High School Classroom Materials

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• Calculus@Internet (courses with links to math software systems)
  An interactive WWW server at San Joaquin Delta College, Stockton, CA that integrates a common curriculum backbone with links to various computer algebra systems (Theorist, Maple, Mathematica, and others planned) which can be launched automatically by your WWW reader. (Directions are given for configuring your browser.) Math curriculum areas: Precalculus; Differential Calculus; Integral Calculus; Calculus II; Vector Calculus; Differential Equations; Linear Algebra.

• Calculus and Mathematica Course
  A computer-based calculus course that the instructor can use as soon as the computers are unloaded at the classroom door. A complete electronic text combined with a set of problems for the students to do. Course Syllabus; Annotated example with Pedagogy; Calculus Lab.

• Interactive Learning in Calculus and Differential Equations with Applications
  The Mathematics Department at Indiana University of Pennsylvania (IUP) has established a computerized learning environment, consisting of a classroom with 31 Macintosh Centris 650s and a laboratory with 12 Macintosh LCs, all equipped with Mathematica. Mathematica's notebook feature enables science students to actively learn calculus and differential equations with guided discovery and exploration. Mathematica notebooks: Finding Areas with the Gauss-Green Formula, Newton's Method and Fractals, Vibrating Drumheads, Some Multivariable Calculus Ideas, Orthogonal Curvilinear Coordinates, Basic Complex Numbers for Applied Mathematics, The Drag Force on a Sphere. In order to disseminate these Mathematica notebooks, one of the PIs in this grant wrote mma2html, a program to convert Mathmematica notebooks to HTML documents. This program is available to the public.

• Massachusetts Curriculum Frameworks for Math and Science (draft)
  "The Department of Education is pleased to present the drafts of the first two frameworks: Mathematics, and Science and Technology. With the development of the first state curriculum frameworks, Massachusetts embarks on a new era in educational improvement. The frameworks are designed as tools to be used by educators in planning instructional programs from pre-kindergarten through grade 12 and for adult basic education. Although school districts will not be required to adopt the Curriculum Frameworks, they may refer to the Frameworks as guidelines to bring about improvement in the education of all the students in the Commonwealth."

• New Polyhedral Surface
  Main entry point for pages that describe the recently discovered tight polyhedral immersion of the surface of Euler characteristic -1 into three-space and demonstrate one way that mathematics can be presented by means of a network-based multimedia hypertext course.

• Project Mathematics (CalTech)
  Videotape-and-workbook modules that explore basic topics in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. The tapes use live action, music, special effects, and imaginative computer animation. The goal of the project is to attract young people to mathematics through high-quality instructional modules that show mathematics to be understandable, exciting, and eminently worthwhile.

• Scientific Visualization Course
  Announcement of an Internet hypertext course on Visualization and Communication Tools for Mathematics and Science Teaching at the Univ. of Montana, summer 1995 for K12 teachers with an interest in mathematics and science education and computer technology. Image processing and analysis (measuring Mars, global sea surface temperatures, phytoplankton pigment concentrations); NASA's SIR-C CD-ROM (Mission to Planet Earth, How Radar Imaging Works); Euclidean and Non-Euclidean Geometries (Geometer's Sketchpad, Hyperbolic and Fractal Geometry); Explore the Internet.

• Transitional Mathematics Project at Imperial College London
  Learning modules in mathematics, based on the computer algebra system Mathematica, for first-year science and engineering students. Complex numbers, Differentiation, Integration, Matrices, Sequences and Series, Trigonometry, Vectors.

• WCAT (Math Tutoring/Animations)
  Workshop for Computer-Aided Tutoring (Simon Fraser University). A laboratory facility for undergraduate students to enhance their learning of mathematics by using the latest computer technology. Students use various software packages including Maple, Mathematica, The Geometer's Sketchpad, Cabri Graph, ISETL, and various other colourful and fascinating programs, in order to learn more about calculus, linear algebra, geometry, graph theory, set theory, and other areas of mathematics. Also a virtual laboratory.

• Mathematical Quotation Server
  A collection of mathematical quotations culled from many sources. The pages are listed alphabetically by author's last name. Samples from math history.

• On-line glossary of technical notation
  Definitions for many of the symbols, mathematical functions, and abbreviations used in technical documents. Given an unknown symbol, select the character or heading from a given list that most closely resembles that unknown symbol and then go to that page. Greek and Roman alphabets, ASCII characters, other symbols.

• Online Mathematics Dictionary
  Alphabetical listing of words used in mathematics, constantly being added to. Suggestions for terms that should be added may be sent to lexicographer@MathPro.com. Also an on-line glossary of technical notation for details about unfamiliar mathematical symbols.

• Electronic Games for Education in Math and Science (E-GEMS)
  A collaborative effort by scientists, educators, and professional video game and educational software developers to do research on and develop teaching materials that integrate video games and computer-based explorations with existing classroom practices. The aim of this research is to increase the proportion of children in Grades 4-8 who enjoy learning, mastering, and using underlying concepts of math and science.

• Gallery of Interactive On-Line Geometry
  Interactive On-Line Geometry from The Geometry Center at the Univ. of Minnesota. Interactive programs: QuasiTiler (nonperiodic tilings), Lafite (discrete symmetry groups), Teichmuller Navigator (Teichmuller space), Cyberview (3D viewer), Unifweb (Riemann surfaces), and Kali (symmetric patterns).

• Games John Conway likes, Knot Theory, and new Puzzles (Nancy Casey, MegaMath author)
  "Clever Games for Clever People" - Games from the book On Numbers and Games by John Conway (New York: Academic Press, Inc., 1976). How games can be used to describe numbers. The games: Stop-Gate, Col, Snort, Coin-strip, Moneybags, Kayles, Rim, Rayles, Traffic jam, Welter's game, All the King's Horses, Digital Deletions, Hackenbush Unrestrained, Hackenbush Restrained, Hackenbush Hotchpotch, Technicolor Hackenbush.

• John Conway's Game of Life
  The Game of Life is played on a field of cells, each of which has eight neighbors (adjacent cells). A cell is either occupied (by an organism) or not. The rules for deriving a generation from the previous one are these: Death - If an occupied cell has 0, 1, 4, 5, 6, 7, or 8 occupied neighbors, the organism dies (0, 1: of loneliness; 4 thru 8: of overcrowding). Survival - If an occupied cell has two or three neighbors, the organism survives to the next generation. Birth - If an unoccupied cell has three occupied neighbors, it becomes occupied.

• Ancient Mathematics (Vatican Exhibit materials, Library of Congress)
  Math history: math and astronomy in the ancient world. Greek Mathematics, Ptolemy's Geography, Greek Astronomy. Scholarship supported science in this world where faith and science were not yet seen as two irreconcilable cultures. Euclid, Elements, Optics; Archimedes, Works; Piero della Francesca, De quinque corporibus regularibus; Apollonius; Pappus; Ptolemy, Almagest, Geography, Handy Tables; Byzantine Astronomical Collection.

• A Brief History of Algebra and Computing: An Eclectic Oxonian V
  By Jonathan Bowen. Math history: Chapters on: The Origins of Algebra; Early English Algebra; Algebra and Analytical Engines; Boolean Algebra; Algebra and Computing; Recent Developments in the Algebra of Programs. References.

• History of math lesson
  "Bringing the History of Mathematics into the Mathematics Classroom," by Carol A. Waldron. A math history lesson plan aimed at accomplishing two of the five goals of the NCTM Standards. "The first goal states that students should learn to value mathematics through numerous, varied learning experiences that illuminate the cultural, historical, and scientific evolution of mathematics. The second goal states that students should become confident in their mathematical abilities. The following lesson plan involves the study the evolution of mathematics with emphasis on the various people and cultures that shaped it."

• History of Mathematics
  Part of the Mathematical MacTutor system developed at the School of Mathematical and Computational Sciences of the University of St Andrews for learning and experimenting with mathematics. Contains the biographies of more than 550 mathematicians, about 200 of them fairly detailed and most accompanied by pictures of the mathematicians themselves. Also a series of math history articles on the development of mathematical ideas cross-referenced to the biographies. The archive contains a Birthplace Map and a collection of other good web sources of information concerning the history of mathematics.

• Math History (Clark University)
  Web resources - sources, books and articles online; Regional mathematics - Babylonia, Egypt, China, Greece, India, Arab sphere, Japan, Europe; Books and other nonweb resources - Bibliography of source books, Journals, Bibliographies and catalogues, Texts on the history of mathematics; Chronological list of mathematicians by century/decade; Timelines; Index of files.

• Mathematicians of the Seventeenth and Early Eighteenth Centuries
  Math history: accounts of the lives and works of mathematicians of the seventeenth and first half of the eighteenth century, adapted from A Short Account of the History of Mathematics by W. W. Rouse Ball (4th Edition, 1908).

• Museum of HP Calculators
  The math history of early Hewlett Packard calculators (page is not affiliated with the Company. The Museum currently displays most HP scientific calculators introduced from 1972 to 1977 and a few significant later models, and is growing. Classics, classic printers, the 20 and 90 series, 2nd generation mag card programmables, interesting later models. Information on repairs, other calculator sites.

• Women Mathematicians
  A web page for biographies of women in mathematics, part of an ongoing project by students in mathematics classes at Agnes Scott College to illustrate the numerous contributions by women to the field of mathematics. Extensive list of mathematicians; books and articles about women in mathematics, other resources.

• A selection of Alan Selby's Lessons and Appetizers for Math and Logic
  Three Skill For Algebra (a first image of mathematics after arithmetic - why letters or symbols are favored in algebra in place of numbers); Two logic puzzles to show the difference between a one-way and a two-way rule; Painless Theorem Proving; Longer Chains of Reason: What is Mathematical Induction?; Complex numbers Etc. - A geometrical story based on the addition and multiplication of arrows in the plane; Chains of Reason - math-free examples of rule-based reasoning; How Logic or Rule-Based Reason Appears in Math; VNR Concise Encyclopedia of Mathematics. Also Appetizers on Other WWW Pages.

• Selected ERIC and Big Sky Lesson Plans
• FUTURES II Teacher's Guide - Excerpt
  An excerpt offered to Internet users by the series producers, the Foundation for Advancements in Science and Education (FASE), as an example of the ancillary support resources available for the FUTURES series.

• Mathematics lessons (Explorer, University of Kansas)
  Outline of math problems for levels K-12, by category, available from The Explorer, an R&D effort to establish an on-time and user friendly means of delivering a full range of information resources to educators and students.

• Newton's Apple (PBS science education show)
  26 lessons for the 12th season of the show (1994-95 school year). Lesson plans: Hang Gliding, Karate, Arctic Survival, Arctic Nutrition, Aircraft Carrier, Brain, Brain Mapping, Garlic, Movie Dinosaurs, Bread Chemistry, Movie Sound Effects, Sun, Dinosaur Extinction, Floods, Internet, Antibiotics , Ethnobotany, Hubble Telescope, Raptor Hospital, Photography, Redwoods, Electricity, Printing Money, Gravity, Bridges, Earthquakes. Each lesson includes Insights about the topic, Connections to encourage classroom discussion, Resources, and Vocabulary. Lessons also include a Main Activity and several Try This activities related to each topic. Also indexes to seasons 9-12 of the show.

• North Carolina DPI Lesson Plans
  From the Department of Public Instruction: Computer Skills (keyboarding, word processing, databases, spreadsheets, telecomputing) and Mathematic Strategies (Competencies) Curriculm Lessons (the entire Strategies for Instruction in Mathematics can be ordered from DPI Publications - Strategies for Instruction in Mathematics Strategies and Activities for Instruction and Assessment correlates to the N.C. Standard Course of Study and includes special activities called Week-By-Week Essentials). Also Lesson Plans from ERIC (searchable by keyword).

• Thomas Banchoff's Project List
  Remake of _The Flat Torus in the Three-Sphere_, a film originally created in 1968; "Complex Function Graphs"; self-linking of curves on the 3-sphere (research in progress); "Monge and Desargues, Identified" (requires Sketchpad); a "sketchpad" for spherical geometry, with interactive demonstrations in Fnord; short treatment of the geometry of least squares; the volume of an n-dimensional ball; the Klein bottle rotating in four-dimensional space; a module for constructing examples of arbitrarily high topological complexity a long-standing and extensive effort to study the life and works of Edwin Abbott Abbott; a partially updated 1990 article concerning Flatland and Hypergraphics.

• Complex Systems
  A public domain repository of complex systems information and software on ANU's BioGopher Server and a mailing list on complex systems. From ecology to economics, from particle physics to parallel computing, a new vocabulary is emerging to describe discoveries about wide-ranging and fundamental phenomena. Many of the terms have already become familiar: artificial life, biocomplexity, cellular automata, chaos, criticality, fractals, learning systems, neural networks, non-linear dynamics, parallel computation, percolation, self-organization, and many more. Together they point to the emergence of new paradigms, cutting across traditional disciplines, for dealing with complex systems.

• Data Powers of Ten
  A collection of estimates of the quantities of data contained by the various media. Each is rounded to be a power of 10 times 1, 2 or 5. Most of the links are to small images. Bytes, Kilobyte, Megabyte, Gigabyte ("1 Gigabyte: A pickup truck filled with paper OR A symphony in high-fidelity sound OR A movie at TV quality"), Terabyte, Petabyte, Exabyte, Zettabyte, Yottabyte.

• Formulae for Pi
  From Roy Williams: Arctangent formulas for PI. "What is a reasonable way to compute Pi? Methods that have been chosen for many of the groundbreaking digitstorms in the past have been based on arctangent formulae."

• The Largest Known Primes
  An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself. Primes are the building blocks of the positive integers: every positive integer is a product of prime numbers in one and only one way, except for the order of the factors. The Sieve of Eratosthenes is still the most efficient way of finding all very small primes (those less than 1,000,000); most of the largest primes are found using special cases of Largrange's Theorem from group theory.

• Multidimensional Analysis
  A brief introduction to Multidimensional Analysis, a generalization of linear algebra which incorporates ideas from dimensional analysis. The central idea is that vectors and matrices as used in science and engineering can be thought of as having elements which are not just real (or complex) numbers, but formally have different types, such as length or voltage. Quantities with different types do not form an algebraic field as they are not closed under addition, e.g., 1 meter + 1 volt is undefined. Traditional linear algebra assumes that vectors and matrices are isomorphic to arrays of elements which are closed under addition, and so raditional linear algebra is not formally valid for many applications in science and engineering.

• Non-Euclidean Geometry
  NonEuclid: an interactive simulation of the Poincare Model of Hyperbolic Geometry for use in high school and undergraduate education. How to get a copy of the NonEuclid Software (NonEuclid 4.0b); Background and Objectives of NonEuclid; Introduction to Non-Euclidean Geometry; Parallel Line Example; Distance Example; Technical Discussion of the Poincare Model and Algorithms used in NonEuclid.

• Numbers on the Internet (Fort Collins H.S.)
  Pi; e to 1,000,000 digits; a googleplex; square root of 2 to 1,000,000 digits and to 5 million digits; first 100,000 prime pumbers. Long documents, may be slow to load.

• Pi Page
  A mere 50000 Digits of the Famous Transcendental; A program to compute it; Some Arctangent Formulae for computing it; Some little-known quaint numerical facts.

• Random number generators: The pLab Project Home Page
  Inversive random number generators: results of statistical tests of inversive generators in comparison to classical generators; tables of parameters to implement inversive generators and algorithms to obtain such parameters; portable implementations in C of inversive (``ICG'') and explicit-inversive (``EICG'') congruential generators; readable accounts of the theoretical background; a What's new in this field that directs you to important new results; a First Reading List helpful for novices.

• The Slide Rule
  Recent math history: all about this ancestor of the calculator and computer. What is a Slide Rule?; Types of Slide Rules; How Do They Work?; The Oughtred Society; Other Sites of Interest; Slide Rule Archive; Slide Rule Related Stuff.

• Synergetics
  R. Buckminster Fuller's "explorations in the geometry of thinking" is detailed in two thick volumes, Synergetics and Synergetics 2. Synergetics thoroughly permeates the rest of Fuller's writings as well. The invention for which Fuller is most famous, the geodesic dome, derives from his geometric explorations. Current Topics on this page (partial listing): Concentric Hierarchy of Polyhedra; Isotropic Vector Matrix; Geodesic Domes and Spheres; Dymaxion Map; Desovereignization?; General Systems Theory.

• Xmorphia
  Xmorphia is intended to show the variety of patterns that may be exhibited by a relatively simple parabolic partial differential equation. Such systems are the focus of mathematical research, attempting to reconcile the complex organic look of the solutions with the simplicity of the equations being solved.

• 21st Century Problem Solving
  A server from SureMath dedicated to promoting problem solving literacy. How to solve problems (Problem Solution Paths; Organization of A Problem Solution; Common Sense in Problem Solving); Algebra Story Problems (A collection of simple story problems illustrating concept-based problem solving, typical of problems in high school textbooks and in a variety of competency tests); Introductory Physics; About Problem Solving; Journal of Modern Problem Solving.

• Frequently Asked Questions in Mathematics (sci.math FAQ)
  Non-trivial mathematical trivia: a compilation of math history and knowledge of interest to most professional and amateur mathematicians, ranging from advanced topics such as Wiles' proposed proof to Fermat's Last Theorem to the list of Fields Medal winners.

• Geometry Forum Newsgroup Archives
  Eight newsgroups, an online electronic community for all those interested in geometry. Here you may access current news or follow a link to threaded past discussions to browse or search the archive by keyword. The Forum's Problem of the Week is posted to the most active newsgroup, geometry.pre-college.

• Internet Center for Mathematics Problems
  An attempt to identify and list all sources of mathematics problems and related information on the Internet. Problem Columns from Mathematics Journals (Fibonacci Quarterly, Mathematics and Informatics Quarterly, Missouri Journal of Mathematical Sciences); Problem Columns and Mathematics Problems on the WWW; Newsgroups (alt.algebra.help, alt.math.iams, geometry.puzzles, rec.puzzles, sci.math); Problem Columns via Electronic Mail; Journals with Problem columns on the Web; On-line Book Reviews of Problem Books; On-line Bookstores that stock Problem Books

• Math Magic Activities
  Nine magic tricks based on simple mathematics. Card Tricks, Calculational Wizardry, Geometry and Topology Curiosities.

• Rec.Puzzles Archive
  An archive of questions and answers for puzzle enthusiasts. Samples from the index: "Four bugs are placed at the corners of a square. Each bug walks always. . ." "Cache and Ferry (How far can a truck go in a desert?)" "Without finding their numerical values, which is greater, e^(pi) or (pi)^e?" "Snow starts falling before noon on a cold December day. At noon. . ." "Is there an arithmetic progression of 20 or more primes?" "What is the minimum number of dice painted with one letter. . ." . Puzzles are alphabetical by category: analysis, arithmetic, combinatorics, competition, cryptology, decision, geometry, group, induction, language, logic, physics, pickover probability, real-life, references, series, trivia.

• Rec.Puzzle Archives (hypertext version)
  Puzzles and brain teasers archived from the newsgroup rec.puzzles and categorized by subject. Both the puzzles and their solutions are given, in the following categories: analysis, arithmetic, combinatorics, competition, cryptology, decision, geometry, group, induction, language, logic, physics, pickover, probability, real-life, references, series, trivia.

This page is part of the Geometry Forum's project: Organizing Internet Resources for Math Teachers By Math Topic, Grade Level, and Pedagogical Issue
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