121. Contents | Science And Creationism: A View From The National Academy Of Sciences Considers the science that supports the theory of evolution from the National Academy of Sciences. http://bob.nap.edu/readingroom/books/creationism/

Notice Committee Acknowledgments National Academy of Sciences Notice Committee Acknowledgments National Academy of Sciences ... Non-JavaScript Version

122. Diamond Theory: Symmetry In Binary Spaces Plato tells how Socrates helped Meno's slave boy remember the geometry of a diamond. Twentyfour centuries later, this geometry has a new theorem. http://m759.freeservers.com/

Related sites: The 16 Puzzle Bibliography On the author Diamond Theory by Steven H. Cullinane Plato's Diamond Motto of Plato's Academy Abstract: Symmetry in Finite Geometry Symmetry is often described as invariance under a group of transformations. An unspoken assumption about symmetry in Euclidean 3-space is that the transformations involved are continuous. Diamond theory rejects this assumption, and in so doing reveals that Euclidean symmetry may itself be invariant under rather interesting groups of non continuous (and a symmetric) transformations. (These might be called noncontinuous groups, as opposed to so-called discontinuous (or discrete ) symmetry groups. See Weyl's Symmetry For example, the affine group A on the 4-space over the 2-element field has a natural noncontinuous and asymmetric but symmetry-preserving action on the elements of a 4x4 array. ( Details By embedding the 4x4 array in a 4x6 array, then embedding A in a supergroup that acts in a natural way on the larger array, one can, as R. T. Curtis discovered, construct the Mathieu group M which is, according to J. H. Conway, the "most remarkable of all finite groups."

123. 60: Probability Theory And Stochastic Processes Part of Dave Rusin's excellent Mathematical Atlas. http://www.math.niu.edu/~rusin/known-math/index/60-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 60: Probability theory and stochastic processes Introduction Probability theory is simply enumerative combinatorial analysis when applied to finite sets; thus the techniques and results resemble those of discrete mathematics. The theory comes into its own when considering infinite sets of possible outcomes. This requires much measure theory (and a careful interpretation of results!) More analysis enters with the study of distribution functions, and limit theorems implying central tendencies. Applications to repeated transitions or transitions over time lead to Markov processes and stochastic processes. Probability concepts are applied across mathematics when considering random structures, and in particular lead to good algorithms in some settings even in pure mathematics. History A list of references on the history of probability and statistics is available. Applications and related fields Some material in probability (especially foundational questions) is really measure theory . The topic of randomly generating points on a sphere is included here but there is another page with general discussions of spheres . Probability questions given a finite sample space are usually "just" a lot of counting, and so are included with

124. Quantum Theory And Wave/Particle Duality Repudiates Wave/Particle Duality and provides a new interpretation of Schroedinnger's equations. http://www.geocities.com/hotquanta/wpd.html

Quantum Theory and Wave/Particle Duality A work in Progress; modified: 7-March-2001 Many interpretations of quantum physics incorporate the idea that particles (or some property associated with particles) propagate as waves. The object of this article is to examine the core assumptions behind this wave/particle idea with a view to developing a different model that is consistent with relativity, observation and the mathematical formalism. John K. N. Murphy , Kohimarama, Auckland, New Zealand. Home Page Site Index About MySelf Sign Guestbook ... View Guestbook Contents Comments and feedback welcome - E- Mail John Murphy 1.0 Introduction 1.1 Basic Issues 1.2 Generating a New Approach ... 5.0 The Ahranhov-Bohm Effect 1.0 Introduction Next Essentially, wave/particle duality employs the notion that an entity simultaneously possesses localized (particle) and distributed (wave) properties. The idea has been introduced into modern physics to account for observations in which particles of matter interact to produce effects that appear to be identical to the effects that occur when waves diffract and interfere. However, the concept of rests on an assumption. It is assumed that wave propagation mechanisms can provide the only possible explanation for scattering effects observed in experiments such as the Twin Slit experiment.

125. The Juliana Theory - Squad Studios Official site. Includes photographs, lyrics, a band biography, news, and a list of upcoming shows. http://www.thejulianatheory.com/

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126. Allen Hatcher's Homepage Contains textbooks in Algebraic Topology, Ktheory, and 3-Manifolds. http://www.math.cornell.edu/~hatcher/

Allen Hatcher Office: 553 Malott Hall Phone: (607)-255-4091 E-mail . The address is hatcher@math.cornell.edu Cornell Math Dept Homepage Cornell Topology Festival Remington Brook - photos On This Webpage: Book Projects: Algebraic Topology Vector Bundles and K-Theory Spectral Sequences in Algebraic Topology ... Books by other authors Book Projects Real and Imaginary Algebraic Topology This is the first in a series of three textbooks in algebraic topology having the goal of covering all the basics while remaining readable by newcomers seeing the subject for the first time. The first book contains the basic core material along with a number of optional topics of a relatively elementary nature. The other two books, which are largely independent of each other, are provisionally titled "Vector Bundles and K-Theory" and "Spectral Sequences in Algebraic Topology." These are only partially written see below. To find out more about the first book or to download it in electronic form, follow this link to the download page Vector Bundles and K-Theory The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. For further information, and to download the part of the book that is written, go to

127. Chaos Theory And Fractals History of chaos as well as extensive information on Chaos theory and fractals. Contains several pictures of fractals and links to other Chaos theory and fractals pages. http://www.mathjmendl.org/chaos/

Chaos Theory and Fractals By Jonathan Mendelson and Elana Blumenthal Outline Introduction to Chaos Determinism Early Chaos Edward Lorenz ... Works Cited Introduction to Chaos The dictionary definition of chaos is turmoil, turbulence, primordial abyss, and undesired randomness, but scientists will tell you that chaos is something extremely sensitive to initial conditions. Chaos also refers to the question of whether or not it is possible to make good long-term predictions about how a system will act. A chaotic system can actually develop in a way that appears very smooth and ordered. Determinism Sir Isaac Newton Determinism is the belief that every action is the result of preceding actions. It began as a philosophical belief in Ancient Greece thousands of years ago and was introduced into science around 1500 A.D. with the idea that cause and effect rules govern science. Sir Isaac Newton was closely associated with the establishment of determinism in modern science. His laws were able to predict systems very accurately. They were deterministic at their core because they implied that everything that would occur would be based entirely on what happened right before. The Newtonian model of the universe is often depicted as a billiard game in which the outcome unfolds mathematically from the initial conditions in a pre-determined fashion, like a movie that can be run forwards or backwards in time. Determinism remains as one of the more important concepts of physical science today. Early Chaos

128. Sixth Great Lakes K-theory Conference Fields Institute, Toronto, Canada; 2526 March 2000. http://www.math.uwo.ca/GL6.html

Third Announcement GL6: The Sixth Great Lakes K-theory Conference Fields Institute Toronto, Ontario, Canada March 25-26, 2000 The sixth Great Lakes K-theory Conference will be held at the Fields Institute in Toronto. The following mathematicians have agreed to speak at this meeting: P. Balmer (Western Ontario) T. Goodwillie (Brown) L. Hesselholt (MIT) A. Merkurjev (UCLA) M. Rost (IAS) V. Voevodsky (IAS) M. Walker (Nebraska) March 25-26 is a Saturday-Sunday. The conference will begin at 9:00am on the Saturday and finish by 1:00pm on Sunday. Here is a Schedule of Lectures A block of rooms for the conference has been booked at the Toronto Colony Hotel for the evenings of March 24-25. Consult this page for more information: Travel and Hotel Information . All conference participants should make their own hotel reservations. This conference is supported by the Fields Institute and NSERC. The organizers for this meeting are: Rick Jardine jardine@uwo.ca Manfred Kolster kolster@mcmaster.ca Dan Grayson dan@math.uiuc.edu

129. INI Programme MAA Research session at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK; 17 January 15 July 2005. http://www.newton.cam.ac.uk/programs/MAA/

@import url("/css/prog-non_n4.css"); Institute Home Page Programmes Web-Seminars Programme Home Seminars Workshops Participants Long Stay Short Stay Additional Links Contacts Mailing List Isaac Newton Institute for Mathematical Sciences Model Theory and Applications to Algebra and Analysis 17 Jan - 15 Jul 2005 Organisers Professor Z Chatzidakis ( CNRS ), Professor HD Macpherson ( Leeds ), Professor A Pillay ( Illinois ), Professor A Wilkie ( Oxford Programme theme Model theory is a branch of mathematical logic dealing with abstract structures (models), historically with connections to other areas of mathematics. In the past decade, model theory has reached a new maturity, allowing for a strengthening of these connections and striking applications to diophantine geometry, analytic geometry and Lie theory, as well as strong interactions with group theory, representation theory of finite-dimensional algebras, and the study of the p-adics. The main objective of the semester will be to consolidate these advances by providing the required interdisciplinary collaborations. Model theory is traditionally divided into two parts pure and applied. Pure model theory studies abstract properties of first order theories, and derives structure theorems for their models. Applied model theory on the other hand studies concrete algebraic structures from a model-theoretic point of view, and uses results from pure model theory to get a better understanding of the structures in question, of the lattice of definable sets, and of various functorialities and uniformities of definition. By its very nature, applied model theory has strong connections to other branches of mathematics, and its results often have non-model-theoretic implications. A substantial knowledge of algebra, and nowadays of algebraic and analytic geometry, is required.

130. 11: Number Theory Dave Rusin's guide to number theory. http://www.math.niu.edu/~rusin/known-math/index/11-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11: Number theory Introduction Number theory is one of the oldest branches of pure mathematics, and one of the largest. Of course, it concerns questions about numbers, usually meaning whole numbers or rational numbers (fractions). Elementary number theory involves divisibility among integers the division "algorithm", the Euclidean algorithm (and thus the existence of greatest common divisors), elementary properties of primes (the unique factorization theorem, the infinitude of primes), congruences (and the structure of the sets Z /n Z as commutative rings), including Fermat's little theorem and Euler's theorem extending it. But the term "elementary" is usually used in this setting only to mean that no advanced tools from other areas are used not The remaining parts of number theory are more or less closely allied with other branches of mathematics, and typically use tools from those areas. For example, many questions in number theory may be posed as Diophantine equations equations to be solved in integers without much preparation. Catalan's conjecture are 8 and 9 the only consecutive powers? asks for the solution to

131. The Vectorial Theory Of The Universe of the inert mass as the attribute of the space.......Basing on the hyperspace conception attempt of the explanation what is the movement in surrounding us threedimensional space. http://www.sggw.waw.pl/~plewicki/vtu.htm

I do not say that it is so, I say that it maybe so The Vectorial Theory of the Universe Tomasz Plewicki Basics. The velocity in the space. Changes are a matter of the existence. I found that every element has constant velocity in the multidimensional hyperspace S n . The velocity observed in the surrounding us three-dimensional space S is a projection of the constant velocity in the space S n on the space S . The change of the velocity relies only on the change of direction of the vector in S n what causes the change of the length of the projection of the vector on the space S The composition of the velocity. Let us consider the case of the composition of the velocity in the two-dimensional space. Let us mark the constant maximum velocity in the space as the vector C and its projection on the one-dimensional space as V. So we have: V = C cos a Because C is a maximum length of the projection of the vector on the one-dimensional space the maximum change of the vector V length under of the composition with a vector C amounts: V ad max = C - V = C(1 - cos a Because: cos a = V/C We have: V ad max = C(1 - V/C) If the vector causing the change of the velocity has in the one-dimensional space the length V then: V ad = V (1 - V/C) Then the vector sum of the velocity amounts: V sum = V + V (1 - V/C) = V + V - V*V /C And is less or equal C.

132. Experience From A Course In Game Theory The second edition of an interactive paper originally published in Games and Economic Behavior, focused on webbased teaching. Contains links to more than 40 experiments and their results. Provided by Ariel Rubinstein at Princeton University. http://www.princeton.edu/~ariel/99/gt100.html

Second Edition: Oct 1999 Academic Press Ariel Rubinstein Abstract This is a revised version of my paper with the same title published in Games and Economic Behavior , 28 (1999), 155-170. The paper summarizes my experience in teaching an undergraduate course in game theory in 1998 and in 1999. Students were required to submit two types of problem sets:pre-class problem sets, which served as experiments, and post-class problem sets, which require the students to study and apply the solution concepts taught in the course. The sharp distinction between the two types of problem sets emphasizes the limited relevance of game theory as a tool for making predictions and giving advice. The paper summarizes the results of 43 experiments which were conducted during the course. It is argued that the crude experimental methods produced results which are not substantially different from those obtained at much higher cost using stricter experimental methods. My sincere thanks to my two excellent research assistants, Yoram Hamo, during the 1998 course, and Michael Ornstein, during the 1999 course and in the writing of the paper and its revised version. 1. Introduction

133. Algebraic Areas Of Mathematics Topics include number theory, groups and sets, commutative rings, algebraic geometry, and linear algebra. http://www.math.niu.edu/~rusin/known-math/index/tour_alg.html

Search Subject Index MathMap Tour ... Help! Algebraic Areas of Mathematics Return to start of tour Up to The Divisions of Mathematics The algebraic areas of mathematics developed from abstracting key observations about our counting, arithmetic, algebraic manipulations, and symmetry. Typically these fields define their objects of study by just a few axioms, then consider examples, structure, and application of these objects. We have included here the combinatorial topics and number theory ; each is arguably a distinctive area of mathematics but (as the MathMap suggests) these parts of mathematics, shown in shades of red, share definite affinities. The list on this page includes a rather large number of fields in the MSC scheme. It is also common to interpret the phrase "abstract algebra" in a more narrow sense - to view it as the fields obtained by adding successive axioms to describe the objects of study. Arguably then, abstract algebra is limited to sections 20 and 22 (Group Theory), 13, 16, and 17 (Ring Theory), 12 (Field Theory), and 15 (Linear Algebra), taken in this way as a succession from fewest to most restrictive sets of axioms. The use of algebra is pervasive in mathematics. This particularly true of group theory - symmetry groups arise very naturally in almost every area of mathematics. For example, Klein's vision of geometry was essentially to reduce it to a study of the underlying group of invariants; Lie groups first arose from Lie's investigations of differential equations. It is also true of linear algebra - a field which, properly construed, includes huge portions of Numerical Analysis and Functional Analysis, for example hence that field's central position in the MathMap.

134. Grounded Theory Institute-The Grounded Theory Methodology Of Barney G. Glaser, P dedicated to the evolving methodology of Barney G. Glaser. http://www.groundedtheory.org/

The Grounded Theory Institute a nonprofit organization Text Translator Home Review Seminars ... Sociology Press Welcome to the internet home of The Grounded Theory Institute dedicated to the evolving methodology of Dr.Barney G. Glaser, Ph.D NEW!! One day Grounded Theory troubleshooting seminar with Barney G. Glaser PhD for advanced PhD condidates at dissertation stage on Aug 14 in San Francisco. American Sociological Association Annual Conference participants welcome. APPLY HERE. Dr Glaser will be holding a new seminar in New York city on the 26th and 27th of October 2004. He will work personally and closely with participants and their data and do Grounded Theory exercises. APPLY HERE. NEW!! Order the first in a series of Grounded Theory videos " Grounded Theory Questions and Answers" - Hi-Lites of an on-line video conference with Dr Barney Glaser Available on DVD Dr Glaser gave a talk at Stanford University on April 15th. PHOTOS The seminar/conference held in Malmo, Sweden - September 23-25. with Dr Barney G. Glaser was a success and a great time was had by all!! More Photos NEW!

135. Southampton GR Explorer Home Page An introduction to Einstein's theory of General Relativity and related topics. These pages include informative text, pictures and movies. http://www.maths.soton.ac.uk/relativity/GRExplorer/

Welcome to the Southampton GR Explorer. On these pages you will find an overview of Einstein's theory of General Relativity and related topics. We focus on subjects that are close to the research interests of the Southampton group. A more technical description of our various ongoing research projects can be found here This site is best viewed with frames, which are not supported by your browser. You can either: or Internet Explorer alternatively Turn the frames off

136. Updated 4 June 2004 A theory that can't be dismissed with ease. Science, medical science, physics, astronomy. http://geocities.com/aaron_stiles/

Updated   4 June 2004 Introduction   ..                 Well Folks I’m Back by popular demand.  About a year ago I shut this website down do to the fact that my work had been copied and claimed by others.  One such incident I found on a prominent website.   I have decided that I would rebuild this web site with much a few changes.  Being since my book is so close to coming out I shall only  put parts of my research on line other than the entire manuscript. Thank you for visiting Aaron Stiles Coming Soon     . Ghost – A scientific look into the creation of Ghost     “NEW” What could be the beginning of a “Unified Theory of the Universe”        “NEW” Time”   A different point of view on what Time is and how it effect the Universe    “Updated” An “Advanced Theory of Evolution”   Religion, A scientific and physiological look into its creation and prominence        “Updated” We must always remember that science is the search for answers to the unknown, our ideas of the world change every day,  We, as a human race should not shy away or grow fearful of those things that we do not understand.  We must also learn to better judge fact from fiction, and fiction from scientific possibility, irregardless of how improbable.  Faith can only take you so far, let the facts guide you through the rest of your journey. Rebuilding this site will take a little time, but it shall also be better than ever too.  If you have comments or questions fill free to e-mail.  If you are a Professional and would like to discuss some of my idea’s you may also E-mail me or contact me directly.Â

137. GTEM - Post-doc Positions Research training network coordinated in Paris, uniting twelve teams from July 2000 until June 2004. http://www.math.jussieu.fr/~leila/gtem/gtem.html

A Research Training Network of the European Community European Research Training Network GTEM Galois Theory and Explicit Methods in Arithmetic Programme Teams Hiring Positions ... Reporting This network unites twelve European teams for a period of four years, from October 1, 2000 until September 30, 2004, for the purpose of initiating joint research projects and conferences, and hiring pre- and postdoctoral researchers. For information about workshops and conferences particularly interesting for young researchers, click on the Workshops button in the menu!! For any information about the GTEM network not provided in this page, please contact the Network Coordinator, Dr. Leila Schneps in Paris leila@math.jussieu.fr To be eligible for pre- or postdoctoral positions in the network, a candidate must: be a young researcher (under 35 years of age, although older candidates may exceptionally be considered); be able to contribute to one of the areas of activity described in the scientific programme of the network; satisfy one of the following conditions: - be a national of a Member State of the European Community (Austria, Belgium, Denmark, England, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden)

138. Links To Low-dimensional Topology Topics General, Conferences, Pages of Links, Knot theory, 3manifolds, Journals. http://www.math.unl.edu/~mbritten/ldt/ldt.html

Links to low-dimensional topology Any comments/suggestions? Send them to me! Enter your comments here: Most recent additions: hard to say, I've stopped keeping track... This page was getting just a little too large, so I've cut it into pieces. General Conferences Pages of Links Knot Theory ... Home pages

139. 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. http://www.earlham.edu/~peters/knotlink.htm

Knots on the Web Artwork credits Unfortunately I'm much too busy with real, paying work nowadays to update Knots on the Web as often as I used to. Consequently, it has far too many dead links and omits far too many good, new sites. I wish I could say that this will change soon, but it won't. Until it does, please use what is still useful here and forgive the weak spots. If you have a specific knot need or question, and the surviving links here don't help you with it, then try posting your question to rec.crafts.knots or running a search on Google Welcome to my collection of knotting resources. My major sections are on Knot Tying Knot Theory , and Knot Art . But knot lovers will understand that these distinctions are artificial. For example, a good practical knot is both a nugget of hard-won technology and a thing of beauty. Decorative knotting can be useful, and in any case requires uncommon dexterity and practical tying ability. Software developed to help mathematical knot theorists has produced some of the most beautiful knot images ever seen. So look at all three sections even if you think your interests are narrow. You might become happily entangled. My fourth section is on Knot Discussion . Use these discussion forums to find answers to your knotting questions and to help others who know less than you do. My fifth section is on Knot Software . You'll be surprised at how knotting software can make it easier for you to learn to tie knots, to explore the mathematical properties of knots, and to create stunning images of knots, including knots never seen on Earth.

140. Game Theory Von Neumann and Morgensterns mathematical theory of bargaining, introduced by Don Ross University of Cape Town. http://plato.stanford.edu/entries/game-theory/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change JUN Game Theory Game theory is the study of the ways in which strategic interactions among rational players produce outcomes with respect to the preferences (or utilities ) of those players, none of which might have been intended by any of them. The meaning of this statement will not be clear to the non-expert until each of the italicized words and phrases has been explained and featured in some examples. Doing this will be the main business of this article. First, however, we provide some historical and philosophical context in order to motivate the reader for all of this technical work ahead. 1. Philosophical and Historical Motivation 2. Basic Elements and Assumptions of Game Theory 2.1 Utility 2.2 Games and Information ... Related Entries 1. Philosophical and Historical Motivation The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern ( ). For reasons to be discussed later, limitations in their mathematical framework initially made the theory applicable only under special and limited conditions. This situation has gradually changed, in ways we will examine as we go along, over the past six decades, as the framework was deepened and generalized. Refinements are still being made, and we will review a few outstanding philosophical problems that lie along the advancing front edge of these developments towards the end of the article. However, since at least the late 1970s it has been possible to say with confidence that game theory is the most important and useful tool in the analyst's kit whenever she confronts situations in which one agent's rational decision-making depends on her expectations about what one or more other agents will do, and theirs similarly depend on expectations about her.

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