 Set Theory and Foundations (MathPages)  Kevin Brown
About 30 "informal notes" by Kevin Brown on set theory and foundations: what is fuzzy logic, fractal logic, Cantor's diagonal proof, are all triangles isosceles?, on Gauss's mountains, problems with the luminiferous aether, and many more.
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 Set Theory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to set theory. Naive set theory considers elementary properties of the union and intersection operators  Venn diagrams, the DeMorgan laws, elementary counting techniques such as the inclusionexclusion
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 Setting the Stage with a Story  Suzanne Alejandre
Article about the development, and implementation, of online lessons created by Varnelle Moore at a Math Forum summer institute. Originally published in the June, 2013, issue of the CMC ComMuniCator, journal of the California Mathematics Council.
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 Several Complex Variables and Analytic Spaces  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to several complex variables, the study of (differentiable) functions of more than one complex variable. The rigid constraints imposed by complex differentiability imply that, at least
locally, these
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 Shai Simonson
Shai Simonson is an associate professor of computer science and mathematics at Stonehill College. The site contains the article "How to Read Mathematics," which uses the probability of two people having the same birthday as an example. The site also
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 Shelley's Mathematics Articles  Shelley Walsh
"Little selfcontained articles [that] write up more than you can normally fit in a lecture, and ... hopefully put together enough explanation so that there's something for a great variety of different ways of thinking." Organized into Geometry; Analytic
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 Shelley Walsh
Syllabi and notes for math courses from arithmetic review to beginning calculus. Download MathHelp a tutorial program with problem sets for Mac or PC, or learn how to use MathHelp to create your own tutorials. Brief Mathematics Articles present concepts
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 Shock and Vibration Software and Tutorials  Tom Irvine, Vibrationdata.com
Free downloadable Windows software and tutorials with an emphasis on acoustics, shock, vibration, and signal processing. Much of the material is based on Fourier transforms, Laplace transforms, and other mathematical functions. The author also offers
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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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 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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 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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 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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 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  Jim Loy
A description of Eratosthenes' method for finding a list of the prime numbers from 2 to 100.
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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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 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 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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 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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 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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 Simon Plouffe  Simon Plouffe
Home page of Simon Plouffe, pi expert and originator of Plouffe's Inverter. Contains links to his articles and algorithms for his approximations of various constants.
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 Simple Minds, Smart Choices  Bruce Bower  Science News Online
The Center for Adaptive Behavior and Cognition at the Max Planck Institute for Human Development in Berlin has launched a project to explore the impact of bounded rationality on human judgment. The group focuses on what it calls "fast and frugal" formulas
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 Simulating Society  Ivars Peterson (MathTrek)
Computer simulation offers a powerful tool for studying human social behavior, contends Richard J. Gaylord of the University of Illinois at UrbanaChampaign. A theoretical physicist turned computational sociologist, Gaylord has developed models of social
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 Simulations Nab Proteinfolding Mistakes  Ivars Peterson  Science News Online
The human body manufactures thousands of different proteins, which act as enzymes, structural elements, or carriers. Each protein starts out as a long strand that must fold itself into the proper shape to perform its specific function. To gain insights
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 Simultaneous Perturbation Method for Optimization  James C. Spall
A site devoted to a powerful method for optimization of processes dependent on more than one variable. The method pertains to "stochastic optimization," that is, optimization in the presence of random variation (such as measurement noise). The site provides
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 SINUS transfer  University of Bayreuth
Spurred by the outcome of the Trends in International Mathematics and Science Study (TIMSS), Germany launched a nationwide "model programme for increasing efficiency in mathematics and science education." Between 1998 and 2007, more than 1800 of the
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 Sir William Rowan Hamilton  D.R. Wilkins; School of Mathematics, Trinity College, Dublin
Material relating to Sir William Rowan Hamilton, including his letters and papers describing mathematical optics and conical refraction, dynamics, the theory of algebraic couples (complex numbers), the theory of equations, and quaternions; a memorial
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 Skill in Algebra  Lawrence Spector
An introduction to algebra, with questions that, when moused over, reveal their answers: algebraic expressions, signed numbers, adding and subtracting signed numbers, multiplying and dividing signed numbers, reciprocals and zero, removing grouping symbols,
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 Skimming A Century of Calculus  Cut the Knot!, Alexander Bogomolny
A comprehensive effort is under way to modernize instruction in undergraduate mathematics. In the November issue of the FOCUS newsletter, MAA has announced a twoyear $900,000 grant from the NSF to construct the Mathematical Sciences Digital Library (MATHDL).
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 Sliders  Cut the Knot!, Alexander Bogomolny, with Don Greenwell
A variation of the Fifteen puzzle invented by Sam Loyd in the early 1870's: puzzles on graphs, including a proof independent of Wilson's theorem that all Lucky 7 permutations are possible; and variations of Sliders, a Fifteenlike puzzle that can be played
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 Sliding Pi  Ivars Peterson (MathTrek)
"The entrance to the Downsview subway station in Toronto presents visitors with a striking vista. A vast mosaic of square tiles sweeps across a curved wall, inviting viewers to trace its lines and ponder intriguing irregularities
in its color scheme
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 Small Group Interactions (Learning and Mathematics)  Susan Bobbitt Nolen; Math Forum
In this 1991 article, "Smallgroup interactions as a source of learning opportunities in secondgrade mathematics," Yackel, Cobb, and Wood, of Purdue University Calumet, Vanderbilt University, and Purdue University, respectively, describe an experiment
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 A Small Puzzle  Joe Fields
The site offers a visual proof that the sum of the first n consecutive odd numbers is n^2, the "L"decomposition.
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 SMART Catalog  Science and Math Advancement and Resources for Teachers (SMART)
A searchable list of professional development and resource providers for mathematics, science, and technology, organized alphabetically or according to the California Math and Science Frameworks. Articles spotlight professional challenges and successes.
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 SMART: Science and Mathematics Advancement and Resources for Teachers  Los Angeles Educational Partnership
A program designed to help teachers in Los Angeles County (California, USA) develop their professional teaching skills and content knowledge. Links for Teachers, Students, Businesses and Institutions, Parents, and Community Members. Includes the SMART
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 Só Matemática  Só Matemática
Material para ensino fundamental, médio e superior, além de provas online, biografias de matemáticos, trabalhos de alunos, um acervo de softwares matemáticos, artigos, jogos, curiosidades, histórias, fóruns de
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 Séminaire Lotharingien de Combinatoire
An electronic journal on combinatorics. Abstracts of the papers are available online, and the full articles can be downloaded.
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 Soap Films and Grid Walks  Ivars Peterson (MathLand)
A simple, physical demonstration of a mathematical truth can produce a lasting impression  one that inspires new questions and speculations. For Christopher C. Chang, a student at Henry M. Gunn Senior High School in Palo Alto, Calif., and one of 40 finalists
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 Society for Mathematical Biology
A forum for discussion of research in biology, mathematical biology, and mathematics applied to or motivated by biology  interdisciplinary research such as biophysics, computational biology, and many other similar realms. Information on membership and
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 Sociological Foundations Supporting the Study of Cultural Diversity  Hugh Mehan, Univ. of California at San Diego
In order to understand the barriers to educational equality faced by lowincome cultural and linguistic minority youth, we need to understand the ways in which social class and ethnicity interact with language and culture. This paper examines various
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 The Socratic Method: Teaching by Asking Instead of by Telling  Rick Garlikov
An example and explanation of how to use students' (including young children's) inherent reasoning abiltiy to guide them gently and easily into an understanding of difficult ideas.
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 Soft Mathematics: The Mathematics of People  Keith Devlin
Keith Devlin describes the blending of mathematics with other disciplines, an approach that is increasingly being adopted in the study of people and their actions.
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 Software's Origin  Ivars Peterson (MathTrek)
Librarian Fred R. Shapiro of the Yale Law School in New Haven, Conn., searched for the word software among scholarly journals electronically archived in the JSTOR database and found that the term software used to describe computer programs dates back
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 Solitairey Sequences  Ivars Peterson (MathTrek)
Solitaire on the computer screen  called Klondike or Idiot's Delight, this form of solitaire has resisted mathematical analysis. Partly because Klondike involves player choice, no one has yet been able to construct a mathematical model of the game from
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 Solomon Papers  Sorin Solomon
Links to papers on microscopic representation of stock markets, and some papers on clusters and multiscale, artificial creativity and novelty emergence, Vision, psychophysics, and cognitive development, Sand piles, and Lattice QCD.
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 Solving the Quintic by Iteration [PDF]  Peter Doyle, Curt McMullen
This paper, which appeared in Acta Mathematica, gives explicitly a new solution to the quintic polynomial, in which the transcendental inversion of the icosahedral map (due to Hermite and Kronecker) is replaced by a purely iterative algorithm. The algorithm
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 Solving the Quintic with Mathematica  Wolfram, Inc.
Solving the Quintic  The impossibility of solving general quintics in radicals, Tschirnhaus's transformation, Klein's approach to the quintic, Solutions based on series, Solutions based on differential equations, Equations of higher degree. Steps to
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 Some disasters attributable to bad numerical computing  Douglas N. Arnold; Institute for Mathematics and its Applications
Real life examples of what can happen when numerical algorithms are not correctly applied: The Patriot Missile failure (rounding errors); The explosion of the Ariane 5 rocket (a simple overflow); The sinking of the Sleipner A offshore platform (inaccurate
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