Introduction

In the early 1970's, a computer science and mathematics professor named Donald Knuth started writing a large book. His book was going to be a comprehensive, 6-volume treatise on the mathematical foundations of computer programming. The title: The Art of Computer Programming. After he finished the first two volumes, he sent the manuscript to the publisher to be typeset. When he received the typeset proofs of his documents, he was disappointed with the results. The formulæ, type styles, and layout were ugly. The publisher told him that their typesetting was the best that the current technology could manage.

Figure 1: Prof. Donald Knuth

So Professor Knuth decided to take some time to write a program to do a better job at text formatting. He was especially interested in formating math formulæ correctly. After outlining the design goals, he estimated that he'd need about 18 months for the project. Eight years later, Knuth finished his text formatting system. He called it TEX , pronounced tech. In addition to TEX , Knuth also wrote a program called for designing typefaces. He reformatted the first two volumes of the Art of Computer Programming with TEX , and he published these volumes as second editions. He also published a 5-volume set of books about the TEX and systems.

Knuth set out to do TEX right. By many accounts, he did. TEX formats complex, intricate math formulæ beautifully, and plain text also looks excellent. Knuth paid lots of attention to the spacing between letters, symbols, and words. Many professional publishers use TEX as their typesetting system of choice, and virtually all publishers use TEX for mathematical typesetting.

If you have heard of TEX , then you have probably also heard of L^ATEX . L^ATEX is actually written in TEX ; it is a collection of macros that another mathematician named Leslie Lamport wrote. The main design goal of L^ATEX was to provide text formatting commands for the logical structure of documents. For example, L^ATEX includes commands for formatting titles, lists, theorems, and chapters. Instead of specifying that the text of a theorem should be italicized, numbered, and indented, a L^ATEX user simply marks the text of a theorem with the L^ATEX command \theorem. L^ATEX knows how theorems should be formatted, so the user doesn't have to. L^ATEX knows how to format books, reports, articles, letters, and other document types. A L^ATEX user only needs to know how to tell L^ATEX what logical role various of pieces of text play in the document. This abstraction helps with speed, consistency, and flexibility in document formatting.

What is TeX

TEX has variously been described as:

• A desktop publishing system;
• A programming language;
• A text processor;
• A markup language.

All of these are true to a degree. But they all fall short of the mark:

TEX is designed to typeset professional quality documents.

TEX 's job is to translate the text you type into a beautiful typeset page. This may include using multiple fonts and complex mathematics, while ensuring:

• the right margin is justified;
• proper justification is achieved without letter spacing;
• interword spacing is neither too tight, nor too loose;
• the page is evenly grey;
• multiple fonts are properly aligned;
• hyphenation is automatic and correct.

Note that TEX is a text processor, not a word processor, which means that you have to type the text in one file, compile it using TEX , and then print or preview the output.

Why use TEX ?

The development cycle of a TEX document is slower than using a word processor because you have to type, compile, preview, correct until you are done. However the advantages of TEX more than make up for this apparent loss of time.

• TEX is unsurpassed at typesetting mathematics;
• You can use a variety of fonts--and even create your own;
• TEX typesets a paragraph at a time to get the optimal appearance;
• TEX understands the rules of typesetting so you don't have to;
• TEX offers a variety of tools for the creation of lists, tables, figures etc.;
• Full support for running headers and footers (imagine writing a dictionary);
• Full support for page numbering, labeling, referencing and citation;
• Fully extensible;
• Precise control over the placement of elements on a page;
• Full use of user defined macros.

All of these points make TEX very powerful and fast, although the wealth of features make it a little hard to get started.

However there is more. Once you have your document can you print it out somewhere else? The answer is yes. Here are some of TEX 's advantages in the bigger picture:

Completely portable

A TEX input file is a plain text 7-bit ASCII file, with no special formatting or control characters. It can be cut, copied, pasted and emailed anywhere (although beware of those leading ``From''s).

Consistent output

The same input file will produce the same output on any TEX system on any platform, provided fonts and resolutions are available. A program that calls itself ``TEX '' must conform to a rigorous suite of tests to ensure consistency.

Available anywhere

TEX has been ported to just about every platform (hardware/OS combination) there is.

Free

The copyright for TEX is owned by the American Mathematical Society (AMS). TEX is truly free in that you can do what you want with it. Auxiliary programs are usually covered by the Gnu Public License (GPL), but the core is free with only the stipulation that if you call it ``TEX '' then it must satisfy the test suite.

How do you pronounce it?

TEX is a rendering in capitals of the Greek letters ${\tau\epsilon\chi}$; pronounced properly, TEX rhymes with ``blecchhh,'' as in the ch in the Scottish loch or German ach, or as in the Spanish j or Russian kh. The name comes from the Greek root `` $\tau\epsilon\chi$'' for words such as ``technical'' and is meant to emphasize that the printing of mathematical texts is an integral part of the program. The proper spelling in typewriter-like fonts is TeX and not TEX or tex.

cmr

What Every Young Mathematician Should Know
BY DR. S. ELF RIGHTEOUS

ABSTRACT: We evaluate an interesting definite integral.

The purpose of this paper is to call attention to a result of which many mathematicians seem to be ignorant.

Theorem 1   The value of $\int_0^{\infty}e^{-x^2}\,dx$ is

$$\int_0^{\infty}e^{-x^2}\,dx = \sqrt{\pi} \ .$$

Proof. We have

$$\left(\int_0^{\infty}e^{-x^2}\,dx\right)^2 = \left(\int_0^{\infty}e^{-x^2}\,dx\right) \left(\int_0^{\infty}e^{-y^2}\,dy\right)$$

$$= \int_0^{\infty}\int_0^{\infty}e^{-x^2}e^{-y^2}\,dx\,dy$$

$$= \int_0^{\infty}\int_0^{\infty}e^{-(x^2+y^2)}\,dx\,dy$$

$$= \int_0^{2\pi}\int_0^{\infty}e^{-r^2}r\,dr\,d\theta$$

$$= \int_0^{2\pi}\left[\int_0^{\infty}e^{-r^2}r\,dr\right]d\theta$$

$$= \int_0^{2\pi}\left[\left.-\frac{e^{-r^2}}{2} \right\vert _{r=0}^{r=\infty}\,\right]d\theta$$

$$= \int_0^{2\pi}\left[\frac{1}{2}\right]d\theta$$

$$= \pi \ .$$

$\qedsymbol$

cmr

Grades of Math 175 students

The following table gives the grades from Math 175 exam 2.

We can display these quite effectively as a bar graph:

Figure 3: A lithium cation with two hydration spheres

Figure 4: The caffeine molecule

Figure 5: From the sonata in C-major K545 by Mozart