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.

General Math

FAQs / Reference

• FAVORITE: Mathworld (accessed 2015-07-19), formerly 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 (accessed 2015-07-19) answers lots of questions about high-school and undergraduate math. You may want to consult the sci.math FAQ (accessed 2015-07-19) for more advanced questions.

Help Desks

• Ask Dr. Math your question (accessed 2015-07-19). (Check Dr. Math’s FAQ first.)
• S.O.S. Mathematics (accessed 2015-07-19) 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 (accessed 2015-07-19) 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 (accessed 2015-07-19).
• You may want to look at the University of Tennessee, Knoxville’s list of math history sites (accessed 2015-07-19).

Subject Areas

Algebra

• I’ve written a number of articles on algebra topics, especially exponents, logarithms, and conversions.
• FAVORITE: Elizabeth Stapel’s Purplemath site (accessed 2015-07-19) 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 (accessed 2015-07-19).
• Johan Claeys of Belgium has an excellent set of tutorial articles (accessed 2015-07-19) 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 √(3+√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 (accessed 2015-07-19) and the other called Simplifying Radicals (accessed 2010-12-22).
• 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 (accessed 2015-07-19).
• 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 (accessed 2015-07-19).

  Does the Bible define π as 3? Look here (accessed 2015-07-19) 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 (accessed 2015-07-19).
• Have a sequence of numbers and need to know the general term? Consult Sloane’s On-line Encyclopedia of Integer Sequences (accessed 2015-07-19).
• I could do the calculations, but I never really understood eigenvalues and eigenvectors until I read An Introduction to the Conjugate Gradient Method Without the Agonizing Pain by Richard Shewchuk (accessed 2015-07-19).

Geometry and Analytic Geometry

• FAVORITE: Silvio Levy has put a huge number of Geometry Formulas and Facts (accessed 2015-07-19) on line, for both plane and solid geometry.
• Does that equation graph as a parabola, ellipse, or hyperbola? Consult The General Quadratic Equation (accessed 2015-07-19).

Statistics

• FAVORITE: Gerald Dallal’s Little Handbook of Statistical Practice (accessed 2010-12-22) 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.

• Since 2001 I’ve taught introductory statistics using the TI-83 calculator. Many students and teachers from other institutions have found my Stats without Tears and standalone articles helpful.
• Aside from the one I wrote, ☺ the best online textbook I know is the StatSoft Electronic Textbook (accessed 2015-07-19). You can read up on particular topics or search for terms when you need definitions.
• These aren’t exactly FAQs, but they are handy answers to questions that aren’t always answered in an intro stats course (accessed 2015-07-19):
  • 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”?

    Zbigniew Kmietowic has a more detailed treatment, with fully worked-out examples, at Sampling Errors in Political Polls (accessed 2015-07-19).

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 (accessed 2015-07-19). There’s a particularly nice diagram of all six functions as lengths of line segments on the unit circle.

Software

Software on Line

• QuickMath (accessed 2015-07-19) has stepped into the niche left vacant by the demise of Vanderbilt’s MathServ Calculus Toolkit. QuickMath can integrate, differentiate, solve equations and systems of equations, and more.
• Wolfram.com offers the free Integrator (accessed 2015-07-19).
• Martindale’s Calculators On-Line Center (accessed 2015-07-19) features over 18,000 calculators for anything and everything, not just math.
• CodeCogs Equation Editor (JavaScript required) has a very nice graphical editor and produces output in both LaTeX and display formats (accessed 2015-07-19).
• Calculator.net (accessed 2015-07-19) has a bunch of math calculators, including a triangle solver.
• The University of Minnesota Assignment Calculator (accessed 2015-07-19) 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”.

  On 2015-07-19, I was unable to verify this one. SourceForge, where it has been hosted, was down and according to its blog had been down for several days. If or when it comes back, use caution in downloading Euler because SourceForge has been bundling extra unrequested programs with its downloads. Hopefully the author will make a non-SourceForge version available.

• Mathscribe (accessed 2015-07-19) is a free dynamic graphing and mathematical modeling tool designed for algebra, trigonometry, and pre-calculus.
• There’s an amazing variety of computer algebra software available, much of it very good and free. Have a look at Wikipedia’s list of computer algebra systems.
• Winplot (accessed 2015-07-19) is a general-purpose 2-D and 3-D graphing utility with animations.
• If you’re looking for math software, the University of Tennessee at Knoxville maintains a huge Windows/MS-DOS Software Collection, categorized by math subject (accessed 2015-07-19). Many of the programs are freeware.
• For an annotated list of free statistics software on the Web, see Statistical Science Web (accessed 2015-07-19).
• You’ll find lots of downloadable free Windows and Linux software at Free Statistics on the Web (accessed 2015-07-19). Despite the name, this list also covers software for general graphing and symbolic manipulation.

Calculators

• Lucas Allen has a blog, Tech Powered Math (accessed 2015-07-19), about math technologies, focusing on handheld calculators. I teach with the TI-83/84, and his site gave me some eye openers.
• TI-83/84/89/92 Procedures and Help, on my other site BrownMath.com, has procedures and downloadable utility programs for common tasks in statistics, calculus, algebra, and trigonometry.

Revision History

• 24 Oct 2015: There will be no further updates to this page.
• (intervening changes suppressed)
• 1999(?) First publication.