 Oliver Knill
Research, teaching, and media by this preceptor in Harvard's math department. Knill began in dynamical systems, tackling first ergodic and spectral theoretical questions, then probability theory and elementary number theory. This led to his "passion for
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 On Beyond Newton: from Simple Rules to Stability, Fluctuation, and Chaos (Serendip: Complex Systems)  Bryn Mawr College
An interactive exhibit on homeostasis/autonomy/chaos centered around population dynamics. The phenomenon of rules giving rise to not only order but also disorder, and, beyond that, to previously unknown forms of order, is the terrain currently being explored
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 Once in a Millennium (Math Chat)  Frank Morgan, MAA Online
Challenge: The year 2000 can be represented as the sum of consecutive integers:
2000 = 398 + 399 + 400 + 401 + 402. The year 2001 can be represented as the sum of consecutive integers: 2001 = 1000 + 1001. In fact, every year in the millennium from 2000
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 OnePage Proof of Fermat: Critique (Math Chat)  Frank Morgan, MAA Online
Critique the following short proof of Fermat's Last Theorem sent in by
reader Rob Connelly. (In perhaps the biggest mathematics news of the century, Andrew Wiles recently came up with a very long and complicated proof of this 350year old problem.) Answer:
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 One Trip to the Attic? (Math Chat)  Frank Morgan, MAA Online
In the lobby of a hotel there are three on/off switches. One is attached to a light bulb on the third floor; the other two are attached to nothing at all. You may work the three switches as often as you please. How many times do you need to visit the
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 On Four 4s and Speed Limits (Math Chat)  Frank Morgan; Christian Science Monitor
Can you get past 30 in forming numbers 0, 1, 2, 3, ... from four 4s and the standard mathematical operations +,  , x, /, decimal point, square root, powers, and factorial(!)?
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 OnLine Encyclopedia of Integer Sequences  The OEIS Foundation Inc.
Before publishing that new sequence you have just found, you might want to check here to see if it's already been discovered. Directions for how to look up a sequence in the table, abbreviations used, sending in a new sequence; how to look up a reference
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 Online games and activities at Syvum  Syvum Technologies, Inc.
Online activities for practicing practice addition, subtraction, multiplication, division, fractions, algebra, and word problems. Workbooktype activities are interactive, with automatic generation of tests, immediate grading, and a new set of problems
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 Online Ideas Maths Resources  James Bancroft
Problems in Microsoft Word, HTML, and JPG, organized into general resources; addition and subtraction; multiplication and division; numbers and the number system; fractions, decimals, percentages, ratio, and proportion; real life problems; measure and
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 Onlineindiaeducation  Atul Mittal
Page after page of questions with links to view answers and explanations: aptitude (area, series, "problems on trains," boats and streams, odd man out, and more), puzzles (sudoku, number, logical, clock, etc.), and reasoning (cause and effect, arithmetic,
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 online intervention.com  Pearson Education
onlineintervention.com assesses students' performance in specific skills and prescribes customized intervention activities, automatically generating summary reports for both teachers and students. Register to take online quizzes, play games, and use learning
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 Online Math Applications  Leung, Jiang, Jiang, Chiu, Klopfer, Chiu; ThinkQuest Junior
Activities, examples, problems, and online quizzes about math applied to real world situations in investing (a stock market simulation game), music (classical MIDI files), history (biographies and anecdotes), science (astronomy, computers, 'math in the
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 Online Math Education  Yordan Petrov Petrov
Math tutorials and quizzes, with some math history information as well. Includes a discussion forum. Available in English or Bulgarian.
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 Online Math Help for All  Ramachandran Seerangan
Primers and problems, a math dictionary, worksheets organized by grade and concept, and more. See in particular Seerangan's YouTube channel, where he posts narrated whiteboard videos of stepbystep solutions to specific problems.
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 Online Math Lab  Eric Bitter, Clovis Unified School District  CAL Online
Modules on fractions, decimals, and percents offer tutorials and problems for students in grades 412.
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 Online Math Tests Home Page  Elias Saab
This site has problems that help sutudents get ready for College Alegbra or Calculus. It also has problems in Geometry and Trigonometry. All the problems have complete solutions that are given when one hits the submit button. Tests covered include: MPE410,
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 Online Math Worksheets  Improving Education Inc.
Random generated K5 math worksheets  each time you load a Web page, new exercises are generated. Match the numbers; 1, 2, and 3digit addition and subtraction; multiplication and division, including long division.
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 Online Resources  Georgia Tech School of Math
Syllabi, course notes, problems, and Maple worksheets for single and multivariable calculus, linear algebra, statistics, and a Math for Management course (statistics, probability, sets, and some calculus). The site also contains sample exams for calculus
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 The Online Test Page  Elias Saab
Math and vocabulary drills, including MathCOUNTS, SAT, ACT, and Missouri MMPT questions, as well as links to relevant sites.
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 On Motivation and Understanding  Cut the Knot!, Alexander Bogomolny
Fourth in a series of columns that draw on Frank Morley's fundamental paper On the Metric Geometry of the Plane nLine  dealing with what amounts to his proof of the Trisector Theorem. Bogomolny outlines Morley's reasoning first and then supplies necessary
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 On the 3x + 1 Problem  Eric Roosendaal
Numerical data and some conjectures on this problem, also known as the Collatz problem or the Syracuse problem. All numbers up to 29,300 * 10^12 (~ 26 * 2^50) have been checked for convergence.
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 On the Puzzles with polyhedra and numbers  Jorge Rezende
Several articles in PDF format, with related links: one on a set of didactic puzzles published by the Portuguese Mathematical Society (SPM); "Jogos com poliedros e permutações", an article in Portuguese describing puzzles with polyhedra
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 On Thin Spaghetti and Nocturnal Animals  Don Cohen (The Mathman)
Function and Graphs for Children. Guess My Rule; Graphing; The Shuttle Puzzle; The Tower Puzzle; The Nautilus Shell. Sample problems with some answers from Chapter 6 of Don Cohen's worksheet book.
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 On This Day in Math  Pat Ballew
Mathematically significant events, births, deaths, and more, posted every calendar day. Ballew's blog reveals his thoughts on teaching math. His links and explanations written using The Geometer's Sketchpad include triangle medians; angle bisectors in
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 OOG: the Object Orientation Game  MCM Productions
MCM Productions' first publicly released software application. This 4in1 tiling puzzle game for the MSWindows environment allows players to test their problem solving ability with over 300 puzzles, including Tangrams, Pentominoes, Hexagons and Polyominoes.
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 .oO worksheeps  Felix Heckert
Generate worksheets of customized math exercises, complete with solutions: basic operations with integers, negatives, and fractions; binomial and quadratic formulas; partial roots; percent calculation; curve sketching; metric; derivations; antiderivatives;
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 OpenEnded Math Problems  Gwenn Holtz and Mary Lee Malen, Levering School and the Franklin Institute
An eightmonth slate of openended problems for middle school students to solve in preparation for standardized testing. The authors have composed and selected problems that lend themselves to multiple solution paths, and then organized them into three
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 OpenIntro  David Diez and Chris Barr, CoFounders
The OpenIntro Statistics textbook the inaugural effort from these makers of educational products that "are free, transparent, and lower barriers to education"  comes with data sets for the statistics software package R; normal, t, and chisquare probability
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 Open Middle  Johnson, Nanette; and Kaplinsky, Robert
"Open middle" problems, hints, and answers, all aligned to the Common Core State Standards (CCSS). Introduced by Dan Meyer, these kinds of math challenges have a "closed beginning," meaning that they all start with the same initial problem; a "closed
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 Open Problem Garden  Matt DeVos and Robert Šámal
A collection of unsolved problems  mainly, graph theory, combinatorics, and number theory. A wiki for each open problem includes relevant bibliographical citations, importance rating, and recommendation for undergraduates. Navigate by math subject,
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 Open Problems for Undergraduates (DIMACS)  Robert Hochberg, Center for Discrete Mathematics and Theoretical Computer Science, Rutgers Univ.
A collection of open problems in Discrete Mathematics in the areas of Graph Theory; Combinatorial Geometry; Geometry/Number theory; and Venn Diagrams, currently being researched by members of the DIMACS community. These problems are easily stated, require
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 Open Problems in Dynamical Systems  Dept. of Mathematics, State Univ. of New York at Stony Brook
A collection of papers outlining unsolved problems in dynamical systems.
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 Open Problems in Dynamical Systems & Ergodic Theory  Sergiy Kolyada
This collection of problems originated in the Katsiveli2000 Open Problems Session (Chairman  Benjamin Weiss). New problems are being added. Copies of the page are also at http://iml.univmrs.fr:80/~kolyada/opds/ and http://www.math.iupui.edu/~mmisiure/open/.
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 Open Problems  Jeff Erickson
Open problems, mostly in geometry, including folding, combinatorial, and algorithmic problems. Contents include: Existence Problems: Does Object X exist?
Combinatorial Problems: How complex is Object X? Algorithmic Problems: How fast can Problem X be
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 Open Problems (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on open problems in geometry: antipodes; bounded degree triangulation; centers of maximum matchings; chromatic number of the plane; combinatorial complexity of spheres; covering points by rectangles; cube
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 Operations Research  J. E. Beasley
ORNotes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). Beasley includes practice questions ("tutorials"), links to other web resources, and past exams.
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 Optical Illusions (SandlotScience.com)  SandlotScience
Interactive explorations of optical effects, illusions, distortions, animations, artwork, stories, PDF projects, games, and more. Impossible objects include columns, an endless staircase and animated stairs, Java triangle models, an interlaced tribar,
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 Optimization Links  Tom Cavalier; Industrial and Manufacturing Engineering, Penn State Univ.
Links to online information on various aspects of optimization; interactive guides/case studies; optimization software/test problems; and other sites. Also general operations research sites; OR/Optimization people. Location/Routing/ Conference Information;
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 The Orbifold Shop (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A symmetry project: the Orbifold Shop offers a free coupon for $2.00 worth of parts, installation included, to anyone acquiring a new orbifold. There are only a few kinds of features for twodimensional orbifolds, but they can be used in combinations:
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 The OU Calculus I Problem Archive  Dept. of Mathematics, Oklahoma University (OU)
Sample problems, with hints, answers, and "the grisly details": 1. Functions, calculus style; Graphs; Machine graphics; What is a function?; A field guide to elementary functions. 2. Amount functions and rate functions; The geometry of derivatives; The
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 Overview of "Mathematician's Secret Room"  Hisanori Mishima
Challenges to unsolved problems in Number Theory, some translated into English from the Japanese.
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 Packing Pentominoes  Mark Michell
For rectangles with a given ratio of height to width, what is the smallest rectangle that will allow the construction of a complete set of pentominoes?
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 Packing Videotapes  NASA Lewis Learning Technologies Project
Roger had to pack videotapes 10 to a box. If he had 178 tapes of one kind and 121 of another kind, how many boxes would he need in order to pack them all and not mix the different types? A detailed answer is provided. From NASA's 9th Grade Math Proficiency
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 Paginedimatematica  Bruno Tomaino
In Italian: Analisi, trigonometria, equazioni differenziali, test a risposta multipla.
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 The Pai Intersect  Jimmy Pai
Blog by an Ottawa (Canada) secondary mathematics teacher and graduate student in education. Posts, which date back to August, 2012, have included "Understanding Fraction Division #2  Part 1," "$100 Tablet Project," "Spiraling through the curriculum,"
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 Palindromic Numbers and Other Recreational Topics  Patrick De Geest
Many odd facts about big (and little) numbers, including circular primes and palindromic triangulars, tetrahedrals, squares, cubes, and primes. Also assorted odd puzzles, etc.
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 Panthera's Puzzle Contest  Dr. Amy Galitzer; Puzzle University
A weekly contest of math, logic, and word puzzles sponsored by the American Mathematical Society and the University of Maryland Mathematics Department. You can submit your own puzzle for the next contest by signing up to participate, or simply read the
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 The Paper Challeran  Ryosuke Ito & TOSS
Starting with a score of 1, trace a route through the Paper Challeran. Add to, multiply, or subtract from this score, as indicated at every edge along the way. Compete by registering scores online. Numbers around each block change every month. Find rules,
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 Pascal's Triangle using Clock Arithmetic  Jay's Corner
Exploring Pascal's triangle when the modulus is a prime; when the modulus is a power of a prime; and when the modulus has at least two different prime divisors. From mod 2 to mod 12, illustrated. (See also Part II.)
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 Passalgebra.com
Pass algebra with this online study guide. Practice with hundreds of problems, with answers worked out step by step. Examples of study guide and exercises provided. $27 for 1 year; stepbystep instruction for $2.50/problem.
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