- Moment of Truth - Keith Devlin (Devlin's Angle)
"Just what do we mean by a 'proof'? It seems that mathematicians - and to avoid generating too many letters of complaint, let me hasten to rephrase that as 'we mathematicians' - are somewhat schizophrenic when it comes to answering this question. When
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- Monocosm: Introduction to Linear Xenology - Vladimir Trifonov; American Mathematical Society (AMS)
A Topos-Theoretic Approach to the Foundations of Physics. The Four-Dimensionality Problem: Why does observable spacetime look four-dimensional? is related to the Compactification Problem. The Effective Metric Signature Problems: Why is the metric of signature
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- Monty Hall Dilemma - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A full discussion (including simulation) of the famous "three doors" problem, also known as the Game Show problem.
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- The Most Common Errors in Undergraduate Mathematics - Eric Schechter
Errors in communication: teacher hostility, student shyness, bad handwriting, not reading directions, loss of invisible parentheses, terms lost inside an ellipsis; Algebra errors: sign errors, everything is additive, everything is commutative, undistributed
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- Mr. Myers' Classroom - Nathan Myers
Read the puzzle of the week and then submit your answers online. Other "brain busters" include matrix logic puzzles, featuring ready-made charts. Explore and identify fraction bars with JavaScript, or geometry with Java applets. Also, fact sheets and
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- MSMS World of Logic - Claudia Carter; Mississippi School for Mathematics and Science (MSMS)
MSMS Logic and Game Theory is a study of logic, symbolic notation, truth tables, simple game theory, and problem-solving strategies. Links to significant figures in the world of logic: Lewis Carroll, George Boole, Giuseppe Peano, Von Neuman, Willard Van
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- m@th IT
A "platform to promote, propagate, and mediate applied mathematics and computer sciences," with emphasis on cryptography, number theory, financial mathematics, logic and knowledge representation, and quantum computation. In particular, m@th IT offers
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- MUltlog - Gernot Salzer et al.
MUltlog is a system that takes as input the specification of a finitely-valued first-order logic and produces a sequent calculus, a natural deduction system, and clause formation rules for this logic. All generated rules are optimized regarding their
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- MUltseq - Gil, Salzer
MUltseq is a generic sequent prover for propositional finitely-valued logics. It is intended as companion for MUltlog, which computes optimized sequent rules from the truth tables of a finitely valued logic. MUltseq uses these rules to construct derivations
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- The n-Category Café - John Baez, David Corfield, and Urs Schreiber
A blog devoted to "that heady interface between physics, mathematics and philosophy." Read posts, many with MathML, that date back to August, 2006.
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- Neutral and Non-Euclidean Geometries - David C. Royster; University of North Carolina at Charlotte
Course notes that include: Origins of geometry; spherical geometry; logic and the axiomatic method; proof; Euclid's mathematical system; incidence geometry; betweenness axioms; congruence theorems; axioms of continuity; neutral geometry; theorems of continuity;
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- New Foundations - Randall Holmes
Developing site for the set theory "New Foundations," first introduced by W.V.O. Quine in 1937. A refinement of Russell's theory of types based on the observation that the types in Russell's theory look the same, as far as one can apparently prove. Site
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- New York Regents Exam Prep Center - Oswego City School District
A site dedicated to assisting high school students in preparing for the "new" New York State Math A Regents Examination. Covers Algebra, Geometry, and Algebra II/Trig. The materials featured for each topic include: general review/formula sheet, Regents
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- Nils Ahbel - Deerfield Academy, Deerfield, MA
Access Ahbel's Blackboard courses as a guest to preview his teaching resources and download Excel files in algebra, functions, statistics, and trigonometry.
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- Nonstandard Analysis and the Hyperreals - Jordi Gutierrez Hermoso; Math Forum, Ask Dr. Math FAQ
An essay introducing the most basic ideas of nonstandard analysis and the hyperreal number system. Contents: A Very Brief History of Almost-Nothing and More-than-Everything; The Hyperreal Wish-List; Construction of the hyperreal numbers; Hyperreal arithmetic;
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- NSDL Middle School Portal: Math Pathway - NSDL; the Ohio State University
A middle school portal into NSDL's math resources, browsable by topic, or choose a pre-selected set of resources on given subjects.
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- Numberplay - The New York Times
Mathematical, logical and scientific puzzles, with solution "recaps." The posts, by Gary Antonick and Pradeep Mutalik, have included "Surreal Hat Tricks," "The Puzzles of Pickover," "Prime Rib at Hogwarts," "Nim for (a) Change," "Phi - The Magic and the
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- Numericana.com - Gérard P. Michon
The online companion of Numericana, this site contains excerpts from Michon's book, including the entire glossary of scientific terms. Browse an index with pithy summaries, browse by popularity, or search nearly two hundred of his "final answers" of readers'
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- Nummňlt - Maurici Carbó Jordi
Java applets: an area "workshop," which explains area and division by converting numbers in area units; an architect's toy blocks, with gravity; connecting and programming elementary logic (in the form of pipes with light bulbs signifying true sentences);
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- Nummòlt - Maurici Carbó Jordi
Math teaching resources built by architects include base 10 block manipulatives; a block construction toybox; a logic construction toybox; an area workshop; and MathCats balance. See, in particular, Nummòlt's open-ended obbl & math toys: adding
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- NuPrl Proof Development System - Cornell University, Ithaca, NY
A tactic-based proof assistant developed over the last 15 years at Cornell University. Its features include: very expressive logical language based on Martin-Lof type theory, extensive library of formal mathematics and automata theory, possibility of
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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-Line Logic Book - Johan Mårtensson
An introductory text, with accompanying Java teaching tools for specific topics. Includes an introduction to logic itself and chapters on ontology and semantics.
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- Onlineunitconversion.com
Oover 225,000 conversions, togethr with explanations of their history and use.
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- An Outline of the Proof of Gödel's Incompleteness Theorem - Michal Wojcik
On this page we give an outline of the proof of Goedel's Incompleteness Theorem. We construct a statement in set theory such that it is not a theorem and its negation is not a theorem. What we show on this page is not a presentation of the proof that
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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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- Paradox (Encarta Encyclopedia 2000) - Microsoft Encarta Online
Paradox, in logic and mathematics, an apparently contradictory conclusion that is derived from what seem to be valid premises.
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- Pass Calculus - Le Site PassCalculus.com
Calculus question solution service. Solutions offered via email, phone, or fax; quotes are free; payment by credit card. Sample solutions and FAQ online.
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- Pattern Based Reason - Alan Selby
This book surveys rule and pattern based thought in daily life, society, science and technology. The first chapters show how reliable implication rules can be employed one at a time or one after another to arrive at conclusions. The middle chapters describe
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- Penn State University Mathematics Department
Course home pages and instructional material; seminars, colloquia, and conferences; and subject area pages for Penn State research centers, with preprints and links to other resources on the Web: Algebra and Number Theory; Dynamical Systems; Mathematical
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- Perfect Symmetry Number Theory - Derek Nalls
A fundamental, educational exposition of a nonstandard number theory based upon perfect symmetry (in contrast to broken symmetry) modelled throughout arithmetic, algebra, analytic geometry, analytic trigonometry and calculus.
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- Permadi.com - F. Permadi
Java and Flash applets: logic games, drawing and pattern-making programs, Conway's Life, and more arcade-style offerings. Also includes tutorials in using Flash and a graphics gallery.
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- Perplexus - flooble
A large archive of mathematically inclined puzzles and problems displayed by category. Includes logic, number theory, geometry, probability and other problems. All are rated by difficulty and quality and discussed in depth by visitors. Most with solutions.
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- Personalized Programming Service Inc.
Educational software for teachers and students. Topical software in Math, English, Social Studies, and Science, as well as Quizmaker and Testmaker programs. Download demos and upgrades, browse the products, or order on site.
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- Physics Forums
Discussions emphasize physics, but "PF" also includes an entire directory on mathematics: General Math; Calculus & Analysis; Differential Equations; Linear & Abstract Algebra; Topology & Geometry; Set Theory, Logic, Probability, and Statistics;
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- Pico Firme Bago - Evan M. Fuchs
A Flash-based logic/deduction game, similar to Mastermind. Originally created as an online version of a game used in the author's 5th grade class.
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- Plastelina Logic Games - Plastelina
Free Flash games include classic constrained "crossing" problems, such as the puzzle of ferrying a wolf, a sheep, and a head of cabbage across a river in a boat that only holds any two of them at once, without leaving the wolf and sheep alone in each
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- Postulates and Theorems of Boolean Algebra - Julie Kenrow; Santa Clara University, Santa Clara, CA
Five postulates (identity, complement, commutative law, associative law, distributive law); and six theorems. Supplementary material for a course in electrical engineering (Logic Design).
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- Powell's Books
Located in Portland, Oregon, USA; the largest independent bookseller in the United States, specializing in technical books and new, used, hard-to-find, and antiquarian titles. An extensive subject and keyword list is available - search database of titles,
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- Powersums, Fermat, Waring; Quotes, History... - Nico F. Benschop
Links to papers on the ideas of Fermat, Waring, Goldbach, Cantor, Hensel, Hasse-Minkowski, and Selmer, and the following mathematical concepts: semigroups, sequential logic synthesis, cubic roots, and state machines and their sequential closure. With
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- The Practice of Logical Frameworks (1996) - Frank Pfenning
A survey article discussing the history of work on logical frameworks and their current open problems. Deductive systems, given via axioms and rules of inference, are a common conceptual tool in mathematical logic and computer science. They are used to
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- Preuve Proof Prueba
A newsletter in French, Spanish, and English, the theme of which is teaching and learning mathematical proofs. Includes an extensive bibliography consisting of books, chapters in books, journal articles, and theses.
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- Principia Cybernetica Web - Turchin, Joslyn, Heylighen, Bollen, eds.
Principia Cybernetica Project (PCP) is an international organization that tries to tackle age-old philosophical questions with the help of the most recent cybernetic theories and technologies. The Project's aim is the computer-supported collaborative
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- Principia Mathematica - A.D.Irvine; Stanford Encyclopedia of Philosophy
The philosophy encyclopedia's entry on Principia Mathematica, the landmark work on mathematical logic and the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell. Next to Aristotle's Organon, it is the most influential book
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- Principia Mathematica II - Michael Meyling
An open source project attempting to present mathematical knowledge in a formal, correct form. It includes a proof verifier which checks a mathematical proof written in a certain formal language and an HTML converter for making mathematical HTML pages.
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- The Prisoner Problem - Anne Arundel Community College
A classic logic problem about three prisoners, each of whom tries to determine what color his own hat is in order to be set free.
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- A Problem Course in Mathematical Logic - Stefan Bilaniuk
A freeware mathematics text, available by anonymous ftp in LaTeX, PostScript, and PDF formats, for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems,
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- Problem Solving in Mathematics - Jim Wilson; Univ. of Georgia
Problems in algebra, geometry, conversion, cryptarithm, "mean," trigonometry, and a mixture of all, many with comments and solutions, from a course given in the Dept. of Mathematics Education at the University of Georgia. The site also provides links
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- Problem Solving Island - Samuel A. Rebelsky
Challenging open-ended word problems on the topics of games, such as Blockade, Finger Multiplication, and The Word Pyramid; puzzles such as Error Correction, Error Detection, The Fake Coin, Friday the 13th, and Leap Birthdays; and problems based on figures,
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- Problems with a Point - Education Development Center, Inc. (EDC)
A collection of problems designed to help students in grades 6-12 learn new mathematical ideas by building on old ones. Varying in difficulty and approaches, these problems are useful for teachers, students, parents, math clubs, home-schoolers, and others.
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