Geometry.Net - Science: Topology

Probabilistic Combination Of Content And Links
It introduces a probabilistic model that integrates link topology (used to identify important pages), anchor text (used to augment the text of cited pages), and activation (spread to linked pages). Experiments are on MSN Directory. PDF format
http://research.microsoft.com/copyright/accept.asp?path=http://research.microsof
Newton's Apple: Teacher's Guides
What does mathematics have to do with mazes? What is the history behind mazes? Are there different kinds of mazes? What is topology? David solves a maze by applying the principles of mathematics.
http://www.tpt.org/newtons/11/mazes.html

Extractions: Try This Beware the Minotaur! This fearsome mythical creature, half man and half bull, lurked in the dark corners of the Cretan labyrinth, waiting to devour young people sent by King Minos. But Theseus conquered the Minotaur and, guided by a golden thread, emerged from the labyrinth a victor! Like the legend of the Minotaur, mazes and labyrinths have long fascinated us. Ancient civilizations left stories of enormous labyrinthian buildings with up to 3,000 rooms. Hedge mazes have decorated gardens for centuries, providing entertainment and secret meeting places. Psychologists use mazes to study how animals learn. What is the difference between a maze and a labyrinth? Actually, the two names are synonymous. However, maze is used more often, perhaps because of the popular hedge mazes. Labyrinthian describes something that has maze-like qualities-your thumbprint or a house with many rooms to wander through.
Easy Trace Group
Cartographic rasterto-vector conversion software with tools for topology creation, checking and editing.
http://www.easytrace.com/
What Is Topology?
What is topology? A short Basically, topology is the modern version ofgeometry, the study of all different sorts of spaces. The thing
http://www.math.wayne.edu/~rrb/topology.html

Extractions: Robert Bruner Basically, topology is the modern version of geometry, the study of all different sorts of spaces. The thing that distinguishes different kinds of geometry from each other (including topology here as a kind of geometry) is in the kinds of transformations that are allowed before you really consider something changed. (This point of view was first suggested by Felix Klein, a famous German mathematician of the late 1800 and early 1900's.) In ordinary Euclidean geometry, you can move things around and flip them over, but you can't stretch or bend them. This is called "congruence" in geometry class. Two things are congruent if you can lay one on top of the other in such a way that they exactly match. In projective geometry, invented during the Renaissance to understand perspective drawing, two things are considered the same if they are both views of the same object. For example, look at a plate on a table from directly above the table, and the plate looks round, like a circle. But walk away a few feet and look at it, and it looks much wider than long, like an ellipse, because of the angle you're at. The ellipse and circle are projectively equivalent. This is one reason it is hard to learn to draw. The eye and the mind work projectively. They look at this elliptical plate on the table, and think it's a circle, because they know what happens when you look at things at an angle like that. To learn to draw, you have to learn to draw an ellipse even though your mind is saying `circle', so you can draw what you really see, instead of `what you know it is'.
G C I 275 - La Esquina Del Movimiento
Coordinates in a unique topology, somewhere between Peru and the web. Links and comments on Peruvian politics, culture and current events.
http://www.gci275.com/log/

Extractions: posted 11:49 PM Washington Post Coca Trade Booming Again in Peru : "For the first time, the U.S. and Peruvian governments this year intend to pull up coca crops by force in the Apurimac and Upper Huallaga river valleys, unless peasants agree to eradicate their crops in return for financial assistance. Until now, most forced eradication has been confined to remote secondary producing regions safe from mass peasant mobilization. The Apurimac and Upper Huallaga, by contrast, are the two primary sources of Peruvian coca and historic redoubts of guerrilla insurgency." A new Post correspondent, Scott Wilson, gets to do his first coca-growing story same facts, but a different time frame.
Midwest Topology Seminar
A topology seminar which has run since the middle 1960's, meeting Fall, Winter and Spring of each Category Science Math topology EventsMidwest topology Seminar. Funding. Recently the NSF awarded $20K to support the Midwesttopology Seminar. This is to fund approximately 10 meetings at $2K each.
http://www.math.wayne.edu/~rrb/MTS/

Extractions: Midwest Topology Seminar The Midwest Topology Seminar is a topology seminar which has run since the middle 1960's, meeting Fall, Winter and Spring of each year. Traditionally, in each year, two of the meetings are in Chicago, and one is outside Chicago. (Updated 17 March 2003) The Midwest Topology Conference for the spring of 2003 will take place at the University of Illinois at Urbana-Champaign on Saturday April 26, 2003. Further information will be posted at http://www.math.uiuc.edu/~mando/midwest as well as here. The speakers for the conference are The National Science Foundation has made some funds available to the Midwest Topology Conference, particularly to support participation by junior mathematicians. If you wish to apply for support, please contact Matthew Ando as soon as possible. Upcoming meetings are: Recently the NSF awarded $20K to support the Midwest Topology Seminar. This is to fund approximately 10 meetings at $2K each. The money can be used to cover travel expenses for speakers and a number of participants: junior faculty and graduate students from outside the area as well as those within who need support.
Rfc2922 - Physical Topology MIB
Physical topology MIB. A. Bierman, K. Jones. September 2000.
http://www.faqs.org/rfcs/rfc2922.html

Extractions: Internet RFC/STD/FYI/BCP Archives Index Search What's New Comments ... Help Alternate Formats: rfc2922.txt rfc2922.txt.pdf ptopo@3com.com Subscription: majordomo@3com.com msg body: [un]subscribe ptopomib Andy Bierman Cisco Systems Inc. 170 West Tasman Drive San Jose, CA 95134 408-527-3711 abierman@cisco.com Kendall S. Jones Nortel Networks 4401 Great America Parkway Santa Clara, CA 95054 408-495-7356 kejones@nortelnetworks.com abierman@cisco.com Kendall S. Jones Nortel Networks 4401 Great America Parkway Santa Clara, CA USA 95054 Phone: +1 408-495-7356 EMail: kejones@nortelnetworks.com Index Search What's New ... Help Alternate Formats: rfc2922.txt rfc2922.txt.pdf Comments/Questions about this archive ? Send mail to rfc-admin@faqs.org
Oporto Meetings On Geometry, Topology And Physics
Formerly Meetings on Knot Theory and Physics held annually in Oporto, Portugal to bring together mathematicians and physicists interested in the interrelation between geometry, topology and physics.
http://www.math.ist.utl.pt/~jmourao/om/

Extractions: Oporto Meetings on Geometry, Topology and Physics Oporto Meetings on Geometry, Topology and Physics (formerly known as the Oporto Meetings on Knot Theory and Physics) take place in Oporto, Portugal, every year. The aim of the Oporto meetings is to bring together mathematicians and physicists interested in the inter-relation between geometry, topology and physics and to provide them with a pleasant and informal environment for scientific interchange. Main Page of TQFT Club Free Counter from Counterart
Tavve Software: Intelligent Network Management Software
Solutions for fault management, root cause analysis, event correlation, network topology mapbuilding and customization, performance reporting, troubleshooting, and distributed network management.
http://www.tavve.com
Links To Low-dimensional Topology: Personal Home Pages
Journals Home pages. Lowdimensional topology links home pages. Colin Adams,at Williams College Ian Agol, at UIC. Selman Akbulut, at Michigan State.
http://www.math.unl.edu/~mbritten/ldt/homepage.html
Rfc2328 - OSPF Version 2
OSPF is a linkstate routing protocol. It is designed to be run internal to a single Autonomous System. Each OSPF router maintains an identical database describing the Autonomous System's topology. From this database, a routing table is calculated by constructing a shortest-path tree.
http://www.faqs.org/rfcs/rfc2328.html
Number Patterns, Curves & Topology
Investigating Patterns, Number Patterns Fun with Curves topology. TOPIC LINKS.
http://www.camosun.bc.ca/~jbritton/jbfunpatt.htm

Extractions: Comment: A natural number is prime if it has exactly two positive divisors, 1 and itself. Eratosthenes of Cyrene (276-194 BC) conceived a method of identifying prime numbers by sieving them from the natural numbers. Web page uses the sieve to find all primes less than 50. Includes a link to a Sieve of Eratosthenes Applet which also begins with a size or upper boundary of 50. Eratosthenes' Sieve contains a similar applet preset to find all primes less than 200. Both applets require a JAVA-capable browser. Title: Prime Number List Comment: Once you have entered the lower bound and upper bound, this javascript applet will display all prime numbers within the selected range. Title: Prime Factorization Machine Comment: A positive integer (natural number) is either prime or a product of primes. This applet decomposes any positive integer less than 1,000,000 into its prime factors. The bigger the number, the longer it will take. Requires a JAVA-capable browser. Title: Comment: Includes a link to Mini-Lessons demonstrating how to find the Common Divisor Factor (GCF) or Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of two or more natural numbers using prime factorization. Features an interactive applet with detailed explanations and solutions.
HERMES - A Tool For Visualizing The Internet Topology
A tool for visualizing the Internet topology.
http://www.dia.uniroma3.it/~hermes/
55: Algebraic Topology
In Dave Rusin's Mathematical Atlas.Category Science Math topology Algebraic topologyAlgebraic topology is the study of algebraic objects attached to topological spaces;the algebraic invariants reflect some of the topological structure of the
http://www.math.niu.edu/~rusin/known-math/index/55-XX.html

Extractions: POINTERS: Texts Software Web links Selected topics here Algebraic topology is the study of algebraic objects attached to topological spaces; the algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fiber bundles and related spaces are included here, while complexes (CW-, simplicial-, ...) are treated in section 57. Finally, the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences; the machinery (mostly derived from homological algebra) is powerful if rather daunting. In all cases, the "naturality" of the construction implies that a map between spaces induces a map between the groups. Thus one can show that no maps of some sort can exist between two spaces (e.g. homeomorphisms) since no corresponding group homomorphisms can exists. That is, the groups and homomorphisms offer an algebraic "obstruction" to the existence of maps. Classic applications include the nonexistence of retractions of disks to their boundary and, as a consequence, the Brouwer Fixed-Point Theorem. (Obstruction theory is, more generally, the creation of algebraic invariants whose vanishing is necessary for the existence of certain topological maps. For example a function defined on a subspace Y of a space X defines an element of a homology group; that element is zero iff the function may be extended to all of X.)
Site Moved To Http://www.math.toronto.edu/~drorbn/
Java applets exploring configuration spaces.Category Science Math topologySite Moved! This web page moved along with its administrator to Toronto.Your browser should take you there automatically in 10 seconds.
http://www.ma.huji.ac.il/~drorbn/People/Eldar/thesis/

Extractions: This web page moved along with its administrator to Toronto. Your browser should take you there automatically in 10 seconds. If for some reason this does not happen, or if you loose your patience before, click on the link below: http://www.math.toronto.edu/~drorbn/People/Eldar/thesis/index.html Please update your links/bookmarks! Dror Bar-Natan
54: General Topology
From Dave Rusin's "Known Math" collection.Category Science Math topology General topologyIntroduction. topology is the study of sets on which one has a notion of closeness enough to decide which functions defined on it are continuous.
http://www.math.niu.edu/~rusin/known-math/index/54-XX.html

Extractions: POINTERS: Texts Software Web links Selected topics here More formally, a topological space is a set X on which we have a topology a collection of subsets of X which we call the "open" subsets of X. The only requirements are that both X itself and the empty subset must be among the open sets, that all unions of open sets are open, and that the intersection of two open sets be open. This definition is arranged to meet the intent of the opening paragraph. However, stated in this generality, topological spaces can be quite bizarre; for example, in most other disciplines of mathematics, the only topologies on finite sets are the discrete topologies (all subsets are open), but the definition permits many others. Thus a general theme in topology is to test the extent to which the axioms force the kind of structure one expects to use and then, as appropriate, introduce other axioms so as to better match the intended application. For example, a single point need not be a closed set in a topology. Does this seem "inappropriate"? Then perhaps you are envisioning a special kind of topological space, say a a metric space. This alone still need not imply the space looks enough like the shapes you may have seen in a textbook; if you really prefer to understand those shapes, you need to add the axioms of a manifold, perhaps. Many such levels of generality are possible.
Topology Course Lecture Notes By Aisling McCluskey And Brian McMaster
By Aisling McCluskey and Brian McMaster. HTML with symbol fonts, DVI and PostScript.
http://at.yorku.ca/i/a/a/b/23.htm
Topology Without Tears
A course in topology by Sidney A. Morris in HTML with embedded GIFs. Some chapters available in PostScript.Category Science Math Publications Online Texts
http://linus.levels.unisa.edu.au/~sid/topology/
An Atlas Of Cyberspaces - Topology Maps
topology Maps of Elements of Cyberspace (page 1). Cobot was developed by CharlesIsbell and Michael Kearns. Go to topology maps page 2 for more examples.
http://www.cybergeography.org/atlas/topology.html

Extractions: Introduction Whats New Conceptual Artistic ... Historical A screenshot of a 3D model of the vBNS network which connects universities and laboratories in the USA. The model was created by Jeff Brown, a researcher at MOAT, National Laboratory for Applied Network Research (NLANR), USA, using his Cichlid data visualisation software . The model is animated to show how traffic flows over the links. More information on their work can be found in the paper "Network Performance Visualization: Insight Through Animation" by J.A. Brown, McGregor A.J and H-W Braun. These striking images are 3D hyperbolic graphs of Internet topology. They are created using the Walrus visualisation tool developed by Young Hyun at the Cooperative Association for Internet Data Analysis ( CAIDA The underlying data on the topological structure of the Internet is gathered by skitter , a CAIDA tool for large-scale collection and analysis of Internet traffic path data.
Topology Web Site
topology Project. The research community, however, has not seen many systematic empiricalstudies of how the Internet topology evolves over time and in space.
http://topology.eecs.umich.edu/

Extractions: The exponential growth of the number of Internet hosts has been well documented in the trade press. The research community, however, has not seen many systematic empirical studies of how the Internet topology evolves over time and in space. Most recently, the authors of [FFF99] report on several power-law relationships observed on Autonomous Systems' (AS) connectivity degree, degree frequencies, and the neighborhood size within any given hop count from an AS. This pioneering work represents a first important step toward a better understanding of the dynamic nature of Internet topology, a topic we explore further in this project. Ramesh Govindan

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