What is written with ease is never read with pleasure.-- Samuel Johnson

**Writing with mathematics:**

For: exercises, quizzes, exams, reports, papers, books, tutorials...everything. This class, other classes, and forever.

It's simple:

First approach: *Imitate.*

Here's
Andres Segovia giving a guitar lesson: ``now listen and play it like I do.''
Not entirely a joke. Just look at any textbook and simply write
math like it does.

Second appraoch: *Intellectualize*

If you can't see what the authors above are doing, it's simple. They are
telling a story *in prose*, and with *Good English
sentence construction and punctuation*, that happens to contain
formulae,
often
set off on their own lines. But if you read it aloud, you get
English, NOT formula, formula, formula...

Third approach: *Induce*.

Here are bad and good examples:

Bad: This is NOT writing mathematics:

x = log_{c} b, y = log_{c} a, z = log_{a} b

c^{x} = b = (c^{y})^{z}

x = yz

z = x/y

log_{a} b = (log_{c} b) / (log_{c} a), a,b,c > 0, a ≠ 1

Good: Compare Weiss, Theorem 1.1 p. 3.

**Why do you care?**

- You want others (today graders, tomorrow your readers, managers, judges, referees) to understand what the hell you're doing.
- Next week you go back to your work and YOU want to understand what the hell you were doing.
- It's the only professional style for doing the job: no other possibilities exist, sorry.
- You lose points for screwing this up.

- Exercise How-To (pdf). How to write up an exercise. Worth a look, may be useful for labs and projects. Stolen from U. Md.
- A theoretical CS (mostly) Cheat-sheet (pdf) .
- Math Preliminaries for Data Structures.
- Exercises and Answers for Math Preliminaries above.
- Math Preliminaries for Analysis of Algorithms.