81. 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

Knot Theory Charles Livingston 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.

82. Math: Topology: Knot Theory: Page 2 Science Directory knot theory. knot theory. Spacetransportation.org - Science Directory - Last Update Fri Apr 23 2004. http://www.spacetransportation.org/Math/Topology/Knot_Theory/more2.html

Science Directory - Knot Theory Home Search Add a Site Modify a Site ... Links SEARCH ADVANCED SEARCH RANDOM LINK Find this: CUSTOM LINKS Yoursite Another Area Somewhere else Home ... Knot Theory : Page 2 Research Oriented Knot Theory - An overview of knot theory from Mathworld Knot Theory - Covers techniques of distinguishing knots, types, applications, and Conway notations. Includes illustrations. Knot Theory Group University of Liverpool - Links to preprints and to programs written in pascal for doing knot calculations. Knot Theory Invariants: The HOMFLY Polynomial - A brief article on the HOMFLY polynomial and how it is calculated. Knot Theory Online - This site is designed for mathematics students at the high school and college levels as an introduction to an area of mathematics seldom explored in the typical math classroom - the Theory of Knots. Knots on the Web (Peter Suber) - The most comprehensive collection of knotting resources on the web. Sections on knot tying, mathematical knot theory, knot art, and knot books. Knotscape - By Jim Hoste and Morwen Thistlethwaite. Provides convenient access to tables of knots. Linux, Solaris.

83. History Of Knot Theory theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson. Theory. History of knot theory. http://www.spacetransportation.org/Detailed/75002.html

Biographies of early knot theorists. Many early papers on knot theory (in pdf format) including papers by Tait, Kirkman, Little and Thomson. Home Math Topology Knot Theory : History of Knot Theory 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. Visit this link Spacetransportation.org - Science Directory - Last Update: Sun May 23 2004

84. What Is Knot Theory ? - Technology Services Physics Help and Math Help Physics Forums Physics General Physics What is knot theory ? View Thread What is knot theory ? What is knot theory ? http://www.physicsforums.com/archive/t-15729

Physics Help and Math Help - Physics Forums Physics General Physics View Thread : What is knot theory ? What is knot theory ? KLscilevothma Hi, I'll attend a lecture around 14 hours later addressed by a Nobel laureate and here's the brief description of the lecture. "Starting from a Parlor Game, I shall show how a deep mathematical problem can be formulated in an elementary way. The steps are understandable to high school students. Applications to knot theory, word problems and to statistical mechanics are indicated." Part of the students attending the lecture will be high school students like me. I want to do a little bit preparation before attending the lecture, so I would like to know what knot theory is. Also what is a Parlor Game? Can anyone please provide me with some elementary information about these or just give me some links with simple descriptions? Thanks. Register Now! Free! Talk Science! HallsofIvy Well first, it doesn't have anything to do with general physics! This might have been better in the "mathematics" section. "Knot theory" is, in its simplest sense, just what it says: imagine tying a rope up in some complicated knot: Is it possible to tell whether that knot is or is not the same as another knot which was tied in a different way? In particular, there are a variety of "knots" which look very complicated but such that, if you pull in a certain way, they collapse into nothing (magicians love those!). All such knots are essentially the same as no knot at all. Is there any way to tell that two knots are the same?

85. Pergunte A Um Físico - Respostas Translate this page Pergunta de Alexandre Tavares Baraviera, Rio de Janeiro, mestre em fisica, aluno de doutorado. Qual a importancia da teoria de nos (knot theory) para a fisica? http://www.if.usp.br/fisico/respostas/4.html

Pergunta de Alexandre Tavares Baraviera, Rio de Janeiro, mestre em fisica, aluno de doutorado Qual a importancia da teoria de nos (knot theory) para a fisica? Ela funciona apenas como uma boa inspiracao para novas ideias matematicas ou de fato tem aplicacoes em modelos mais realistas? Resposta de Daniel Doro Ferrante, estudante de pos-graduacao do IFUSP Caro Alexandre, A Teoria dos Nós tem aplicações sim em física (e aplicações até importantes!), mas eu duvido que o exemplo que eu vou citar seja realista o suficiente para que, por exemplo, um leigo entendesse. A principal aplicação da KT (Knot Theory) em física é na Gravitação Quântica como proposta por Abhay Ashtekar (dê uma olhadinha em: www.phys.psu.edu/GRAVITY/gravity.html ). Desta forma, fica um pouco mais fácil de se resolver alguns problemas técnicos da teoria, como a Renormalização, por exemplo. Quanto a funcionar como inspiração para novos modelos matemáticos, isso já acontece há algum tempo; há aplicações de KT até em modelos de Transição de Fase em Mecânica Estatística!

86. Knot Theory With KnotPlot knot theory with KnotPlot. Equilateral Stick Numbers. This research is in collaboration with Eric Rawdon of the Department of Mathematics http://www.colab.sfu.ca/KnotPlot/ktheory.html

Knot Theory with KnotPlot Equilateral Stick Numbers 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.

87. Página De Matías Graña. ps.gz. Quandle knot invariants are Quantum knot invariants, J. knot theory Ramifications 11 5, (2002), 673681. ps.gz. From racks to pointed Hopf algebras. http://mate.dm.uba.ar/~matiasg/

Universidad de Buenos Aires Pab I - Ciudad Universitaria (1428) Buenos Aires - ARGENTINA TE: (54)(11) 4576-3390 / 6, Int. 914 FAX: (54)(11) 4576-3335 e-Mail / e-Mail CV / Vita (in spanish) cv.html Finite dimensional Nichols algebras of non-diagonal group type ZOO Punteros / Links N. Andruskiewitsch Fotos/Pictures ps pdf Braided Hopf algebras over non-abelian groups . (Con N. Andruskiewitsch). dvi ps.gz Pointed Hopf algebras of dimension Comm.Alg. dvi ps.gz On pointed Hopf algebras of dimension p Glasgow Math. J. dvi ps.gz A freeness theorem for Nichols algebras J. Algebra dvi ps.gz On Nichols algebras of low dimension New Trends in Hopf Algebra Theory, Contemporary Mathematics (AMS) dvi ps.gz Quandle knot invariants are Quantum knot invariants J. Knot Theory Ramifications ps.gz From racks to pointed Hopf algebras . (con N. Andruskiewitsch). To appear in Adv. Math. ps.gz On rack cohomology . (con P. Etingof). To appear in J. Pure Appl. Algebra dvi ps.gz Indecomposable racks of order p To appear in Beitrege zur Algebra und Geometrie dvi ps.gz

88. Knot Theory (M24) knot theory (M24). WBR Lickorish The course knot theory and 4dimensional space Knot concordance, slice knots, examples. Knot signatures http://www.maths.cam.ac.uk/CASM/courses/descriptions/node22.html

Next: Spectral Geometry (L24) Up: Geometry and Topology Previous: Algebraic Topology (M24) Knot Theory (M24) W.B.R. Lickorish The course is an introduction to the theory of classical knots and links from the viewpoints of Combinatorics and Algebraic Topology. A very basic knowledge of the fundamental group, of homology theory and of covering spaces will be needed. Introduction Definition of knots and links, notations and examples - alternating knots, 2-bridge knots, pretzel knots, satellite knots. Orientations and reflections, knot addition and prime knots. Reidemeister moves and linking numbers. The Jones polynomial Definition of the Jones polynomial of a link by means of the Kauffman bracket, proof of invariance. The Jones polynomial of sums of knots and of disjoint unions. Invariance under mutation. The solution to the Tait conjecture about alternating knots. The Alexander polynomial The Alexander module as the homology of the infinite cyclic cover of a link complement, the -th Alexander polynomial. The Seifert form and Seifert matrix methods of calculation. The group of a knot. The free differential calculus and the Alexander polynomial of a torus knot. Skein invariants The skein identities for the Jones and Conway polynomials. The combinatorial construction of the HOMFLY and Kauffman polynomial invariants and some of their properties. The basic idea of a Vassiliev invariant.

89. 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.worldscientific.com.sg/books/mathematics/4542.html

Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Keyword Author Concept ISBN Series New Titles Editor's Choice Bestsellers Book Series ... Series on Knots and Everything - Vol. 26 FUNCTORIAL KNOT THEORY Categories of Tangles, Coherence, Categorical Deformations, and Topological Invariants by David N Yetter (Kansas State University) 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. Contents: Knots and Categories: Monoidal Categories, Functors and Natural Transformations

90. Von Neumann Algebras, Knot Theory, And Quantum Field Theory von Neumann algebras, knot theory, and quantum field theory. Audience knot theory and the Jonespolynomial. Algebraic quantum field theory. http://remote.science.uva.nl/~npl/vna.html

von Neumann algebras, knot theory, and quantum field theory Audience: 4th year mathematics students, theoretical physics students interested in mathematical physics, PhD students in analysis, mathematical physics, or quantum field theory, staff Prerequisites: Real analysis (Elementary functional analysis and Hilbert space theory, Integration theory). Dates: Tuesdays and Thursdays, 3d trimester (1999); April 6,8,13,20,22,27, May 18,20,25,27, June 1,3,8,10,15,17,22,24 (18 lectures) Place and time: Tuesdays: 11:15-13:00, TF.248 (seminar room of the Institute for Theoretical Physics, 2nd floor), Valckenierstraat 65, 1018 XE AMSTERDAM. Thursdays: 11:15-13:00, WZL.286 (seminar room of the van der Waals-Zeeman lab, , 2nd floor), Valckenierstraat 65, 1018 XE AMSTERDAM. Contents: Algebras of operator algebras on a Hilbert space, C*-algebras and von Neumann algebras. Classification of factors. Subfactors, Jones index. Knot theory and the Jones-polynomial. Algebraic quantum field theory. Superselection rules and subfactors. Literature: V.S. Sunder, An Invitation to von Neumann Algebras (Springer, 1987)

91. AMCA: Noncommutative Knot Theory By Tim Cochran Noncommutative knot theory by Tim Cochran Rice University. I will survey some of the recent work of myself and others in applying http://at.yorku.ca/c/a/m/n/10.htm

Atlas Mathematical Conference Abstracts Conferences Abstracts Organizers ... About AMCA Borders in 3-Dim Topology December 57, 2003 The Ohio State University, Department of Mathematics Columbus, OH, USA Organizers Thomas Kerler View Abstracts Conference Homepage Noncommutative Knot Theory by Tim Cochran Rice University I will survey some of the recent work of myself and others in applying techniques of noncommutative algebra and functional analysis to problems in low-dimensional topology (and knot theory in particular). Date received: November 25, 2003 Atlas Mathematical Conference Abstracts . Document # camn-10.

92. :: Ez2Find :: Knot Theory Guide knot theory, Guides, knot theory. ez2Find Home Directory Science Math Topology knot theory (35) Research Oriented (8). Related Categories http://ez2find.com/cgi-bin/directory/meta/search.pl/Science/Math/Topology/Knot_T

Guide : Knot Theory Global Metasearch Any Language English Afrikaans Arabic Bahasa Melayu Belarusian Bulgarian Catala Chinese Simplified Chinese Traditional Cymraeg Czech Dansk Deutsch Eesti Espanol Euskara Faroese Francais Frysk Galego Greek Hebrew Hrvatski Indonesia Islenska Italiano Japanese Korean Latvian Lietuviu Lingua Latina Magyar Netherlands Norsk Polska Portugues Romana Russian Shqip Slovensko Slovensky Srpski Suomi Svenska Thai Turkce Ukrainian Vietnamese Mode All Words Any Word Phrase Results Timeout Depth Adult Filter Add to Favorites Other Search Web News Newsgroups Images Guides Knot Theory ez2Find Home Directory Science Math ... Topology : Knot Theory Research Oriented Related Categories Reference: Knots Science: Math: Topology: Geometric Topology Web Sites Knots on the Web (Peter Suber) [Site Info] [Translate] [Open New Window] The most comprehensive collection of knotting resources on the web. Sections on knot tying, mathematical knot theory, knot art, and knot books. URL: http://www.earlham.edu/~peters/knotlink.htm BraidLink [Site Info] [Translate] [Open New Window] Braidlink is software for knot and braid theory computations. It performs both analytic and numerical manipulations of knots and braids. URL: http://www.knot-theory.org/

93. International Graduate Course Student Workshop For Knot Theory And Related Topic First announcement International Graduate Course Student Workshop for knot theory and Related Topics July 57, 2004 Osaka City University, Media Center 10F http http://math01.sci.osaka-cu.ac.jp/21COE/symposium/PhDStudentWorkshopJuly2004.html

First announcement International Graduate Course Student Workshop for Knot Theory and Related Topics July 5-7, 2004 Osaka City University, Media Center 10F http://www.media.osaka-cu.ac.jp/indexe.html The sponsor is the 21st century COE program "Constitution for wide-angle mathematical basis focused on knots". The aim of this workshop is to encourage graduate course students studying knot theory and related topics. All speakers of this workshop are graduate course students recommended by some international experts of this research area. This meeting is a pre-conference of the conference KOOK Seminar International for Knot Theory and Related Topics July 8-14, 2004 Awaji Yumebutai (International Conference Center in Awaji-Shima Island, Japan) http://www.yumebutai.org The information desk: Yuko Komori (the secretary) Osaka City University Advanced Mathematical Institute (email: y-komori@sci.osaka-cu.ac.jp, phone: 06-6605-2626)

94. [q-alg/9607022] Habilitationsschrift: Renormalization And Knot Theory Habilitationsschrift Renormalization and knot theory. Author Dirk Kreimer Comments 103 pages with 61 figures, uses LaTeX with epsf. Habilschrift. http://arxiv.org/abs/q-alg/9607022

Quantum Algebra and Topology, abstract q-alg/9607022 From: [ view email ] Date: Wed, 17 Jul 96 13:52 EST (275kb) Date (revised): Mon, 28 Jul 1997 18:40:37 +0100 Habilitationsschrift: Renormalization and Knot Theory Author: Dirk Kreimer Comments: 103 pages with 61 figures, uses LaTeX with epsf. Habilschrift. References updated, few minor Typos corrected Report-no: MZ-TH-96-18 Subj-class: Quantum Algebra Journal-ref: J.Knot Theor.Ramifications 6 (1997) 479-581 We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and report on recent results in support of this connection. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv q-alg find abs

95. Dror Bar-Natan Classes 2003-04 Math 1350F - Knot Theory Math 1350F knot theory. Fall Semester 2003. Agenda Use knot theory as an excuse to learning deep and beautiful mathematics. http://www.math.toronto.edu/~drorbn/classes/0304/KnotTheory/

Dror Bar-Natan Classes FEEDBACK Math 1350F - Knot Theory Fall Semester 2003 Agenda: Use knot theory as an excuse to learning deep and beautiful mathematics. Instructor: Dror Bar-Natan drorbn@math.toronto.edu , Sidney Smith 5016G, 416-946-5438. Office hours: Thursdays 12:30-1:30. Classes: Tuesdays 1-3 at Sidney Smith 5017A and Thursdays 2-3 at Sidney Smith 2128 Announcements September 8: Welcome back to UofT! Course Calendar Week of ... September 8 Handout: About This Class Handout: Some Non Obvious Examples Handout: Pathologies Class notes for Tuesday September 9, 2003 (non obvious examples, pathologies, Reidemeister's theorem, 3-colorings, the Kauffman bracket) Homework Assignment 1 Class notes for Thursday September 11, 2003 (R-II and R-III for the Kauffman bracket, R-I, the writhe, the Jones polynomial, a little programming) September 15 Handouts: The Rolfsen Knot Table Torus Knots The Knot 9-32 Class notes for Tuesday September 16, 2003 (The reverse and the mirror of a knot, sketch of the proof of Redemeister's theorem, linking numbers, connected sum, classification of surfaces and the genus of a knot) Homework Assignment 2 Class notes for Thursday September 18, 2003

96. ► Knot Theory [Science: Math: Topology] - WorldSearch.com Selection of sites about knot theory. 3, knot theory Covers techniques of distinguishing knots, types, applications, and Conway notations. http://www.worldsearch.com/science/math/topology/knot_theory/

Home Marketplace Link to us Advertisers ... Add to favorites! English Search : What: Sites Shopping DVD Posters and Photos Calendars Music Books Classical Music Video Magazines Computers Electronics Software Video Games Camera and Photo Kitchen and Housewares Home and Garden Tools and Hardware Toys and Games Apparel and Accessories Baby Car Parts and Accessories Auctions Computers: Hardware Software Virus Protection Financing: Credit Cards Loans Real Estate Internet: Access (ISP) Domain Registration Hosting Shopping: 2004 Calendars Autos Chocolates Computers ... Sports Today Sunday, June 6, 2004 Happy Birthday: Robert Englund Home Science Math ... Topology Knot Theory Web Directory Arts Business Computers Games ... Battle Ready (Book) The Fabric of the Cosmos: Space, Time, and the Texture of Reality (Book) A Short History of Nearly Everything (Book) Fast Food Nation: The Dark Side of the All-American Meal (Book) The Master Cleanser (Book) more... Marketplace Arts Automotive Books and Media Clothing and Apparel ... ZoneAlarm Security Suite - Complete Internet Security, Firewall, Antivirus, ID Protection and more! Add your site Featured Sites Buy Knot Theory Products We link to merchants which offer Knot Theory products for sale.

97. Knot Theory knot theory. knot theory is the study of knotted loops in three dimensional space (or more simply pieces of string with their ends stuck together). http://www.cis.upenn.edu/~mmcdouga/knot.html

Knot Theory 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. I used 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. Some Links about Knots and Links The Geometry Center at the University of Minnesota. Interactive geometry games, papers, software etc.. Knot Plot Home Page. Nice pictures of knots (some in VRML format). Knot Theory at Mega Math at Los Alamos. Lots of information but the links are somewhat tangled.

98. Knot Theory practical, including decorative knotting. It is not a guide to knot tying, nor a treatise on topology/knot theory. Rather, here is a http://biologybooks.net/Knot_Theory.html

Home Search High Volume Orders Links ... Laboratory Manuals Additional Subjects Agricultural Biotechnology Springer-Verlag Animal Biotechnology Baensch Aquarium Atlas: Photo Index 1-5 ... Cell Wall Deficient Bacteria Featured Books The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots In February 2001, scientists at the Department of Energy's Los Alamos National Laboratory announced that they had recorded a simple knot untying itself. Crafted from a chain of nickel-plated steel balls connected by thin metal rods, the three-crossing knot stretched, wiggled, and bent its way out of its predicamenta neat trick worthy of an inorganic Houdini, but more than that, a critical discovery in how granular and filamentary materials such as strands of DNA and polymers entangle and en... Written by Colin C. Adams Published by Owl Books (December 2000) ISBN 0805073809 Price $17.00 Written by J. C. Turner P. Van De Griend P. Van De Griend Published by World Scientific Pub Co (June 1996) ISBN 9810224699 Price $78.00

99. Really Bad Knot Theory Puns These terrible puns are the output of the knot theory Mini course I cotaught at the 2000 Hampshire College Summer Studies in Mathematics with Emily Peters http://cerebro.cs.xu.edu/~smbelcas/knotpuns.html

These terrible puns are the output of the Knot Theory Mini course I co-taught at the 2000 Hampshire College Summer Studies in Mathematics with Emily Peters (undergrad UC, now grad at Berkeley). Read aloud for maximal effect. All that Knot Theory for Naught! Tie him (Wing Mui) into a Wing Knot. We must define a knot, because if we do not, then we do not know what is a knot and what is not a knot. John "Still Chicken" Choi: "Called the 'trefoil' knot. Let's say it again, the 'trefoil' knot. ...Called the 'figure 8' knot... let's knot say it again..." Amanda Redlich: "Knots to you." "She's knots. We're knot able to..." Wing: "Knot Theory Chapter 4. Making a knot not a knot, or an unknot, or not... knot?" "2 types of knots? knot!" John Darius Mangual: "...in knot theory we may be knot sure or not sure." John Basias: "Our not rules for not polynomials." Emily: "Knotting my knitting; I mean not knotting; I mean infinknitting; I mean making bad puns." Wing: "Not cool? That is not true for all knot theorists not working on knotting knots but not slacking in their studies in the theory of knots not for naught." No, These Are Knot Puns

100. Knot Theory (190) Course, Fall 2003 knot theory (190) course, Fall 2003. MondayWednesday-Friday from 2.00-2.50 in room HSS 2321. knot theory. A closed loop of string in 3-space is called a knot. http://math.ucsd.edu/~justin/190.html

Knot theory (190) course, Fall 2003 Monday-Wednesday-Friday from 2.00-2.50 in room HSS 2321. Lecturer: Justin Roberts The traditional first course in topology deals with ``point-set topology'': the study of metric and topological spaces, continuity, compactness, connectedness, and other properties beginning with ``c''. This branch of the subject is really just a part of analysis, and while it is important for the foundations of the subject and can help you learn to write proofs properly, it can all seem very abstract and dry. Where are the doughnuts, coffee cups, pretzels, rubber sheets, knots and so on of popular topology? Traditionally, we teach the more geometric, visual side of the subject after teaching all the basic tools. This is not unreasonable, but it does take a long time to do properly, and is quite hard to motivate because it turns history on its head. After all, people have been using and thinking about knots for thousands of years, but the definition of a topological space is only a hundred years old. Fortunately it isn't necessary to work this way round. With a little care we can do quite a lot of knot theory without needing to talk about the foundational aspects of topology. I intend to start this way, and then try to develop a little bit of the abstract theory only if we really start to need it later on.

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