Useful Links

General

• Math Forum (Fabulous resource to many mathematical links)
• Mathematical Encyclopedia (Hosted by Wolfram)
• Mathematical Fun Facts (Tidbits of interesting mathematics)
• The Mathematical Atlas (Brief descriptions of areas within mathematics)
• MacTutor History of Mathematics archive (Biographies of mathematicians, famous curves index, mathematician of the day)
• MathDL (Mathematical Sciences Digital Library from the MAA)
• Pronunciation guide for names of prominent mathematicians is linked here (A project by Dr. Khristo Boyadzhiev at Ohio Northern University)
• Greek alphabet (Prime web page)
• How to write proofs: a quick guide (by Eugenia Cheng)
• When Will I Use Math? (sponsored by BYU Math)
• Mathematics Matters (Institute of Mathematics and its Applications)
  
• This is What a Scientist Looks Like
  

Study Strategies

• Handouts for ISU's College Learning Strategies
• Math Study Strategies at ISU's Math Center
• Using Sources includes handouts on avoiding plagiarism, available at ISU's Writing Center
• Link to Handouts from ISU's English for Speakers of Other Languages (ESOL)
  

Symmetry

• John Wolfe's Border Pattern Gallery
• ScienceU
• Introduction to tessellations
• Regular Tessellations
• Totally Tessellated (Argument for 8 semi-regular tessellations and templates)
• Pentagonal Tilings
• Perplexing Pentagons
• Mathematics and Art
• Polyhedra and Art
• Platonic Solids
  
• Analysis and Synthesis in Architectural Designs

120-cell

• The Story of the 120-Cell by John Stillwell
• My picture and more pictures from PCMI, and from Helmer Aslaksen's page in Singapore
  
• MathWorld entry
• Expanded 120-cell in Zome by George Hart
• Cardboard models of 3-d slices by Alicia Boole Stott (AMS Feature Column)
  
• Rotating model on page by Bathsheba Grossman
• 4-D regular polytopes
• 4-D polytope viewer by Michael Gibbs
  
• 120-cell foldout
  
• Soap bubble image by John Sullivan
• Polymake data
• List of zome piece data
• Tribute to H.S.M. Coxeter
  

Click here to test the Collatz Conjecture, courtesy of Angelo Mingarelli at Carleton University.

Future Teachers

• NCTM Principles and Standards for School Mathematics
• What to Expect Your First Year of Teaching
• K-12 Mathematics Curriculum Center (NSF funded)

Algebra

• Auto-Graph (Online function plotter)
• Algebra Review (University of Akron algebra tutorial)
• SOS Math  (Algebra and Calculus practice and other useful links)
• Math Archives Algebra List (many links to other tutorials)
• Math Forum Algebra List (many links to algebra sites)

Geometry

• Math Forum College Geometry page (see especially Euclidean, Non-Euclidean, and Transformational)
• Geometry Center page
• Gallery of Interactive Geometry
• Nine-point circle page
• 4-dimensions: Stereoscopic animated hypercube
• Pythagorean Theorem
• Digital Math Archive version
• Jim Loy version
  
• Cut-the-Knot version
  

Trigonomety

• Math Archives Trigonometry List (many good links-try especially the ones marked with Java)
• Introduction to Trigonometry (one particularly good site for a quick review of trigonometry)

Conic Sections

Calculus animations including a plane cutting the cone to produce conic sections

Calculus

Math Forum Calculus List (Long list of Calculus related web sites including several of those below.)

Math Forum Pre-Calculus List (Good for finding links to help in reviewing pre-calculus material.

• CalcJava (Java applets for Calculus from Japan--Check out "Rectangle Approximation Method".)
• Graphics (More applets, mostly for Calculus I.  Check out the second to last, 2.718...)
• Mathematics Animated (Many good calculus and other animations using Mathematica in QuickTime)
• Derivatives (Draw the derivative and then check your answer with lots of examples - very cool!)
• OU Calculus I Problem Archive (Caculus I Problems with hints and solutions)
• Famous Curves Applet Index (Several families of parametrized curves)
• Connected Curriculum Project (A wealth of information on Calculus and connections to other fields.)
• Calculus on the Web (Temple U. modules of problems in Calculus I, II, III.)
• Calculus IV at OU Resource Page (Supplemental graphics of surfaces.)

Matheatre (information on Calculus: The Musical! and fun calculus related lyrics to various songs)

Analysis

• Abstractmath (An excellent site to browse for advice on understanding and constructing proofs)
• Sequence convergence applet (From the article "Applets and Activities for Real Analysis" by Stemkoski and Storm in MathDL.)

Linear Algebra

• MacTutor History of Mathematics page  (A history of matrices and determinants)
• A Brief History of Linear Algebra (A timeline with dates and mathematicians surrounding significant events)
• Online matrix calculator and other tools

Abstract Algebra

• Finite Group Behavior
• Clock (Modular) Arithmetic Pages (very simple explanation and examples of modular arithmetic)
• Numeroscope (related ideas but more sophisticated)
• Development of Group Theory (historical comments from the MacTutor History of Mathematics Archive)
• Polyhedra (Check "Images from the Text" and "Low tech Polyhedron Models")
• Online lecture notes on groups
  
•     Peter Williams
•     Paul Scott
•     Arfur Dogfrey
•     W.D. Joyner
• Abstract Algebra: The Basic Graduate Year (online text chapters by Robert Ash)
• Elements of Abstract and Linear Algebra (online succinct textbook)
• Abstract Algebra OnLine (Definition and theorem summaries from Abstract Algebra by Beachy & Blair)
• Maple Worksheets for Abstract Algebra (mostly on field theory)

Math in Modern Society

Voting Methods

• Washington State University lesson pages on voting methods
  
• Science News article on pitfalls of the plurality method
• Science News article stating Borda count is the best method
• Voting theory page by James Green Armytage (includes strong recommendations against Borda count)
• Wikipedia entries on Borda count, Instant-runoff voting, Condorcet (pairwise) methods, and Arrow's Impossibility Theorem
  
• Vote: The Machinery of Democracy (Smithsonian exhibit on ballots and voting machines)

Weighted Voting Systems

• Electoral College page at the U.S. National Archives and Records Administration
• University of North Carolina page on the Banzhaf Power Index

Collecting Data

• How Gallup polls are conducted
• Methods statement for 2004 National Election Pool Exit Polls
  
• Washington Post article on inaccuracies in 2004 exit polls

Describing Data

• A histogram applet.
• Histogram explorer.

Probability

• Long term empirical probability demonstration.
  

Normal Distributions

• Normal distribution applet.
  
• Ball dropping experiment.
• Applet for changing the mean and standard deviation of a normal distribution.
• Demonstration of the central limit theorem

Fibonacci Numbers, Golden Ratio, and Spiral Growth

• Ron Knott's huge compendium of links and information on Fibonacci numbers.
  
• Page on Fibonacci numbers in nature.
  
• Article from maa.org on the golden ratio (also search at the MAA site for "Fibonacci" or "golden ratio")