Like most people, once I got out of school, I've only needed basic math. However, I've always liked the truth and beauty of math.

• Arithmetic. Too easy!
• Algebra. Mostly easy.
• Trigonometry. Useful but not very pretty.
• Geometry. Probably the most beautiful branch.
• Logic. A wreath of pretty flowers.
• Numbers Theory. Appeals to the dictionary lover in me.
• Probability. Anyone for a game?
• Set Theory. What's yours is mine.
• Statistics. Lies, Damn Lies, and Statistics.
• Calculus. So cool but it sure does get tricky.

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.

-Godfrey Harold Hardy, A Mathematician's Apology

Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

-Bertrand Russel, Study of Mathematics

Rendering Fancy Equations

Pages in my Math section make use of the MathJax [mathjax.org] JavaScript library to display fancy equations.

I will try to consistently use LaTeX [W] instead of Mathematical Markup Language (MathML) [W] because LaTeX is better for hand-made equations as opposed to tool-made equations, plus Wikipedia allows the use of MathJax and LaTeX.

With MathJax and LaTeX, the default math delimiters are $$...$$ and $...$ for displayed (block) mathematics, and $$...$$ for in-line mathematics.

For example:

When $$a \ne 0$$, there are two solutions to $$ax^2 + bx + c = 0$$ and they are
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$


yields:

When $$a \ne 0$$, there are two solutions to $$ax^2 + bx + c = 0$$ and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$

Here are some characters that have special meaning in HTML or LaTeX:

< > & # $% _ { } \ ~ ^  Here are those characters escaped for LaTeX: \lt \gt \&amp; \# \$ \% \_ \{ \} \backslash \tilde{} \verb*^*


Here are those characters as used by LaTex:

$$\lt \gt \& \# \ \% \_ \{ \} \backslash \tilde{} \verb*^*$$

FYI: There are many ways to do the tilde and caret. I also like \sim ($$\sim$$) for a large tilde. See also "How does one insert a backslash or a tilde into LaTeX?" [http://tex.stackexchange.com/questions/9363/how-does-one-insert-a-backslash-or-a-tilde-into-latex].

Here are a few references for LaTeX:

Page Modified: (Hand noted: 2007-10-23 22:44:07Z) (Auto noted: 2013-01-12 23:49:06Z)