# Math Sites and Software

revised 7 Jan 2011

Copyright © 2000–2013 by Stan Brown, Oak Road Systems

**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”
**FAVORITE**s, 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.

**FAVORITE**: Mathworld (accessed 2010-12-22), 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 2010-12-22) answers
lots of questions about
**high-school and undergraduate math**. You may want to consult the sci.math FAQ for more advanced questions.

- Ask Dr. Math your question (accessed 2010-12-22). (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 (accessed 2010-12-22) offers a lot of review questions (with solutions) from algebra to differential equations. There’s also a set of message boards (registration required).

- The MacTutor History
of Mathematics Archive (accessed 2010-12-22) 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 2010-12-22).
- You may want to look at the University of Tennessee, Knoxville’s list of math history sites (accessed 2010-12-22).

- 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 (accessed 2010-12-22).

- I’ve written a number of articles on
algebra topics, especially
**exponents, logarithms, and conversions**. **FAVORITE**: Elizabeth Stapel’s Purplemath site (accessed 2010-12-22) 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 2010-12-22). - Johan Claeys of Belgium has an excellent set of
tutorial articles (accessed 2010-12-22)
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 (accessed 2010-12-22) 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 2010-12-22). - 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 2010-12-22).Does the Bible define π as 3? Look here (accessed 2010-12-22) 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 2010-12-22).- Have a sequence of numbers and need to know the general term? Consult Sloane’s On-line Encyclopedia of Integer Sequences (accessed 2010-12-22).
- 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 2010-12-23).

**FAVORITE**: Silvio Levy has put a huge number of Geometry Formulas and Facts (accessed 2010-12-22) on line, for both**plane and solid geometry**.- Does that equation graph as a
**parabola, ellipse, or hyperbola**? Consult The General Quadratic Equation (accessed 2010-12-22).

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

- The best online textbook I know is the StatSoft Electronic Textbook (accessed 2010-12-22). 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 helpful.
- These aren’t exactly FAQs, but they
*are*handy answers to questions that aren’t always answered in an intro stats course (accessed 2010-12-22):- 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”?

**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 2010-12-22). There’s a particularly nice
diagram
of all six functions as lengths of
**line segments on the unit circle**.

- QuickMath (accessed 2010-12-22) 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 2010-12-22).
- Martindale’s Calculators On-Line Center (accessed 2010-12-22) 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. It’s also downloadable (accessed 2010-12-22).
- Karl’s Function Plotter—enter a function and see the plot, then capture the graphic (accessed 2010-12-22).
- The University of Minnesota Assignment Calculator (accessed 2010-12-22) helps you beat the clock and get it done.

- 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”. - Mathscribe (accessed 2010-12-22) 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 2010-12-22) 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 2010-12-22). Many of the programs are freeware.
- For an annotated list of free statistics software on the Web, see Statistical Science Web (accessed 2010-12-22).
- You’ll find lots of downloadable free Windows and Linux software at Free Statistics on the Web (accessed 2010-12-22). Despite the name, this list also covers software for general graphing and symbolic manipulation.

- Lucas Allen has a blog, Tech Powered Math (accessed 2010-12-22), 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, my site for students at Tompkins Cortland Community College, has procedures and downloadable utility programs for common tasks in statistics, calculus, algebra, and trigonometry.

**7 Jan 2011**: Add computer algebra software.**22–23 Dec 2010**:- Add the Calculators section, beginning with Tech Powered Math and TI-83/84/89/92 Procedures and Help<./li>
- Add the Shewchuk article.
- Check all links; update links to Jeff Miller’s history pages, dead grandmother syndrome, Purplemath, the LHSP, Euler, and Winplot; R.I.P. U of Missouri’s Natural Math, which created a graphic from text representation of an equation.

- (intervening changes suppressed)
**1999**(?) First publication.

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