index: click on a letter A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A to Z index index: subject areas numbers & symbols sets, logic, proofs geometry algebra trigonometry advanced algebra & pre-calculus calculus advanced topics probability & statistics real world applications multimedia entries

1. "Help! I can't remember and I don't know where to look it up."

This website is designed for math students who need an easy-to-use, easy-to-understand math resource all in one place. It is a comprehensive listing of formulas and definitions from beginning algebra to calculus. The explanations are readable for average math students, and over a thousand illustrations and examples are provided.

I have been a math teacher and tutor for high school and college students since 1984. In my experience, only the most enthusiastic and accomplished math students remember everything from earlier coursework. Everyone else spends a lot of time feeling lost.

Existing math reference resources are no help for most math students.

Professional math reference guides are excellent for advanced students and professionals. They are useless, however, for the vast majority of math students. Authors of professional guides are unforgiving in their use of technical language, so the definitions are difficult to read.

Textbooks aren't much help, either. They usually have appendices of formulas and/or glossaries, but these are an afterthought and seldom are helpful. Often the topic a student wants to look up is not covered because it is too elementary. Back-of-the-book glossaries are usually terse, technical, and have no illustrations or examples. They are only helpful to students who already know the material. The arrangement and content of textbook appendices tends to discourage average math students from using them.

2. How the definitions are written

Whenever possible, I tried to have the first words of each definition describe the term precisely, accurately, and with a minimum of jargon.

 Denominator The bottom part of a fraction. For $$\frac{5}{7}$$, the denominator is 7.

Sometimes I could not meet this goal. I could write a precise definition that was hard to follow, or a readable definition that was imprecise. In such cases I gave both versions: the readable definition first, then the precise one.

 Ellipse A conic section which is essentially a stretched circle. Formally, an ellipse can be defined as follows: For two given points, the foci, an ellipse is the locus of points such that the sum of the distance to each focus is constant.

3. What is not in this website

In order to keep the site to a manageable size, I decided early on to exclude obscure specific-purpose formulas and techniques. Such examples include the geometric technique of mass points.

I also decided not to include much from the AP Statistics curriculum or from discrete math. In order to keep the size of this already large site manageable, I chose to limit the scope of mathwords to course content from beginning algebra to calculus.

I did not include a comprehensive listing of postulates and theorems from geometry. The "official list" varies somewhat from text to text, so any overall listing would be of little practical use. A large number of standard Geometry theorems are included, and so is the parallel postulate.

Finally, Idecided to leave certain basic skills and terms undefined. I omitted most basic arithmetic skills (e.g. multiplication of integers, long division), and I decided not to define fundamental terms such as "number".

I encourage readers of this guide to contact me with suggestions for later editions.