 Shodor Education Foundation, Inc.
A nonprofit research and education organization dedicated to the advancement of science and math education, specifically through the use of modeling and simulation technologies. Interactive middle school lessons aligned with curricula are available through
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 The Shoelace Problem  Ivars Peterson (MathTrek)
How should shoes be laced? This seemingly simple question, rooted in everyday life, can provoke passionate argument  and evoke a mathematical response. There are at least three common ways to lace shoes, as illustrated: American (or standard) zigzag,
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 Shoe Size vs. Height  Statistical Analysis and Linear Regression with FATHOM  Jay Yohe; Susquehanna Township High School, Harrisburg, PA
A lesson plan in which students analyze onevariable distributions (histograms and box plots), determine measures of center (mean, median) and spread (standard deviation, range), analyze scatter plots, form lines of best fit, and explore least squares
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 Shooloo  Shooloo Inc.
At Shooloo, students "discover the joy of writing their own math stories" by publishing original word problems, constructing viable arguments, critiquing the reasoning of others, and modeling real life with mathematics. Shooloo then presents the resulting
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 A Short Course in Trigonometry  David Joyce; Dept. of Mathematics & Computer Science, Clark University
An introduction and a guide to trigonometry, with hints and answers to exercises, and Java applets as illustrations. Contents include applications of trigonometry, angle measurement, chords, sines, cosines, tangents and slope, the trigonometry of right
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 Shortcuts to Departments of Physics, Engineering, and Mathematics  Fred Lemmerhirt, Waubonsee Community College
A collection of quick links to departments of physics, engineering, and mathematics at most U.S. universities and fouryear colleges, listed
both by location and alphabetically. Many twoyear colleges are also included.
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 Shortest Enclosures on Surface of Cube (Math Chat)  Frank Morgan, MAA Online
The circle provides the leastperimeter way to enclose given area in the plane. What is the leastperimeter way to enclose given area in the surface of the unit cube? Answer: Al Zimmerman correctly finds that the best way to enclose small area is not
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 A Short Guide to Writing Mathematics  Stephen B. Maurer; Dept. of Mathematics & Statistics, Swarthmore College
A guide to mathematics writing for college students who want to learn mathematical style  math majors or prospective majors, or students who will go into other quantitative fields and expect to communicate with mathematics in their careers. You may contact
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 A Short Introduction to Symmetry and Groups  Jenny Olive
A beautiful and satisfying area of maths that also has many important applications in areas such as crystallography and particle physics. Olive gives some examples of how symmetry can be described by groups, for which no previous maths is required, and
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 Short Signal Harmonic Spectra and Approximation  Dmitriev E.V.
The author writes: "Presently traditional ways to determine signal spectra are based on the expansion of functions in Fourier series or on their representation by Fourier integrals with applying a system of basis ORTHOGONAL functions. For the first time,
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 Should Mathematicians and Mathematics Educators be Listening to Cognitive Psychologists?  Annie and John Selden; Mathematical Association of America
Organized into four sections: Different Questions and (often very) Different Views of Mathematics; Shared Underlying Principles of Knowledge Axquisition; Where is the Mind? and Some Concluding Reflections. Subsections include A Schema Theory; Mathematics
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 Should Nader Voters Flip a Coin? (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: Suppose that in a certain U.S. state 12 million potential voters favor Bush, 10 million favor Gore, and 5 million favor Nader with Gore as second choice. The Nader supporters want to be sure than Gore wins, but they would like
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 ShowMe Center
A National Science Foundation project supporting implementation of standardsbased middle grades mathematics curricula. The site features a calendar listing professional development opportunities; information about five different math curricula (Connected
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 Show Me Your Math  Borden, Lisa Lunney; and Wagner, David
Student projects and resources to support culturally responsive teaching from a program that invites Aboriginal Students in Atlantic Canada to explore the mathematics evident in their own community and indigenous practices. Nova Scotia youth who participate
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 Show N Tell Multiplication Table Tutor  Sheela Belur
Audiovisual practice in the multiplication tables. For Internet Explorer on Windows only.
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 ShowTheMath.org  Alan Degener
Enter an algebra equation and then solve it, step by step  manually: use the pulldown menu to describe steps as combining like terms, distributing, expanding, factoring, adding to both sides, subtracting from both sides, dividing both sides, multiplying
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 Show Your Thinking  Annie Forest
Blog by an instructional specialist in Illinois "passionate about giving all students an equitable math education, making thinking visible, purposeful tech, and teacher collaboration and reflection." Posts, which date back to October, 2013, have included
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 ShtetlOptimized  Scott Aaronson
Blog posts include "Teaching your students not to need a teacher," "Ten Signs a Claimed Mathematical Breakthrough is Wrong," "Essentials of complexitytheoretic standup comedy," "My take on the Koblitz affair, "Logicians on safari," and "Unparadox Contest."
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 SIAM Activity Group on Orthogonal Polynomials and Special Functions  Martin Muldoon
A group for promoting basic research in orthogonal polynomials and special functions; furthering the application of this subject in other parts of mathematics and in science and industry; and encouraging and supporting the exchange of information, ideas,
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 SIAM Activity Groups  Society for Industrial and Applied Mathematics
Activity Groups on: Control and Systems Theory; Discrete Mathematics; Dynamical Systems; Geometric Design; Geosciences; Linear Algebra; Optimization; Orthogonal Polynomials and Special Functions; Supercomputing, etc. Rules of Procedure, Initiation and
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 SIAM Journal on Discrete Mathematics  Society for Industrial and Applied Mathematics
A journal that publishes research articles on a broad range of topics from pure and applied mathematics, including combinatorics and graph theory, discrete optimization and operations research, theoretical computer science, to coding and communication
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 SIAM Journals  Society for Industrial and Applied Mathematics
The journals of the Society for Industrial and Applied Mathematics (SIAM): Applied Mathematics; Computing; Control and Optimization; Discrete Mathematics; Mathematical Analysis; Matrix Analysis and Applications; Numerical Analysis; Optimization; Scientific
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 SIAM's Undergraduate Page (Society of Industrial and Applied Mathematics)  Math Department, Univ. of New Hampshire
SIAM serves the mathematics and industrial communities and offers another way to bring the two together. Mathematics articles and essays submitted by undergraduates; profiles of recent graduates and mathematicians in industry; information about internships
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 Siemens STEM Academy  Siemens Foundation
The Siemens STEM Academy provides professional development to educators as they cultivate junior scientists who will pursue careers in science, technology, engineering, or mathematics (STEM). Opportunities include an annual STEM Institute; interactive
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 Siemens Westinghouse Competition  The Siemens Foundation
The Siemens Westinghouse Competition in Math, Science & Technology fosters individual growth for high school students seeking to challenge themselves through science research. Through this competition, students have an opportunity to achieve national
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 The Sierpinski Carpet Project, 20002001  Tom Canright
Instructions and pictures of The Sierpinski Carpet Project, from Tom Canright and Linda Gazzola's sixth grade mathematics classes at the Latin School of Chicago. All of the carpets are a type of fractal, meaning that the basic patterns are reiterated
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 Sierpinski Shapes  Rick and Donna Joi
An interactive Java applet that allows you to create hundreds of fractal shapes using a variation of the Sierpinski triangle algorithm. Includes a page that provides a nontechnical explanation (with pictures) of the fractal math.
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 Sierpinski Tetrahedron: A Metal Sculpture  Stan Goldade
Pictures and background information on the sculpture, with some Sierpinski facts.
Breckenridge Senior High School students welded 4,096 equilateral metal triangles together to form 1,024 tetrahedra to form a stage5 Sierpinski Tetrahedron. It is located
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 The Sierpinski Triangle  Robert L. Devaney; Dept. of Mathematics, Boston University
Section from the paper "Chaos in the Classroom," describing the deterministic (rather than random) construction of the Sierpinski triangle.
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 Sieve of Eratosthenes  Interactive mathematics Miscellany and Puzzles, Alexander Bogomolny
Sieve of Eratosthenes with an interactive Java illustration. A slight
modification of the Eratosthenes' algorithm leads to a different sieve
that leaves out square numbers. The latter is also accompanied by a Java
illustration.
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 Sieve of Eratosthenes  Program in C
A class assignment for Mathematics 216: Introduction to Mathematical Computation (with C) at the Univ. of Utah. The new part of the C language learned was the array. Problems: Design a program to make a list of primes less than N = 100 using Eratosthenes'
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 Sifting through the Web's data jumble  Ivars Peterson; Science News Online
A combination of text and link analysis underlies a novel method based on analyses of the way Web pages are linked to one another for automatically generating lists of authoritative Web resources.
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 Sight Enhancement Systems
Manufacturers of large display scientific calculators with speech output, and of large display calculators that allow people with low vision to perform scientific, statistical and trigonometric calculations. Download brochures and manuals for the SciPlus
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 Signal Processing Laboratory  Thomas W. Parks, Director; Cornell University, Ithaca, NY
People; wavelets and multiresolution analysis research.
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 The Significance of the NCTM Standards to the Pathways (NCREL)  Cathy Cook; Pathways to School Improvement
Critical Issues in Mathematics. The Standards represent a major effort to develop mathematically literate citizens. They should be viewed as facilitators of reform, rather than as a set of directives. They are designed to help schools achieve national
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 Significant Digits  R. H. Logan, Instructor of Chemistry, El Centro College
An explanation of significant digits, with sections on: Measured Values; Computed Values; Rules for Determining the Number of Significant Digits In Numbers With Indicated Decimals; Significant Digits In Numbers Not Having an Indicated Decimal; Significant
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 Significant Figures and Rounding Rules  Christopher Mulliss
A site dedicated to the discussion of issues relating to the proper teaching of
significant figures and rounding rules in high school and college science courses. Includes a link to a detailed study "On the Standard Rounding Rule for Multiplication and
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 Significant Figures/Digits  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about scientific figures and scientific digits, such as "When are zeros significant and when are they not significant?"
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 Signing Apps  Vcom3D
Illustrated, interactive 3D sign language dictionaries and pictionaries. Vcom3D developed the Signing Math Dictionary (SMD), Signing Math Pictionary (SMP), and other apps for Deaf or HardofHearing students who use American Sign Language (ASL) or Signed
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 Signing Science  National Technical Institute for the Deaf, TERC, Vcom3D
Along with the animated sign translator Sign Smith Player, SigningAvatar signs text in American Sign Language (ASL) or Signed English (SE). This research project plans to evaluate the extent to which the addition of signing promotes achievement of specific
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 SI Guide  James R. Frysinger
SI (International System) measurements and quantities, with pages for: a basic starter set of units and prefixes; the unit compendium (a more complete list); the prefix compendium (a complete list); rules on usage (spelling, capitalization, spacing, plurals,
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 Silicon Champions of the Game  Ivars Peterson  Science News Online
Deep Blue's triumph over Gary Kasparov in May of 1997 marked the first match victory by a chessplaying computer over a reigning world champion. Some of the world's top computer programs are also playing backgammon, bridge, checkers, chess, Go, Othello,
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 The Silicon Mirror and Kaleidoscope  Elliot Leonard
The Silicon Mirror is an interactive tool for creating tessellations. It
operates on the same principles as a kaleidoscope. The Silicon Kaleidoscope is a screen saver that uses the Silicon Mirror to create kaleidoscopic images that flow in real time.
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 The Siluroid Curve  Dario de Judicibus
Formulas, graphs, compassandstraightedge constructions, derivatives, and more about this biquadratic, trilobate curve. Among the torpedo or fishshaped curve's curious properties: connecting its intersection with the generatrix or goniometric circle
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 SIMATH  Marc Conrad
A computer algebra system, especially for number theory. Try out the online version of the SIMATH calculator simcalc; a more detailed overview is available as a .dvi file or you can download the TeXSource of this file.
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 SimCalc Curriculum  James J. Kaput, Principal Investigator; Simulations for Calculus Learning
The SimCalc Project aims to democratize access to the Mathematics of Change for mainstream students. How the math of change can contextualize and organize many other important ideas already in the curriculum, moving to a strands structure that allows
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 SimCalc Library  James J. Kaput, Principal Investigator; Simulations for Calculus Learning
Papers and other writings on the SimCalc Project, which aims to democratize access to the Mathematics of Change for mainstream students: "Learning the Basics with Calculus"; "An introduction to the profound potential of connected algebra activities:issues
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 Simeon's World of Magic  Bob Fay
Interactive card tricks on the Web. Pick a card; whisper it out loud; Simeon will always remove it on the next page.
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 Similarity  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Scaling multiplies lengths by the same factor and produces a similar figure. It
preserves angles and
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 Similarity (SMILE)  Natalia Kee, Harlan Community Academy High School
A lesson designed to teach students to discover the factor of proportionality in similar polygons and relate this factor to the perimeters and areas of similar polygons. From the Geometry and Measurement section of a collection of almost 200 single concept
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