 Number: What Is "How Many"?  B. Sidney Smith; Math Academy Online/Platonic Realms
A "minitext" introducing fundamental concepts in elementary number theory and the foundations of mathematics. Includes discussions of basic set theory; natural numbers; integers; rational, irrational, and real numbers. Also gives a brief list of suggested
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 Numeracy and Quantitative Literacy  EXTEND  Perspectives in Mathematics Education
Links to articles on diverse views on the quantitative demands of today's society and the relation of quantitative literacy to mathematics education.
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 Numeracy in the News  The Mercury/University of Tasmania
Newspaper articles collected from the Tasmanian (Australia) metropolitan daily newspaper, The Mercury, to represent the five areas of the Chance and Data curriculum (Data Collection and Sampling, Data Representation, Chance and Basic Probability, Data
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 Numerical Analysis  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to numerical analysis: the study of methods of computing numerical data. In many problems this implies producing a sequence of approximations; thus the questions involve the rate of
convergence, the
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 Numerical Analysis Digest Search Interface  Netlib
The NA Digest is a collection of articles on topics related to numerical analysis and those who practice it. All issues are indexed using Glimpse. To execute a search, enter a phrase or word into the form and choose the appropriate settings for your query.
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 NYC HOLD  Bas Braams and Elizabeth Carson, editors
Honest Open Logical Debate (HOLD) on Mathematics Education Reform addresses mathematics education in the New York City schools. Organized into Issues in Mathematics Education, Curriculum Reviews, Standards, New York City Issues, Call to Action, NYC News
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 Occam Press  Peter Schorer
"The skeptical mathematician is invited to improve upon the current implementations of the 3x + 1 strategy...." In addition to the Collatz conjecture, Schorer offers a simple proof of Fermat's Last Theorem, articles on Occam's Razor and programming,
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 Occupational Outlook Quarterly Online  U.S. Bureau of Labor Statistics (BLS)
A journal about jobs and careers covering new, emerging, and unusual occupations, training opportunities, salary trends, results of new studies, etc. Includes summaries and excerpts from articles, with full text available for download in PDF format and
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 Oceania  Mathematics and the Liberal Arts  Todd Hammond
Notes on published articles: a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and on the connections between mathematics and other disciplines.
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 Office for National Statistics  Government Statistical Service, United Kingdom
The United Kingdom agency that coordinates national statistics. Tables of key social, economic, and environmental data, press releases, catalogue of publications, articles, and a newsletter. Information about the British census, including articles in
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 Of Men, Mathematics, and Myths  Keith Devlin (Devlin's Angle)
"With the Unabomber now firmly implanted in the public psyche as "a mathematician," the caricature of the mathematician as the misunderstood, antisocial loner has received a considerable boost. That much of mathematics these days is done by two or more
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 Of What Does Mathematical Knowledge Consist?  Annie and John Selden; Mathematical Association of America
Answers to epistemological questions such as "Does mathematical knowledge consist of competencies, or in seeing connections between mathematical concepts and results, or between various representations of a single concept?" Sections include Kinds of Mathematical
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 Old and New Arithmetic  Ivars Peterson (MathLand)
"Three merchants have invested their money in a partnership..." This problem appears in a mathematics textbook known as the Treviso Arithmetic. The original book, written in a Venetian dialect, had no formal title, and its author is unknown. Treviso is
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 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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 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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 On Constructivism  Susan Hanley
"The constructivist approach opens new avenues for learning as well as challenges for the teacher trying to implement it." Hanley outlines problems in traditional teaching methods, describes constructivism as a possible solution, and reviews research
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 On Deciding Whether a Surface is Parabolic or Hyperbolic [PDF]  Peter G. Doyle
An application of Rayleigh's method to the classical type problem for Riemann surfaces, which is really just the same random walk problem, only instead of walking around on an infinite graph the walker is diffusing around on a surface. The aim will be
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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 size fits all?  Mike Robison; Mathematics Dept., Michigan State University
Age based tracking versus ability grouping in elementary school mathematics. A research paper on ability and age grouping that reviews the literature and makes suggestions for math education.
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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 Innovation Institute (OII)  Ferdi Serim
The OII provides educators with a learning environment to support integrating the Internet into their individual teaching styles, offering a combination of online and onsite collaborations in which participants develop projects to use in their classrooms.
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 Online journal publication: two views from the electronic trenches  Jonathan Borwein (CECM), Richard Smith (CPROST)
A report on the experiences of two sets of scholarly publications, the Canadian Mathematical Society and the Canadian Journal of Communication, during their adoption and deployment of new electronic media, drawing on the authors' firsthand experience
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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 Bass Note of a Schottky Group [PDF]  Peter G. Doyle
Using a classical method from physics called Rayleigh's cutting method, Doyle proves the conjecture of Phillips and Sarnak that there is a universal lower bound L2 > 0 for the lowest eigenvalue of the quotient manifold of a classical Schottky group,
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 On the Evolution of Islands  Doyle, Mallows, Orlitsky, Shepp
On islands and seas: an island is a maximal set of adjacent marked cells in a ring or row; a sea is a maximal set of adjacent unmarked cells. An inductive proof and a countingargument proof. A paper that appeared in the Israel Journal of Mathematics.
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 On the Horizon (OTH)  School of Education, University of North Carolina (UNC)
OTH Online: the electronic version of the print publication, with the full text of prior volume years. Also the HORIZON mailing list, seminars and workshops, conferences, and presentations to explore and extend the educational community's thinking about
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 On the Minimax Sphere Eversion  Rob Kusner, Mathematics and GANG, Univ. of Massachussetts at Amherst
A brief paper describing the evolution of the animation of the minimax sphere eversion. Does not include the animation itself.
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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 the Teeth of Wheels (Computing Science)  Brian Hayes, American Scientist
A little history on the importance of gears in the history of computing and the importance of computing in the history of gears. "Designers of gear trains have not merely borrowed ideas from mathematics but have also developed some of those ideas on their
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 Operations Research, Mathematical Programming  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to operations research, which may be figuratively described as the study of optimal resource allocation.
Depending on the options and constraints in the setting, this may involve linear programming,
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 Operator Algebra Resources  N. Christopher Phillips
Lists of some resources useful to mathematicians working in the subject of operator algebras. General operator algebra sites and publications, information on regular series of conferences, and some important general mathematical resources.
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 Operator Theory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to operator theory, which studies transformations between the vector spaces studied in Functional Analysis,
such as differential operators or selfadjoint operators. The analysis might study the spectrum
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 Optics2001
Online optical library with links to papers, theses, and articles on optics for beginner level to researchers. Contents include: General Optics; Optical Detectors; Optical Fibers; Image Processing; Design Techniques; Optical Elements; Optical Instruments;
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 Optics, Electromagnetic Theory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to optics, electromagnetic theory: the study of the propagation and evolution of electromagnetic waves,
including topics of interference and diffraction. Besides the usual branches of analysis, this
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 Orbits and Gravitation  MacTutor Math History Archives
A hypertext essay covering Copernicus through Poincaré, LeviCivita, and Birkhoff, with References.
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 Order, Lattices, Ordered Algebraic Structures  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to ordered sets. Ordered sets, or lattices, give a uniform structure to, for example, the set of subfields of a field. Various special types of lattices have particularly nice structure and have applications
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 Ordinary Differential Equations  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to ordinary differential equations, equations to be solved in which the unknown element is a function rather than a number, and in which the known information relates that function to its derivatives.
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 Ordinary Differential Equations Project  Blanchard, Devaney, Hall; Boston University
This project included the development of a textbook (publisher Brooks/Cole Publishing Co.) as well as various workshops on teaching differential equations. Instructors manuals and selected articles are available from this site: "Teaching Differential
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 The Organic Mathematics Project  Centre for Experimental and Constructive Mathematics (CECM)
A collaborative research project involving a number of researchers at the Centre for Experimental and Constructive Mathematics (CECM). Involves in part the development of WWWbased and Mapleassisted tools for document annotation and math activation.
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 Organic Mathematics Workshop: The Proceedings  Borwein, Borwein, Corless, Jörgenson, Sinclair, eds.
Proceedings of a 1996 workshop held at Simon Fraser University, Vancouver, Canada. Speakers (top experimental and computational mathematicians); their articles, with equations, code, photos, videos, and annotations; and related resources and links. Invited
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 Orthogonal Polynomials, Integral Transforms and Solutions for Dynamics of Multilevel Systems  Vadim Zelenkov; International Sakharov Environmental University
Papers and preprints by a small group (Savva, Mazurenko, Zelenkov) that studies multiphoton excitation of molecules by infrared laser radiation in an attempt to find analytic solutions of the dynamic equations using miscellaneous orthogonal polynomials
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 Ostrich Llama Count  Examining Solution Methods  Suzanne Alejandre
Activity, alignments, directions, extensions, and activity sheets that detail five ways to solve the Problem of the Week (PoW) "Ostrich Llama Count." Originally published in the March, 2013, issue of the CMC ComMuniCator, journal of the California Mathematics
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 The Other Crisis in American Education  Singal (Atlantic Monthly)
A look at potentially high achievers whose SAT scores have fallen, and who "read less, understand less of what they read, and know less han the top students of a generation ago." Includes statements like "schools that had 'severely declining test scores'
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 Overcoming Greatness: The Decline and Recovery of British Mathematics in the PostNewton Era  Robert Bruen; Harvard University
An historical essay on Newton and Leibniz, British Progress, European Progress, and the story of the overthrow of Newton's notation at Cambridge. Includes a bibliography.
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 An overview of Babylonian mathematics  MacTutor Math History Archives
Linked essay exploring the arithmetic and geometry of the Babylonians, who lived in Mesopotamia, a fertile plain between the Tigris and Euphrates rivers. The Babylonian civilization replaced the Sumerian civilisation and the Akkadian civilisation; this
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 An overview of Egyptian mathematics  MacTutor Math History Archives
Linked essay on the development of the Egyptian number systems, and the arithmetical methods they devised to work with their numerals. With references and other related web sites.
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 An Overview of IMP Years 1 and 2  Kim Mackey
An indepth review of the Interactive Mathematics Program (IMP) by a teacher. Contents include: Introduction: Why be concerned about IMP? Brief Synopsis of Year 1 and Year 2 of the IMP curriculum; A more indepth look at Year 2 IMP unit "Solve it!"; A
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 An overview of Indian mathematics  MacTutor Math History Archives
Linked essay on the contributions of Indian mathematics, in particular the number system invented by the Indians, on which much of mathematical development has rested. With references and other related web sites.
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 Overview of the History of Mathematics  MacTutor Math History Archives
Linked overview from the Babylonians through topics from the twentieth century, with additional sections on notation and communication, brilliant discoveries, how we view history, and a challenge, as well as a 700item general bibliography.
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