. Knot theory is a branch of topology that was inspired by observations, as the name suggests, of knots . But progress in the field no longer depends on experiments with twine. Knot theory concerns itself with abstract properties of theoretical knots — the spatial arrangements that in principle could be assumed by a loop of string. When mathematical topologists consider knots and entanglements, they usually imagine a knot by also imagining the space around it. If neither changes, then the knot will persist. In mathematical jargon , knots are embeddings of the closed circle in three-dimensional space. An ordinary knot is converted to a mathematical knot by splicing its ends together. The topological theory of knots asks whether two such knots can be rearranged to match, without opening the splice. The question of untying an ordinary knot has to do with unwedging tangles of rope pulled tight. A knot can be untied in the topological theory of knots if and only if it is equivalent to the unknot , a circle in 3-space.

48. List Of Knot Theory Topics - Wikipedia, The Free Encyclopedia This list contains articles related to the mathematical theory of knots, links, Alternating knot Borromean rings Braid theory Braid group http://en.wikipedia.org/wiki/List_of_knot_theory_topics

List of knot theory topics From Wikipedia, the free encyclopedia. This list contains articles related to the mathematical theory of knots, links, and braids At this time it is far from complete. Alternating knot Borromean rings Braid theory Braid group ... Whitehead link Retrieved from " http://en.wikipedia.org/wiki/List_of_knot_theory_topics Categories Mathematical lists Views Article Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 11:24, 12 August 2005. All text is available under the terms of the GNU Free Documentation License (see for details). About Wikipedia

49. Knot Theory Invariants: The HOMFLY Polynomial A brief article on the HOMFLY polynomial and how it is calculated. http://library.thinkquest.org/12295/data/Invariants/Articles/HOMFLY.html

The HOMFLY Polynomial Historical Background The publication of the Jones Polynomial excited the mathematical community to the point that new polynomial invariants were being created at a stupendous rate. One of the objectives of the time was to find a polynomial that generalized both the Alexander and Jones polynomial. The Oriented Polynomial, or HOMFLY Polynomial was a successful solution, published by several groups of mathematicians simultaneously. The paper was published under the names of H oste, O cneanu, M illett, F reyd, L ickorish, and Y etter. The HOMFLY Polynomial uses a skein relation, like the Jones Polynomial, but the new polynomial uses two variables, unlike the Alexander and Jones Polynomials. Setting Up The HOMFLY Polynomial is derived from an oriented knot diagram like the one below. OpenImage("Oriented_Trefoil"); Also, the HOMFLY Polynomial is calculated using a skein relation like the Jones polynomial. This relation is written as: HP1: P(L) is an isotopy invariant HP2: P(U) = 1 ) + l with the same crossing types as the Jones polynomial. OpenImage("../Jones");

50. History Of Knot Theory Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson. http://www.maths.ed.ac.uk/~aar/knots/index.htm

HISTORY OF KNOT THEORY This home page is devoted to the history of knot theory, and is maintained by Jozef Przytycki and Andrew Ranicki. Our e-mail addresses are a.ranicki@edinburgh.ac.uk and przytyck@math.gwu.edu Please email to either of us any suggestions of additional material. BIOGRAPHIES OF EARLY KNOT THEORISTS Links to biographical entries in St. Andrews Mathematics History Archive M.Dehn P.Heegaard T.P.Kirkman J.B.Listing ... W.Wirtinger BIBLIOGRAPHY OF P.G.TAIT Provisional Bibliography prepared by Chris Pritchard, July, 2001 EARLY PAPERS ON KNOT THEORY A.Cayley, On a problem of arrangements, Proc. Royal Soc. Edinburgh, Vol. 9, 98 (1876-7), 338-342 Crum Brown, On a case of interlacing surfaces, Proc. Royal Soc. Edinburgh, Vol. 13, 121 (1885-6), 382-386 M.G.Haseman On knots, with a census of the amphicheirals with twelve crossings Trans. Roy. Soc. Edinburgh, 52 (1917-8), 235-255 also Ph.D thesis, Bryn Mawr College, 1918 M.G.Haseman Amphicheiral knots Trans. Roy. Soc. Edinburgh 52 (1919-20), 597-602. T.P.Kirkman

51. The Knot Theory MA3F2 Page Includes examples, solutions, knot tables, pretty pictures. Course material includes colouring, Alexander and Jones polynomials, tangles and braids. http://www.maths.warwick.ac.uk/~bjs/MA3F2-page.html

The Knot Theory MA3F2 page Course material Prerequisites Little more than linear algebra plus an ability to visualise objects in 3-dimensions. Some knowledge of groups given by generators and relations, and some basic topology would be helpful. The lectures and mind map that follow (from 2004) will be updated as we go through 2005. Mind map Course structure Lectures Writhe and linking numbers, Reidemeister moves and colouring, Colouring, Splittable links and chess boarding, Quadrilateral decomposition, Application of Cramer's rule, The determinant of a link, The colouring group, The number of colourings, Mirrors and codes, The Alexander polynomial, Knot sums, Bridge number and plats, Daisy chains and braids, Braids and Seifert circles, Alexander's theorem: links to braids, Seifert circles and trees, The bracket polynomial, The Jones polynomial, The skein relations, Alternating links, Span(V) = number of crossings, Tangles, Rational tangles and continued fractions, Tangled DNA, Genus and knot sum, Genus of a numerator

52. MA3F2 Knot Theory Content There has been an explosion of interest in knot theory in the last ten years. knot theory Washington, DC Math. Assoc. Amer., 1993. 240 p. http://www.maths.warwick.ac.uk/undergrad/pydc/pink/pink-MA3F2.html

Search University Contact Us A-Z Index Overview (White) ... webadmin@maths Pink (Year 3) PYDC 2005-2006 Term 2 Knot Theory 15 CATS Status List A Prerequisites MA106 Linear Algebra , MA130 From Geometry to Groups. MA242 Algebra I and MA245 Algebra II would also be useful, as would MA3F1 Introduction to Topology Commitment : 30 lectures Content : There has been an explosion of interest in knot theory in the last ten years. Surprising connections with quantum physics, statistical mechanics and the action of enzymes on DNA have emerged. A knot may be regarded as a continuous loop of (thin rubber) string. There are two fundamental problems: Is the loop really knotted? When is a loop got from another by continuous deformation? The problem is tackled by computing invariants. If for instance we have a computable way to assign invariant numbers to knots then two knots with different numbers can not be equivalent. Another approach is to look at the topology of the complement of the knot. Can we find a surface with the knot as boundary? What properties does it have? Aims : To introduce a variety of ways of representing knots and explore the value and novelty of different approaches.

53. Knot Theory knot theory. The use of knots goes back to prehistory, but the mathematical study of knots goes back This is listed in a bibilography of knot theory. http://grail.cba.csuohio.edu/~somos/knots.html

Knot Theory The use of knots goes back to pre-history, but the mathematical study of knots goes back only to the 19th century. Some of the early investigators were Gauss, Listing, Kirkman, Tait, and Little. Due to connections with applied fields like physics and biology there is increased research today. For examples look at the Titles in Series on Knots and Everything edited by Louis H. Kauffman . There are books which explain the topic for a more popular audience. One favorite is The Knot Book by Colin Adams. This is listed in a bibilography of knot theory . Now I prefer Knots: Mathematics With A Twist by Alexei Sossinsky (translation published 2002) which is more elementary and interesting. The story behind Making a Mathematical Exhbition by Ronald Brown and Tim Porter describes some of the issues involved in presenting knot theory. There are web sites which you can visit to find out more. You can start with the Mega-Math section on knots. Then switch to the KnotPlot site for great color graphics. A less ambitious site is Geometry and the Imagination section on knot notation.

54. Knot Theory A very short introduction into knot theory. In the knot theory until 1984 the main tool to tell the knots apart was the Alexander polynomials so named http://www.cut-the-knot.org/do_you_know/knots.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Knots... Every one knows from experience how to create a knot. We do this all the time, often unwittingly. Knots whose ends were glued together and their classification form the subject of a branch of Topology known as the Knot Theory. On the left there is a picture of the Left Trefoil knot. On the right there is the Right Trefoil knot. It's impossible to continuously (i.e. stretching and twisting but without causing damage to either of them) deform one into another. However, it must be noted that the two knots are topologically equivalent in the sense that there exists a topological transformation that maps one into another. The knots are mirror reflections of each other. In the real world, it can be argued that mirror reflections are only mental images whose existence is entirely different from that of the objects whose reflections they are. In Mathematics, reflections are as real as the objects themselves. Mathematically, reflections are topological transformations that could not be carried out on the real world objects. But

55. MATHnetBASE: Mathematics Online knot theory. Vassily Manturov. Read it Online! Buy it Today! Since discovery of the Jones polynomial, knot theory has enjoyed a virtual explosion of http://www.mathnetbase.com/ejournals/books/book_summary/summary.asp?id=1332

56. The KnotPlot Site Has a large number of beautiful graphics of knots created with KnotPlot. Contains an introductory section on mathematical knot theory. KnotPlot software for various platfroms can be downloaded. http://www.cs.ubc.ca/labs/imager/contributions/scharein/KnotPlot.html

The KnotPlot Site Welcome to the KnotPlot Site! Here you will find a collection of knots and links, viewed from a (mostly) mathematical perspective. Nearly all of the images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions. You can download KnotPlot and try it on your computer (see the link below), but first you may want to look at some of the images in the picture gallery. Also, have a browse through the Guestbook or sign it yourself Knot Pictures Check out the mathematical knots M ) page as well to see more knot pictures. Or try some of the following examples to see some knots in a different light. The pages marked with have been updated or created as of 11 Feb 2003. Those marked with an M have at least one MPEG animation. Various Collections The KnotServer (experimental, still not too useful), : 3D interactive viewer (which can save 3D models). Knots as radiating tubes M More knots as radiating tubes Decorative knots: on white on black goth Fancy Knots and Links,

57. Knot Theory And Cryptography Research Group knot theory and Cryptography Research Group. Department of Mathematics Korea Advanced Institute of Science and Technology http://knot.kaist.ac.kr/

Knot Theory and Cryptography Research Group Department of Mathematics Korea Advanced Institute of Science and Technology About Our Group Intro What is knot theory? (Korean) Home of Braid Cryptography Members Photo Collection Our Group in News (Korean) Seminar Schedule Topology Seminar 2005 Spring 2005 Fall Address (members only) KCRG Archive (members only) Sites Run or Supported By Our Group East Asian School of Knots and Related Topics 1st (Feb,2004) 2nd (Aug,2005) KAIST Geometric Topology Fair 1st (Aug,2004) 2nd (Feb,2005) 3rd (June, 2005) KNOTS 2000, KAIST ... Korean traditional knots(Korean Maedup) (Korean) The Home of Hangul TeX in the internet (Korean) Mathematical Problem Solving Group Orchard BBS (Korean) KAIST Cyber Remote Education - Mathematics (Korean) Topology Research Group supported by KRF Last modified: April 20, 2005

58. Mathematics And Knots High school level introduction to knot theory. Covers colourings, connected sums, torus knots, prime knots and applications of knot theory. http://www.bangor.ac.uk/cpm/exhib/

Mathematics and Knots An Exhibition Presented by the Division of Mathematics, School of Informatics, University of Wales, Bangor Aims Table of Knots Borrowing the Exhibition Acknowledgements ... Credits Basic Knots Same Knots Sorting out the bowline Crossovers Unknotting Bridge Number Colouring Mirror Images Arithmetic Prime Knots DNA DISCUSSION : Analogy Classification Invariants History of Knots

59. Knot Theory knot theory is a great topic for exciting students about mathematics. Participants will be able to do research in knot theory. http://www.maa.org/prep/adams.html

Search MAA Online MAA Home Knot Theory Wake Forest University, June 24-28 Organized and Presented by: Colin Adams, Williams College Knot theory is a great topic for exciting students about mathematics. It is visual and hands on. Students can begin working on problems the first day with their shoelaces. Knot theory is also an incredibly active field. There is a tremendous amount of work going on currently, and one can easily state open problems. It also has important applications to chemistry, biochemistry and physics. This workshop is aimed at college and university teachers who are interested in knowing more about knot theory. There is no assumption of previous background in the field, however a familiarity with basic topology will help. The goals of the workshop are as follows: 1. Participants will be able to teach an undergraduate course in knot theory. 2. Participants will be able to do research in knot theory. 3. Participants will be able to direct student research in knot theory. Each day will be divided into a morning session when we learn about specific topics in knot theory and an afternoon session, when we conjecture wildly, throw around ideas, and do original research. Information about the workshop presenter: Colin Adams is the Francis C. Oakley Third Century Professor of Mathematics at Williams College. He wrote "The Knot Book: an Elementary Intorduction to the Mathematical Theory of Knots" and has taught an undergraduate course on knot theory many times. He has published over 30 articles on knot theory and related subjects. He has directed over 40 undergraduate students on research in knot theory and co-authored papers with a total of 33 different undergraduates. Adams received the Haimo Distinguished Teaching Award of the MAA in 1998, was a Polya Lecturer for the MAA 1998-2000, and is currently a Sigma Xi Lecturer.

60. Using Topology To Probe The Hidden Action Of Enzymes Describes how knot theory is used to understand the action of enzymes that affect DNA topolgy (in pdf format). http://www.ams.org/notices/199505/sumners.pdf

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