Math Sites and Software

Summary:  This page started as my own collection of useful math links, either for my own interest or because they gave information frequently requested by students. I’ve marked my own “seven plus or minus two” FAVORITEs, in case you’re interested.

If you have a favorite math site, particularly one that does well with a subject area I don’t yet cover, please let me know about it. Obviously I can’t link to every math site in the world, but I’d like to link to one or two good ones in most categories.

General Math

FAQs / Reference

• FAVORITE: Eric’s Treasure Trove of Mathematics is an excellent starting point when you need the definition of a math term, or a fast introduction to an unfamiliar concept.
• Just the FAQs, Ma’am! Dr. Math’s FAQ answers lots of questions about high-school and undergraduate math. You may want to consult the sci.math FAQ for more advanced questions.

Help Desks

• Ask Dr. Math your question. (Check Dr. Math’s FAQ first.)
• Ask questions on the alt.algebra.help newsgroup and you’ll usually get answers from several people, letting you pick the approach that works best for you. A second newsgroup, uk.education.maths, covers similar subject matter but has less traffic: that may be a good thing or a bad thing, depending on your viewpoint.
• S.O.S. Math offers a lot of review questions (with solutions) from algebra to differential equations. There’s also a set of message boards (registration required).

History of Math

• The MacTutor History of Mathematics Archive is just what its name implies. It’s a good supplement to Eric’s Treasure Trove for historical topics.
• Jeff Miller helps you answer questions about when a particular mathematical symbol or word was used for the first time.
• You may want to look at the University of Tennessee, Knoxville’s list of math history sites.

Humor

• Why do do many students’ grandmothers seem to die at exam time? Mike Adams analyzes this phenomenon in The Dead Grandmother/Exam Syndrome and the Potential Downfall Of American Society. (If that link doesn’t work, try this one.)

Subject Areas

Algebra

• I’ve written a number of articles on algebra topics, especially exponents, logarithms, and conversions.
• FAVORITE: Elizabeth Stapel’s purplemath site has many modules with simple, practical explanations of topics in basic algebra, including a dozen or so kinds of the dreaded word problems.
• Students often ask “What was that proof that 1 = 2?” One such proof is in the Dr. Math archives.
• Johan Claeys of Belgium has an excellent set of tutorial articles on many topics, mostly within algebra and analytic geometry. They’re aimed at “upper secondary” students, which would be late high school and early college in the US. The alphabetical index is here, and the home page categorized by topic is here.
• A perennial question is how to solve a cubic or quartic equation. If you can’t guess a root and then divide to reduce it to a quadratic, you can look at these links.
• Nested radical expressions like sqrt(3+sqrt(2)) come up occasionally, for instance in computing trig functions of half angles. Dr. Math has two approaches to simplifying this sort of expression, one called Un-nesting Radicals and the other called Simplifying Radicals.
• Another perennial question is how to find square roots and cube roots without a calculator. There’s a good article by Steve Monson, archived here.
• Didn’t some state define π = 3? Not quite, though one house of the Indiana legislature passed a bill to define π as 3.2.

  Does the Bible define π as 3? Look here for the answer, with a history of attempts to calculate the true value of π.

• 0.999... equals 1, it does not “approach” 1; but why? Dr. Math gives a good explanation.
• Have a sequence of numbers and need to know the general term? Consult Sloane’s On-line Encyclopedia of Integer Sequences.

Geometry and Analytic Geometry

• FAVORITE: Silvio Levy has put a huge number of Geometry Formulas and Facts on line, for both plane and solid geometry.
• Does that equation graph as a parabola, ellipse, or hyperbola? Consult The General Quadratic Equation.

Statistics

• Gerald Dallal’s Little Handbook of Statistical Practice is a series of great short pages for students on a range of statistical topics. The two sections that I particularly recommend are
  • Confidence Intervals and
  • Is Statistics Hard?

  The latter is a very good short run-down on how hypothesis testing works.

• The best online textbook I know is the StatSoft Electronic Textbook. You can read up on particular topics or search for terms when you need definitions.
• Since 2001 I’ve taught introductory statistics using the TI-83 calculator. Many students and teachers from other institutions have found my class notes and my TI-83/TI-84/TI-89 procedures helpful.
• These aren’t exactly FAQs, but they are handy answers to questions that aren’t always answered in an intro stats course:
  • Dr. Math’s Two Random Variables, Each Correlated to a Third gives the range of possible correlations of X and Y when each is correlated to Z
  • Dr. Math’s Correlation Coefficients of Random Numbers explains how to construct two sets of numbers that are random but correlated with a desired coefficient.
  • From ap-stat, how do you handle a difference in preferences in a sample with three choices or two plus “undecided”?

Trigonometry

• FAVORITE: Okay, I’m biased, but I think my Trig without Tears is a good presentation. Not only does it cover a lot of trig in a small space, but it shows you how to remember all that stuff without memorizing it.
• Lawrence Spector has a very good series of Topics in Trigonometry. There’s a particularly nice diagram of all six functions as lengths of line segments on the unit circle.

Software

Software on Line

• QuickMath has stepped into the niche left vacant by the demise of the MathServ Calculus Toolkit. QuickMath can integrate, differentiate, solve equations and systems of equations, and more.
• Wolfram.com offers the free Integrator.
• Martindale’s Calculators On-Line Center features over 18,000 calculators for anything and everything, not just math.
• Natural Math takes a text representation of an algebraic expression and serves up a graphic, very useful for Web pages.
• CodeCogs Equation Editor (JavaScript required) has a very nice graphical editor and produces output in both LaTeX and display formats. It’s also downloadable.
• Karl’s Function Plotter — enter a function and see the plot, then capture the graphic.
• The University of Minnesota Assignment Calculator helps you beat the clock and get it done.

Software for Download

• Euler is a freeware numerical lab with real and complex numbers, functions, graphs, vectors, matrices — “not a MatLab clone, but very similar to this program”. (Try this link if frames are a problem for your browser.)
• Mathscribe is a free dynamic graphing and mathematical modeling tool designed for algebra, trigonometry, and pre-calculus.
• Winplot is a general-purpose 2-D and 3-D graphing utility with animations. The University of Exeter maintains a comprehensive tutorial in several languages.
• If you’re looking for math software, the University of Tennessee at Knoville maintains a huge Windows/MS-DOS Software Collection, categorized by math subject. Many of the programs are freeware.
• For an annotated list of free statistics software on the Web, see Statistical Science Web.
• You’ll find lots of downloadable free Windows and Linux software at Free Statistics on the Web. Despite the name, this list also covers software for general graphing and symbolic manipulation.

Revision History

• 16 Feb 2009: add CodeCogs Equation Editor