 First Digits  Ivars Peterson (MathTrek)
Take a look at a newspaper page listing stock market prices. You might think that each of the numbers from 1 to 9 would occur equally often among the first digits of all the listed prices. Instead, however, you're very likely to find that numbers starting
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 First occurrences of squarefree gaps and an algorithm for their computation
 Louis Marmet
This page reports the results of a search for first occurrences of squarefree gaps using an algorithm based on the sieve of Eratosthenes. The source code is supplied.
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 First Order Ordinary Differential Equations  Scott Hoffner
An electronic book covering Ordinary Differential Equations using CAS LiveMath examples. It requires users to have the free LiveMath Viewer or the full LiveMath program to view its examples. Both are available at LiveMath.com.
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 Fisher's Exact Test  Øyvind Langsrud
A calculator for testing statistically whether there is any relation between two categorical variables (with two levels). With examples.
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 The Five Percent Solution  Keith Devlin (Devlin's Angle)
"Mathematical disciplines such as statistics, optimization theory, probability theory, queuing theory, control theory, game theory, and operations research are all used routinely in making difficult choices in public policy, health, business, manufacturing,
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 FiveThirtyEight  Nate Silver, Editor in Chief
Quantitative features, interactives, and "datalabs" on politics, economics, sports, and other topics by Silver, Carl Bialik, and others. Science posts have included "How Statisticians Could Help Find That Missing Plane," "Toilet Seat Covers: To Use or
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 Fixedpoint arithmetic: multiplication  Paul Molitor; Universitat Hälle
A collection of Java applets, each showing a different method of fixedpoint multiplication: Binary representation, the Schoolmethod, Booth's algorithm, and Parallel multiplication, written for a course in Computer Science ('Computer Arithmetic'). After
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 Fixed Point Theory on the Web  M. A. Khamsi
Fixed Point Theory and Applications sites; Mailing List; Conferences: previous and forthcoming; books on fixed point theory; other interesting sites on the Web; bibliography database; abstracts; papers on fixed point theory; general information.
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 The FlashSort Algorithm  KarlDietrich Neubert
The problem of insitu sorting with minimal auxiliary space in minimal time. A new O(n) sorting algorithm: by advance calculation of the place where each element to be sorted has to go, sorting is performed by permutation of the elements. As an important
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 Flatland: the Movie  Flat World Productions, LLC
This movie, available in DVD format, is based on Edwin A. Abbott's classic novel, Flatland: A Romance of Many Dimensions. Flatland is a world that exists entirely on a twodimensional plane. All different kinds of shapes live, work, and play in this world.
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 Flexagon  Magnus Enarsson
"A flexagon is a polygon folded from paper with a very remarkable quality: you can turn it inside out to make it reveal hidden surfaces." History, including the original discovery of the trihexaflexagon by Arthur H. Stone, as he folded strips of paper
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 Flexagons  Conrad, Hartline
Introduction: The story of the Flexagon; Building and Operating the Flexagon; The Covering Space Representation of Flexagon Operation.
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 FloatingPoint Number Tutorial  Joseph L. Zachary
A tutorial designed to help you understand the significance of mantissa size and exponent range and the meaning of underflow, overflow, and roundoff error. Includes a Java applet in a separate window for use alongside the tutorial. From a Computer Science
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 Flooble :: Perplexus  Lev Epshteyn
A searchable, categorized collection of all sorts of puzzles, from simple logic questions and word tricks to indepth math problems in probability and geometry. Users can talk to one another and collaborate on solutions, as well as post their own problems
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 FlowingData  Nathan Yau
FlowingData explores how designers, statisticians, and computer scientists use data to understand ourselves better  mainly through data visualization. This blog, by a PhD candidate in statistics with a background in computer science and design, dates
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 Fluid Mechanics, Chaos and Mixing  Julio M. Ottino, Chemical Engineering Dept., Northwestern University
Research Interests of the Chaos and Mixing Group include: Granular Flows and SolidSolid Mixing; Competition Between Chaos and Order; LiquidLiquid Mixing; Mixing in 3D Flows; Mixing in Cell Culture Systems; SolidLiquid Mixing; and Geometric Aspects
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 Fluid Mechanics  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to fluid mechanics, which studies air, water, and other fluids in motion: compression, turbulence, diffusion, wave propagation, and so on. Mathematically this includes study of solutions of differential
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 Fluid v1.0  Maciej Matyka
A shareware program for solving incompressible, viscous, free surface fluid flow, using the Mac Method to solve NavierStokes equations on the Euler 2D grid. Source code with documentation is available.
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 FlyBase: A Database of the Drosophila Genome  Berkeley & European Drosophila Genome Projects
A searchable database of maps, genes, transposons, aberrations, stocks; genome projects, references, people, and images (body parts).
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 Flying Colours Maths  Colin Beveridge
Maths tutoring services by the author of Basic Maths for Dummies, Numeracy Tests for Dummies, and The Little Algebra Book: technical writing, "bespoke Excel solutions," project feedback, and "translating maths into less complex English." Blog posts, which
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 fMath: Mathematics on Web  Ionel Alexandru
fMath is a free Flash and Javascript library for displaying mathematics on the web: display equations in your site, edit the equations online, display graphs in your site.
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 Focus on Calculus  John Wiley & Sons, Harvard University
A newsletter for the Calculus Consortium based at Harvard University, from John Wiley & Sons College, publisher. Sample articles, conference announcements, new and forthcoming textbooks.
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 Focus on Mathematics  Department of Mathematics and Statistics, Boston University
Focus on Mathematics (FoM) seeks to "improve student achievement by providing mathematics teachers with the content knowledge and skills valuable in their profession." FoM programs have included math expos and math fairs of student research projects;
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 Folding and Unfolding  Eric Demaine
A series of pages detailing research and findings in origami, including: fold and cut, folding silhouettes and wrapping polyhedra, map folding, unfolding polyhedra, folding polygons into polytopes, linkages, protein folding, hinged dissections, hyperbolic
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 Folding Maps  Ivars Peterson (MathTrek)
Erik D. Demaine of the computer science department at the University of Waterloo
in Ontario and his coworkers have developed an efficient method for recognizing when a creased sheet is foldable into a flat package (results are reported in an unpublished
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 Folding Paper in Half 12 Times  The Historical Society of Pomona Valley
In 2001, a high school junior from California successfully folded a single sheet of paper in half 12 times, dispelling the longheld conventional wisdom of 7 folds as the maximum. See the limiting equation for single and alternate direction folding that
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 FOLDOC: Free Online Dictionary of Computing  Denis Howe
A searchable dictionary of acronyms, jargon, programming languages, tools, architectures, operating systems, networking, theory, mathematics, telecoms, institutions, companies, projects, products, history, in fact anything to do with computing  and broad
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 Following Benford's Law, or Looking Out for No.1  Malcolm W. Browne; The New York Times Company
An article from the New York Times on the Web: Dr. Theodore P. Hill asks his mathematics students at the Georgia Institute of Technology to go home and either flip a coin 200 times and record the results, or merely pretend to flip a coin and fake 200
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 Forecasting: Methods and Applications  Rob Hyndman
A book by Spyros Makridakis, Steve Wheelwright, and Rob Hyndman on mathematical methods of forecasting future trends in business and related areas. The site includes features of the book, detailed table of contents, example data series to download, errata,
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 Forecasting Principles  J. Scott Armstrong and Fred Collopy
A guide designed to summarize useful knowledge about forecasting as principles (guidelines, prescription, rules, conditions, action statements, or advice) about what to do in given situations. The principles apply to management, operations research, and
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 Forget 'Back to Basics.' It's Time for 'Forward to (the New) Basics.'  Keith Devlin (Devlin's Angle)
What is the best way to prepare our children for life in the twentyfirst century? The first thing to realize is that the nation needs only 3 or 4 percent of the population to be highly skilled in mathematics. Of the remainder, hardly any will ever need
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 Formula Database  students at the University of WisconsinMadison
FormulaDatabase is a free webbased math and physics equation search engine. It is an open collaborative project like a wiki, which will allow anyone to add and edit its content.
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 A Formula for C(n,k)  Jay's Corner
We would like to obtain a formula to calculate C(n,k) without writing down Pascal's triangle (although, to be honest, it is generally faster to write down Pascal's triangle than it is to use this formula, especially if you need a number of these binomial
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 Formulas for fairness  Ivars Peterson  Science News Online
Applying the math of cake cutting to conflict resolution: researchers turn to the mathematics of cake cutting and point allocation to develop improved methods for people to use to settle disputes.
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 Formula Sheet  Timothy Setterfield
Formula Sheet gets images of formulae or copies them to LaTeX or Microsoft Word, and lets you upload, organize, share, render, and store them all in one place.
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 Formulas  Math Forum; Ask Dr. Math FAQ
Formulas for: Defining Geometric Figures (plane and solid figures, and a note on dimensions); Geometric Formulas (two and threedimensional figures: perimeter, area, volume, etc.); Analytic Geometry Formulas (one, two, and three dimensions: points, directions,
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 Formulator MathML Suite  Hermitech Laboratory
MathML authoring and educational software, video processing and digital signage. MathML editors can insert clean mathematical notation into your documents or web pages, and the educational component can be used to print jigsaw puzzles, dominoes, and more.
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 for the learning of mathematics  FLM Publishing Association
for the learning of mathematics aims to stimulate reflection on mathematics education at all levels, and promote study of its practices and its theories: to generate productive discussion; to encourage enquiry and research; to promote criticism and evaluation
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 Forum Geometricorum  Paul Yiu, Editor; Department of Mathematical Sciences, Florida Atlantic University
A journal on classical Euclidean geometry and related areas. The goal is to bring to a wide, international readership the beauty, elegance, and
usefulness of elementary geometry, in research and in teaching. The journal focuses on concrete but challenging
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 Foundations of Computational Mathematics
The FoCM's primary aim is to further the understanding of the deep relationships between mathematical analysis, topology, geometry and algebra and the computational process as they are evolving together with the modern computer. The meetings are unified
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 Foundations of Greek Geometry  Michael Tirabassi; Tufts University
A linked historical essay outlining the contributions of Thales, Pythagoras, and Plato to the study of geometry.
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 Foundations of Infinitesimal Calculus  Henle and Keisler
Free download, PDF format.
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 Four Coloring Maps  Mario Stefanutti
Personal notes and ideas from a computer software engineer in pursuit of a "very easy pencil and paper proof of the four color problem." Posts, which date back to January, 2011, have included "Four color theorem: slow motion maps" and "Counting maps."
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 Four Colors Suffice: How the Map Problem Was Solved  Robin Wilson; Princeton University Press
"On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in historyone that would confound thousands of puzzlers for more than a century. This is the
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 The Four Color Theorem  Robertson, Sanders, Seymour, Thomas; Georgia Tech
A brief summary of a new proof of the Four Color Theorem, with a fourcoloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas, illustrated using a map of the United States. Contents: History; Why a new proof?; Outline
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 The Four Colour Theorem  MacTutor Math History Archives
Linked essay describing work on the theorem from its posing in 1852 through its solution in 1976, with two other web sites and 9 references (books/articles).
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 Four Construction Problems  Cut the Knot!, Alexander Bogomolny
Construct a triangle, given the three points in the plane that are the outer vertices of equilateral triangles constructed outward on the sides of the desired triangle. Construct a triangle, given the three points in the plane that are the centers of
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 Fourier Analysis  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to Fourier analysis, which studies approximations and decompositions of functions using trigonometric
polynomials. Of incalculable value in many applications of analysis, this field has grown to include
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 Fourier Synthesis  Manfred Thole
A periodic signal can be described by a Fourier decomposition as a Fourier series, i.e. as a sum of sinusoidal and cosinusoidal oscillations. By reversing this procedure a periodic signal can be generated by superimposing sinusoidal and cosinusoidal waves.
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 The Four Learning Styles in the DVC Survey  Suzanne Miller, Diablo Valley College
Descriptions of and strategies for four learning styles: visual/verbal, visual/nonverbal, tactile/kinesthetic, and auditory/verbal style. With tips for studying mathematics and a link to the Learning Styles Survey online.
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