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  Selected Sites   (see also All Sites in this category)

  1. The Beginnings of Set Theory - MacTutor Math History Archives
    Linked essay describing the rise of set theory from Cantor (with discussion of earlier contributions) through the first half of the 20th century, with another web site and 25 references (books/articles). more>>

  2. 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 inclusion-exclusion principle, partially ordered sets, and so on. This is perhaps as much of set theory as the typical mathematician uses. Indeed, one may "construct" the natural numbers, real numbers, and so on in this framework. However, situations such as Russell's paradox show that some care must be taken to define what, precisely, is a set. Axiomatic Set Theory studies the axioms used to describe sets. While alternatives have been proposed (for example the von Neumann-Bernays-Godel and Morse-Kelley formulations), most sets of axioms for Set Theory include the Zermelo-Frankl axioms (ZF). Again, within this formulation one may define the natural numbers, the real numbers, and so on, and thus in principle carry out most ordinary mathematics. This formulation is rich enough to prove, for example, the Schoeder-Bernstein theorem (If X and Y are isomorphic to subsets of each other, then they are isomorphic). History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>


 
  All Sites - 75 items found, showing 1 to 50

  1. 0h h1 - Martin Kool
    A "little logic game" related to Takuzu and Binario: complete grids of 4 × 4, 6 × 6, 8 × 8, or 10 × 10 so that all rows and columns have an equal number of each color, but none has three adjacent tiles of the same color or shares the ...more>>

  2. Algebra and Trigonometry Web Site: Semester 1 (MQ5) - Gary Jaye, Department of Mathematics, Stuyvesant High School
    Algebra and trigonometry exams, dating back to 1995, given by a Stuyvesant High School mathematics teacher. Answers accompany all the tests, making them suitable for practice, review, or self-assessment. ...more>>

  3. Bell Package - Jacek Kisynski
    This package provides functions which are useful while dealing with set partitions. We provide (hopefully) fast methods for sets of size up to 15 and methods with no set size restrictions which use BigInteger objects. The later ones are constrained ...more>>

  4. The Boise Problem Book - Marion Scheepers; Dept. of Mathematics, Boise State University, Boise, ID
    Combinatorial games and set theory. Chapters include: Covering games and Memory; Peculiar sets of real numbers and games; Gdelta properties and games; The precipitous ideal game; Cardinal numbers related to the real line; Embedding problems; Gaps; The ...more>>

  5. Books: Professional & Technical: Professional Science: Mathematics - Amazon.com
    Browse bestselling math books from the Professional and Technical Bookstore at Amazon.com, in such categories as Applied; Chaos & Systems; Geometry & Topology; Mathematical Analysis; Mathematical Physics; Number Systems; Pure Mathematics; Transformations; ...more>>

  6. Bounded Set Theory - Vladimir Sazonov
    Bounded Set Theory (BST) is a weak version of the ordinary set theory. Its main feature is paying main attention to using bounded quantification (as in the ordinary everyday mathematical practice) and other analogous bounded constructs. The language of ...more>>

  7. The Cantor Set - Math Academy Online/Platonic Realms
    An article describing a paradox of infinite sets in measure theory. ...more>>

  8. Cantor's Theorem - Math Academy Online/Platonic Realms
    An article describing Cantor's diagonal argument, which proved that infinity comes in many different sizes. ...more>>

  9. Classification (SMILE) - Delores B. Wilburn, Shakespeare School
    A lesson designed to motivate students to understand classification, and to teach decision-making, how certain objects relate to the number system, and the meanings of some words used to express mathematical ideas. From the Patterns and Logic section ...more>>

  10. Combinatorics, Probability & Computing - Cambridge University Press
    Now published bimonthly, the journal covers combinatorics, probability theory, and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial ...more>>

  11. A compendium of NP optimization problems - Crescenzi & Kann
    A continuously updated catalog of approximability results for NP optimization problems. Because no NP-complete problem can be solved in polynomial time (unless P=NP), many approximability results (both positive and negative) of NP-hard optimization problems ...more>>

  12. Computational Mathematics Research Group - University of Brighton
    Current areas of research include bubble dynamics, acoustics, diffusion in gels, and space plasmas. Read their bibliography of recent publications. ...more>>

  13. A Crash Course in the Mathematics of Infinite Sets - Peter Suber; Philosophy Department, Earlham College
    An introductory guide for philosophers, explaining the use of infinitary set theory. ...more>>

  14. Division by Three [PDF] - John Conway, Peter Doyle
    A formal proof that it is possible to divide by three. This assertion is easy to prove using the axiom of choice, but becomes a much more difficult problem if the axiom of choice is not allowed (as is the case here). From this proof, and the much simpler ...more>>

  15. Duke University Math Union - Jadrian Miles
    The Duke University Math Union (DUMU) writes and hosts the annual Duke Math Meet. Download PDFs of problems and solutions from meets dating back to 1998. ...more>>

  16. Exercises in Math Readiness for University (EMR) - Dept. of Mathematics and Statistics, University of Saskatchewan
    A collection of exercises with solutions/tutorials for high school mathematics topics important for university study in mathematics, sciences, engineering and commerce. Exercises at three degrees of difficulty, covering graphing, solving inequalities, ...more>>

  17. First Curriculum - Patricia Simis Lundy
    A first grade early literacy curriculum. In the Discovery Zone introduces the scientific method; Weather or Not uses grids, mapping, measurement, and number sense; see Our Big Backyard, showing the integration in the various lessons of literature and ...more>>

  18. General Mathematics, N-Z (Funk & Wagnalls Multimedia Encyclopedia) - Lycos Zone: Mathematics
    Short articles on basic mathematics, including biographical information about mathematicians, from John Napier to Zeno of Elea. ...more>>

  19. HAKMEM - Beeler, Gosper, Schroeppel; Artificial Intelligence Laboratory, MIT
    A list of math and computer-related problems, unsolved in 1972 when the list originated, compiled "with the hope that a record of the random things people do around here can save some duplication of effort - except for fun." Topics include: Geometry, ...more>>

  20. Hand Made Manipulative Instructions - Margo Lynn Mankus
    Pattern block cutouts: triangles, squares, smaller and larger rhombuses, trapezoids, and hexagons. Base-ten blocks in sets of ones, tens, and hundreds; and base-five blocks in sets of ones, fives, and twenty-fives. XY-block sets of X, X2, XY, Y, and Y2 ...more>>

  21. herp, derp, math nerd
    A Tumblr "documentary of my journey, mistakes and all," by a Canadian undergraduate double major at UC Berkeley. Posts, which date back to May, 2012, have included "mr cauchy, teach us your ways," "closed, open, and clopen: yes, it's possible," "real ...more>>

  22. Infinity: You Can't Get There From Here! - B. Sidney Smith; Math Academy Online/Platonic Realms
    A "mini-text" offering a concise introduction to the concept of infinity. Includes historical background, Cantor's set theory, and an introductory discussion of cardinality, as well as suggested reading. ...more>>

  23. Institute for Logic (Institut für Formale Logik) - University of Vienna, Vienna, Austria
    Research in the group is concentrated on axiomatic set theory, in particular: Inner models and large cardinals; Constructible models of set theory / core models; Consistency strengths; Coding; Forcing; and Descriptive set theory. Abstract Server; People ...more>>

  24. Introducing Mathematics
    This website looks at some areas of mathematics that are not familiar to most people, such as Ramsey theory and set theory, but introduces them in an uncomplicated manner. ...more>>

  25. An Introduction To Sets (SMILE) - John P. Belton, Jones Metropolitan High School
    A lesson designed to teach students to recognize the symbol for set and to demonstrate the rules for sets. From the "Miscellaneous" section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement. ...more>>

  26. Investigating LCM and GCF Using Rods - Margo Lynn Mankus
    The objective of the lesson plan Investigating LCM and GCF Using Rods is to look at the Least Common Multiple (LCM) and Greatest Common Factor (GCF) from "hands-on" pattern-building to using set theory. With teachers as the intended audience, the activity ...more>>

  27. LEARNINGlover - AfterMath
    Resources to understand "the interactions between mathematics, computer science and probability." JavaScript flash cards and implementations -- each with auto-scoring, randomly-generated problems, some with pseudocode -- include the a priori algorithm, ...more>>

  28. Light Mixer - Cary and Michael Huang
    Type "c" for cyan, "m" for magenta, or "y" for yellow, then click and drag in the grey box to draw a path of pigment in that color. Toggling the switch lets you "draw" in light on a black background: "b" for blue, "r" for red, or "g" for green. Regions ...more>>

  29. Logic and Reasoning (SMILE) - Pearline Scott, Greeley School
    A lesson designed to teach students to use logic and reasoning strategies to classify blocks by their attributes; recognize one, two and three attribute differences; use Venn diagrams to form sets and show their intersection; and use the attribute blocks ...more>>

  30. Logic and Set Theory (Mathematics Archives) - University of Tennessee, Knoxville (UTK)
    An extensive list of links to sites with information about logic and set theory, classified by level and type of resource. ...more>>

  31. M2C: Maricopa Mathematics Consortium - Alan Jacobs, Project Director
    A Consortium for creating mathematics programs in which students learn the knowledge, skills, principles, and applications they can use throughout life to become smarter employees, consumers, citizens, and learners; and to build a coalition of schools ...more>>

  32. Making Predictions (SMILE) - Lucille Chambers, Lyman Trumbull School
    A lesson designed to teach students at any level to classify and make predictions as they learn about ecology and plant life. From the Practical and Applied Math section of a collection of almost 200 single concept lessons by the Science and Mathematics ...more>>

  33. Margo Lynn Mankus - Margo Lynn Mankus
    Talks include Using Virtual Manipulatives on the Web to Develop Number Sense, Connecting Whole Number Arithmetic to Algebra: Hands-On/Number Sense Activities, and Learning About Nutrition Using the TI-73 and the Web. Also, online or downloadable classroom ...more>>

  34. Math500.com - Joe Cunningham
    Self-guided problems to solve with automated feedback based on the strategy you select from among the multiple choices presented at each step, or upon the intermediate calculation you enter. Worked examples provide additional step-by-step support. Choose ...more>>

  35. Math Celebrity - Don Sevcik
    Free online calculators and instructional screencasts in actuarial science, accounting and taxes, algebra, basic math, calculus, capital budgeting, conversions, discrete math, economics, engineering, finance, gaming, geometry, linear algebra, physics, ...more>>

  36. Math Club - Mary Kathryn Eisemann, Tomasz Jan Klosowski, Micjal Andrzej Zabicki--ThinkQuest 2000
    Brief tutorials, puzzles, and brain teasers for students aged 12-17. Some topics include: equations, trigonometry, geometry, set theory, logic, and induction. The games range from mazes to magic squares to Victorian parlor games. Students may log in ...more>>

  37. Mathematical Connections - Whittle, Luoma; Dept. of Learning Support, Augusta State University
    "Exploring the Interplay Between Mathematics and the Humanities." A forum for exploring the interplay between mathematics and the humanities, including, but not limited to, the relationship between mathematics and the arts, anthropology, history, literature, ...more>>

  38. Mathematical Logic - Department of Mathematics, Manchester University, U.K.
    There is a strong tradition in mathematical logic at Manchester. The first logician at Manchester was Alan Turing, now considered to be the father of artificial intelligence and one of the great visionaries of the twentieth century... The present group ...more>>

  39. Mathematical Logic Group - Department of Mathematics, University of Bonn
    Research in the group is concentrated on axiomatic set theory, in particular: Inner models and large cardinals; Descriptive set theory and Determinacy; Consistency strengths; and Forcing. Members, recent publications, lectures, and links. ...more>>

  40. Mathematics Applications - Arlen Strader
    Areas of mathematics for which Strader has developed Java applets: Algebra, Probability, Statistics, Set Theory, and Geometry. Statistics, developed for an undergraduate behavioral statistics class, is the most developed; algebra and geometry are aimed ...more>>

  41. Mathematics - Nancy McGough, Infinite Ink
    Infinite Ink's primary mathematical interest is foundations of mathematics, including standard and non-standard logics, set theories, and other mathematical frameworks. This page contains links to other Web resources and information on Infinity, Set Theory, ...more>>

  42. Math How-To's - FindHow: the How-To Search Engine
    How-Tos from well-recognized brand names, governmental, and educational institutions, with a particular focus on academic topics--in this case, mathematics. ...more>>

  43. maths online - University of Vienna, Austria
    A modern mathematics learning site on the Web: details of the project, persons and institutions participating, or project proposals (only in German). The Gallery consists of interactive multimedia learning units (Java applets), each of which includes ...more>>

  44. MathSource - Wolfram Research
    An extensive electronic library of Mathematica material and notebooks, with over 100,000 pages of immediately accessible Mathematica programs, documents, examples, and more. You may browse the archive or search by author, title, keyword, or item number. ...more>>

  45. Math WWW VL: Bibliographies - Dept. of Mathematics, Florida State University
    Links to bibliographies in college-level mathematics. ...more>>

  46. Math WWW VL: Specialized Fields - Dept. of Mathematics, Florida State University
    Links to sites for resources in specialized fields in college-level mathematics. ...more>>

  47. Matthew J. Saltzman's Home Page - Matthew J. Saltzman
    A study guide for basic math courses, titled "How to Survive Your College Math Class (and Take Home Something of Value)," includes sections on study skills, reading and understanding mathematics (featuring "An Equation is a Sentence," "Deriving Conditions ...more>>

  48. Melkamu Zeleke
    Melkamu Zeleke is a graduate student in combinatorics. His papers and solutions to some problems from American Mathematics Monthly and Math Magazine may be downloaded as TeX, .dvi, or PostScript files. The code for accompanying Maple packages RADON, ...more>>

  49. The Mutilated Checkerboard in Set Theory - John McCarthy
    An 8 by 8 checkerboard with two diagonally opposite squares removed cannot be covered by dominoes each of which covers two rectilinearly adjacent squares. This site presents a set theory description of the proposition and an informal proof that the covering ...more>>

  50. New Foundations - Randall Holmes; Boise State University
    Set theory was introduced by W. V. O. Quine in 1937. This refinement of Russell's theory of types is based on the observation that the types in Russell's theory look the same, as far as one can apparently prove. Mailing list; links to fans; Definition; ...more>>


 
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