 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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 Operations Research Society of the Philippines
Activities, officers and members, the ORSPCorps, and links to related OR sites.
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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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 OpsResearch  DRA Systems
A collection of Java classes for developing operations research programs and other mathematical applications. The site includes documentation and tutorials, and software download is free. Also features a bookstore and related links.
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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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 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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 OpticsNotes.com  NIXAR
An index of optics and photonics tutorials, references, and resources. Fundamentals, Design, Components, Manufacture, Applications, References, Industry. Books, software, dictionary, formulas, industry directories, journals, materials, newsgroups, patents,
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 Optimal Control Theory with Applications  Elmer G. Wiens; Egwald Web Services Ltd.
Interactive Models: Applications of Optimal Control Theory using the Pontryagin Maximum Principle. Solve the rocket car, missile intercept, and harmonic oscillator (linearized pendulum) problems online. Learn how the control and adjoint (costate) variables
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 Optimalcut Web Software
Fee JavaScript optimization solver for cutting stock and bin packing problems. Specify pieces and rolls to linearly cut rectangles out of bars, pipes, tubes, metal profiles, extrusions, linear wood boards, and more (1D cutting); or sheets made of glass,
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 Optimalon Software  Denis Smirnov, Optimalon Software
Developing software for general linear programming tasks arising in educational, research and production areas. Includes an introduction to linear programming problems in the links section.
Products: GIPALS is a linear programming environment that combines
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 OptimalView  Sheela Belur
A Windows standalone program for minimizing a function by the simplex method
of Nelder and Mead. The trial software is twodimensional.
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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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 Optimization Technology Center  Argonne National Laboratory and Northwestern University
A research center dedicated to optimization problems. The "optimization tree," with descriptions of the different subfields of numerical optimization; interactive demonstrations and case studies, including the diet problem and minimum surface area; linear
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 Optique & Cabri  Charrier et Cortial
A collection of classic diagrams created using Cabri Géometre, reworked in Paint Shop Pro, and some have animated GIFs. Optique Géométrique (reflections and mirrors, refractions and diopters, thin lenses, optical instruments); Optique
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 OptNet  Michael Jünger; SIGOPT, Deutsche Mathematiker Vereinigung (DMV)
An electronic forum for the optimization community organized by SIGOPT under the auspices of the Deutsche Mathematiker Vereinigung (DMV). The basic services are a weekly digest containing a moderated list of contributions, a unique email address and
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 Orbifold Pinball  Yevgeniy Dodis; The Geometry Center
A game in which you roll a ball on an unusual playing field. The game board is like ordinary pinball in that it features 'bumpers' off which the ball can bounce. But in this game, the board is 'curved' in such a way that a ball barely missing the bumper
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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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 Orbit Research
Developers and manufacturers of Orion Talking Scientific calculators the TI84 Plus and the TI36X, the iBill Talking Banknote Identifier, and other "products that enable an independent lifestyle for the physically challenged"  the visually impaired
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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  Kluwer Online
A journal on the theory of ordered sets and its applications. Order occurs throughout mathematics and especially in algebra, combinatorics, geometry, model theory, set theory and topology.
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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 for Reliability, Maintainability and Availability  Harry A. Watson; Math Forum
A public domain textbook on ordinary differential equations, freely available online, by Harry A. Watson, a mathematician with the U.S. Naval Warfare Assessment Station. The entire document is available in DVI and TEX format on the Math Forum server;
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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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 O'Reilly  O'Reilly & Associates, Inc.
Computer books, software, and online publishing. Search the O'Reilly catalogue for concepts and keywords having to do with mathematics. Bookstores, conferences, software, how to order, contacts, affiliated companies.
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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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 Orig4mi  Jorge C. Lucero
Origami na ciência, tecnologia e design. Desde outubro, 2008, este profesor da Universidade de Brasília tem escrito neste blog artigos diversos sobre origami, inclusive abrigos dobráveis de bambu, origami com moléculas de DNA,
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 Origami Mathematics  Tom Hull
Information on origami and the mathematics of paper folding. With an origami math bibliography and pictures and tutorials in origami geometric construction, as well as links to other origami sites and events.
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 Origami Page  Joseph Wu
Origami is the art of paper folding. The word is Japanese, literally meaning "to fold" (oru) "paper" (kami). Links to photo galleries, information on origami, files and diagrams, other origami home pages, and areas related to origami (A paper on Molecular
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 Origami (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on the Japanese art of paper folding, obviously geometrical in nature. Some origami masters have looked at constructing geometric figures such as regular polyhedra from paper. In the other
direction, some
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 Original Lesson Plans  Mathematics  Thirteen/WNET New York
Original Webbased activities developed by Thirteen Ed Online Master Teachers. Each lesson consists of an overview with learning objectives, procedures for teachers, and "organizers" for students  handouts, bibliographies, and other materials. Math
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 Orlando Sessions: Math Education Reform  Math Forum
The 1996 Joint Mathematics Meetings in Orlando, Florida featured presentations on math education reform.
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 Orlando Sessions on Interdisciplinary Math
The 1996 Joint Mathematics Meetings in Orlando, Florida featured presentations on interdisciplinary programs.
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 Orlando Sessions on PreService Teacher Ed  Math Forum
The 1996 Joint Mathematics Meetings in Orlando, Florida featured presentations on "Creating an Active Learning Environment  Preparing PreService
Teachers."
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 ORLibrary  J. E. Beasley; Imperial College of Science, Medicine and Technology
A collection of test data sets for a variety of Operations Research (OR) problems, available via emailing to o.rlibrary@ic.ac.uk a message containing the name of the required file, or via FTP/WWW using the links provided. Also at http://mscmga.ms.ic.ac.uk/info.html.
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 OR/MS Today
Online version of the magazine for members of the Institute for Operations Research and the Management Sciences (INFORMS). Current and previous issues, with full text of many articles; subscription information; software surveys; classified ads and list
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 ORNotes  J. E. Beasley
Introductory originally used in an introductory OR course at Imperial College. Topics: Introductory (basic concepts); Deterministic (data envelopment analysis, facility layout and location, graph theory, integer programming, inventory control, justintime,
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 Orthocenter  Paul Kunkel
What is significant about the orthocenter of a triangle? Why does it even have a name? This investigation was prepared for a geometry teachers' workshop. It includes a lesson handout in Word format and was written for use in a computer lab with the Geometer's
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 Oscience.info  Subash Chandra
Introductions to limits and continuity, derivatives and antiderivatives, functions and graphs, matrices and determinants, properties of triangles, set theory, basic trigonometric formulae, and trigonometric functions and identities. See also Oscience's
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 Other Maths  Jon Perry
Notes, applets, and proofs on a variety of open problems and conjectures: roots of x^p, highest power of 2 that divides ab + bc + ca, a prime product paradox, consecutive integers, (n + 1)!, Collatz, nsecting a line, the first lower digit, Fibonacci,
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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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 The Oughtred Society  Oughtred
An organization dedicated to the history and collection of slide rules. Meet William Oughtred, inventor of the modern slide rule; learn about the history and background of the Oughtred Society and its principles; join or renew membership; browse tables
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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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 Overthinking My Teaching  Christopher Danielson
Blog by a community college math teacher "interested in hard questions about teaching." Posts, which date back to July, 2009, have included "Wump hats," "An unnoticed rule for number language," "The end of word problems," "Cubeyness," "Cardinal and ordinal
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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 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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