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Knot Theory
knot theory. Charles Livingston. Series Carus Mathematical Monographs.The author's book would be a good text for an undergraduate
http://www.maa.org/pubs/books/cam24.html

Extractions: Series: Carus Mathematical Monographs The author's book would be a good text for an undergraduate course in knot theory...The topics in the book are nicely tied together...The topics and the exercises together can provide an opportunity for many undergraduates to get a real taste of what present day mathematics is like. -Mathematical Reviews This monograph by Charles Livingston is a most accessible introductory survey of serious, mathematical twentieth century knot theory...At a time when non-trivial topics are required for so many student projects, no school library with a mathematics section should be without this book. It is a thoroughly well written, well thought out account of a subject of current mathematical research which anyone of a mathematical orientation can enjoy. -Mathematical Gazette Knot Theory is a concise, comprehensive, and well-written introduction to the definitions, theorems, techniques, and problems of knot theory...the expository sections of the text are quite well organized. The Mathematics Teacher Knot Theory , a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented.
Louis H. Kauffman
A topologist working in knot theory discusses the connection between knot theory and statistical mechanics. Sections on cybernetics and knots, Fourier knots and the author's research papers.
http://bilbo.math.uic.edu/~kauffman/

Extractions: Louis H. Kauffman I recently taught Mathematics 300, a course on writing mathematics. See Write Math! This is an exercise in the writing course and it is an introduction to the mathematics of G. Spencer-Brown and Charles Sanders Peirce. I am currently teaching Applied Linear Algebra, Math 310. See Vector Algebra. KNOTS A short course in knot theory from Reidemeister moves to state summations to Vassiliev Invariants and quantum fields. NOTES A FULL course in knot theory from Reidemeister moves to state summations to Vassiliev Invariants and quantum fields. These notes are a scan of handwritten notes to a course given in fall 1997 at Institute Henri Poincare in Paris, and a continuation of that course in the winter of 1998 at UIC. This pdf scan is 49 megabytes in size. Enjoy the download! Knot Tables Rolfsen's Knot Tables Rendered by Dror Bar-Natan.
Knot Theory
knot theory. Wake Forest University, June 2428. knot theory is a great topicfor exciting students about mathematics. It is visual and hands on.
http://www.maa.org/pfdev/prep/adams.html

Extractions: 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: 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.
Geometry And The Imagination
Has a small section on knot theory at an introductory level. Also has sections on orbifolds, polyhedra and topology.
http://math.dartmouth.edu/~doyle/docs/gi/gi/gi.html

Extractions: C. Dennis Thron has called attention to the following passage from The Adventure of the Priory School , by Sir Arthur Conan Doyle: `This track, as you perceive, was made by a rider who was going from the direction of the school.' `Or towards it?' `No, no, my dear Watson. The more deeply sunk impression is, of course, the hind wheel, upon which the weight rests. You perceive several places where it has passed across and obliterated the more shallow mark of the front one. It was undoubtedly heading away from the school.' Discuss this passage. Does Holmes know what he's talking about? Try to come up with a method for telling which way a bike has gone by looking at the track it has left. There are all kinds of possibilities here. Which methods do you honestly think will work, and under what conditions? For example, does your method only work if the bike has passed through a patch of wet cement? Would it work for tracks on the beach? Tracks on a patch of dry sidewalk between puddles? Tracks through short, dewy grass? Tracks along a thirty-foot length of brown package-wrapping paper, made by a bike whose tires have been carefully coated with mud, and which has been just ridden long enough before reaching the paper so that the tracks are not appreciably darker at one end of the paper than the other? Try to determine the direction of travel for the idealized bike tracks in Figure Figure 1: Which way did the bicycle go?
Search Results
Search for papers held at LANL with the word 'knot' in them.
http://arXiv.org/find/math/1/fr: knot/0/1/0/past,all/0/1
FUNCTORIAL KNOT THEORY
26 FUNCTORIAL knot theory Categories of Tangles, Coherence, Categorical Deformations,and Topological Invariants by David N Yetter (Kansas State University
http://www.wspc.com/books/mathematics/4542.html

Extractions: Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory. This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.
BRAID GROUP, KNOT THEORY AND STATISTICAL MECHANICS II
17 BRAID GROUP, knot theory AND STATISTICAL MECHANICS II edited by ML Ge (NankaiUniv.) CN Yang (SUNY, Stony Brook) It has been four years since the
http://www.wspc.com/books/physics/2138.html

Extractions: "It has been four years since the publication in 1989 of the previous volume bearing the same title as the present one. Enormous amounts of work have been done in the meantime. We hope the present volume will provide a summary of some of these works which are still progressing in several directions." from the foreword
Knot Theory And Cryptography Research Group
knot theory and Cryptography Research Group. Department of Mathematics Korea AdvancedInstitute of Science and Technology. Intro. What is knot theory?(Korean).
http://knot.kaist.ac.kr/

Extractions: Intro What is knot theory? (Korean) Home of Braid Cryptography Members Photo Collection Our Group in News (Korean) Seminar Schedule Address (members only) KCRG Archive (members only) KNOTS 2000, KAIST EMIS Mirror Site Korean traditional knots - Maedup The Home of Hangul TeX (Korean) Msquare and Orchard BBS (Korean) KAIST Cyber Education - Mathematics (Korean) BK21 - Topology on Manifolds Team (Korean) National Lab. - Cryptography Lab. Home
Knots And Links In Braid Notation
Listing of every knot of up to 11 crossings in braid notation. Useful for computer calculations in knot theory.
http://www.scoriton.demon.co.uk/knots.html

Extractions: a This document (this page with its associated tables) is intended as a resource for anyone interested in knots and links. Every knot up to 11 crossings and every link up to 10 crossings is listed here. The main feature of the listings is that every knot and link is shown with both its numeric notation and a braid notation. The numeric notation allows cross-reference with other works, while the braid notation is by far the easiest form to manipulate by computer. An n -crossing knot or link has a braid notation on at most 5/9.( n +2) strings [A] This section records the significant changes to this document, so that you can quickly tell if you need to download any information since your last visit. The most recent entries are at the top. 2002-01-06: Links added. This has expanded the tables to include all links up to 10 crossings, and expanded the list of errors in [C] to include those relating to links. 2000-10-19: My thesis [A] uploaded, and pointers to it added to this document. 2000-07-24: Braid index of 11(C123) is at least 4. No ? left anywhere in the tables. Removed 10(6VI) because it is the same as 10(5II), the Perko pair. Thanks to Richard Hadji and Hugh Morton.
A SHORT INTRODUCTION TO KNOT THEORY AND CRYPTOGRAPHY RESEARCH GROUP
A SHORT INTRODUCTION TO knot theory AND CRYPTOGRAPHY RESEARCH GROUP. Jae ChoonCha(jccha@knot.kaist.ac.kr) Applications of knot theory in cryptology.
http://knot.kaist.ac.kr/intro/

Extractions: Jae Choon Cha( jccha@knot.kaist.ac.kr In the language of experts, the mathematical theory of knots and links is the study of embeddings of one manifold in another. For example, An easy-to-imagine case is embeddings of circles into the Euclidean three space. Tying a string and joining the ends, one may obtain an embedding of a circle in the three dimensional space. By mathematicians, it is called a classical knot. This is generalized to higher dimensional knots and links. The theory of knots and links is a hot subject which is being rapidly developed, based on the remarkable progress of topology in the 20th century. Recently, surprising new relationships of knot theory with other fields than topology have been recovered and actively studied. It includes fields outside mathematics like quantum mechanics, statistical physics, chemistry, and the study of structures of DNA, as well as other branches of mathematics like representation theory, combinatorics, and cryptology. The research fields of our group cover all the subjects of the theory of knots and links, including:
Knot Theory
knot theory. knot theory is the study of knotted loops in three dimensionalspace (or more simply pieces of string with their ends stuck together).
http://www.cs.mcgill.ca/~mfmcd/knot.html

Extractions: Right Handed Trefoil Knot Knot theory is the study of knotted loops in three dimensional space (or more simply: pieces of string with their ends stuck together). I studied knot theory in summers of 95 and 96 with Prof. Prakash Panangaden . I've written software in Scheme that calculates some knot polynomials (HOMFLY, Kauffman, Jones, Alexander) and a presentation of the fundamental group. Currently I'm using Linktool for NeXT for entering links graphically and I'm looking for other software that displays edits or displays knot diagrams, especially something that will work with many platforms. If anyone else has written knot software please write me, as I'd like to compare various ways of representing knots for computation. Coming Soon: Home Phage
Knot Theory
knot theory. see also knot theory. Adams, Colin Conrad. 329358, 1970. Crowell, RHand Fox, RH Introduction to knot theory. New York Springer-Verlag, 1977. $?.
http://www.ericweisstein.com/encyclopedias/books/KnotTheory.html

Extractions: 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.
Knot Theory
TOPOLOGY OF 3MANIFOLDS AND knot theory. Mark Brittenham has builta page for Low-dimensional Topology. See the page of Rob Scharein
http://www.math.uiowa.edu/~wu/knot.html
Conference In Goemetric Topology
Special Sessions on knot theory and Quantum Topology. Special Sessions onknot theory and Quantum Topology I. August 12, 2002, 13301710pm.
http://www.math.uiowa.edu/~wu/gtc/knot.htm
Knot Theory -- From MathWorld
knot theory, The mathematical study of knots. knot theory considersquestions such as the following 1. Given a tangled loop of string
http://mathworld.wolfram.com/KnotTheory.html

Extractions: The mathematical study of knots . Knot theory considers questions such as the following: Although there has been almost explosive growth in the number of important results proved since the discovery of the Jones polynomial , there are still many "knotty" problems and conjectures whose answers remain unknown. Knot Link
DNA AND KNOT THEORY
DNA AND knot theory Question How can knot theory help us understand DNApacking? How can we estimate the rates at which enzymes unknot DNA?
http://www.tiem.utk.edu/~harrell/webmodules/DNAknot.html

Extractions: DNA AND KNOT THEORY Introduction: DNA is the genetic material of all cells, containing coded information about cellular molecules and processes. DNA consists of two polynucleotide strands twisted around each other in a double helix. The first step in cellular division is to replicate DNA so that copies can be distributed to daughter cells. Additionally, DNA is involved in transcribing proteins that direct cell growth and activities. However, DNA is tightly packed into genes and chromosomes. In order for replication or transcription to take place, DNA must first unpack itself so that it can interact with enzymes. DNA packing can be visualized as two very long strands that have been intertwined millions of times, tied into knots, and subjected to successive coiling. However, replication and transcription are much easier to accomplish if the DNA is neatly arranged rather than tangled up in knots. Enzymes are essential to unpacking DNA. Enzymes act to slice through individual knots and reconnect strands in a more orderly way. Importance: We can gain insight into the unknotting of DNA by using principles of topology. Topologists study the invariant properties of geometric objects, such as knots. Tightly packed DNA in the genes must quickly unknot itself in order for replication or transcription to occur. This is a topological problem.
Bigchalk: HomeworkCentral: Knot Theory (Advanced Topics)
Looking for the best facts and sites on knot theory? This Policy. HIGHSCHOOL BEYOND Mathematics Advanced Topics knot theory.
http://www.bigchalk.com/cgi-bin/WebObjects/WOPortal.woa/Homework/High_School/Mat
Bigchalk: HomeworkCentral: Knot Theory (Advanced Topics)
Looking for the best facts and sites on knot theory? This HomeworkCentral LinkingPolicy. Mathematics Advanced Topics knot theory.
http://www.bigchalk.com/cgi-bin/WebObjects/WOPortal.woa/Homework/Teacher/Math/Ma
Knot Theory With KnotPlot
knot theory with KnotPlot. Equilateral Stick Numbers. This research isin collaboration with Eric Rawdon of the Department of Mathematics
http://www.colab.sfu.ca/KnotPlot/ktheory.html

Extractions: This research is in collaboration with Eric Rawdon of the Department of Mathematics at Duquesne University in Pittsburgh. We've used KnotPlot to find equilateral polygonal representatives of all knots to 10 crossings with the fewest number of sides. This number of sides is known as the equilateral stick number. It can be compared to the stick number, which is the same quantity when the constraint of being equilateral is dropped. Surprisingly, for 242 of the 249 prime knots examined, all have an equilateral stick number equal to their stick numbers. Title: Upper Bounds for Equilateral Stick Numbers Authors: Eric J. Rawdon and Robert G. Scharein Abstract: We use algorithms in the software KnotPlot to compute upper bounds for the equilateral stick numbers of all prime knots through 10 crossings, i.e. the least number of equal length line segments it takes to construct a conformation of each knot type. We find seven knots for which we cannot construct an equilateral conformation with the same number of edges as a minimal non-equilateral conformation, notably the 8 knot.
Professor Lomonaco: Knot Theory References
knot theory References. Home Page. *** Under Construction *** Charilaos Aneziris'knot theory Primer; Cartoon based on three of Lomonaco's knot theory papers.
http://www.cs.umbc.edu/~lomonaco/knot-theory/Knot-Theory.html

Extractions: Home Page *** Under Construction *** Charilaos Aneziris' Knot Theory Primer Cartoon based on three of Lomonaco's knot theory papers. A lecture on knots and electrodynamics by Lomonaco Five Dimensional Knot Theory by Lomonaco ( Figures Viewable in HTML) Rob Scharein's Knot Zoo Foxy Knots , and Knot Table Snapshots from the video "Not Knot" The Geometry Center Archives Images The Journal of Knot Theory and Its Ramifications JKTR Knot Theoretic Thought for the day

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