Guide to Typesetting

Overview

Homeworks that are typeset will receive up to 4% extra credit. Full extra credit is easier if typesetting is done in LaTeX. Many students have had success with Overleaf, but you can also use pdflatex on Linux and MiKTeX on Windows. LaTeX sources are available for each assignment, and make good templates for your submissions. 

Requirements for typesetting credit:

• • You must use the correct symbols. The symbol for implication is →, not ->.

    • • It is better to write the symbols by hand than to use ASCII-art.

      • Reminder: this does not apply to reading assessments. 

  • If you need to find a symbol, I recommend the detexify webpage.

Elements of typesetting that I look for.

• • Problems are clearly numbered and separated.

  • If problems are restated (always nice to see), then they are clearly separate from the solutions.

  • Within each solution, spacing and indentation reflect the logical flow of the document. 

  • Arguments that should be paragraphs are in paragraph form, while arguments that should be itemize or enumerated are itemized or enumerated. You should almost never have one-sentence paragraphs.

Mathematical Writing

Many suggestions and examples taken from The Book of Proof by Richard Hammock

1. Never begin a sentence with a mathematical symbol.  Certain mathematical symbols (A) have an English meaning, Sentences begin with capital letters, but mathematical symbols are case sensitive.

   • • Bad: A is a subset of B. 

     • Good: The set A is a subset of B.

2. End any sentence with a period, even if the sentence ends with a mathematical expression. If there is English anywhere in the sentence, it needs a period. The only time you can not have English in your sentence is if it is part of a series of equations.

3. Separate mathematical symbols with words.

   • • • Bad: Because x^2 - 1 = 0, x = 1 or x = -1. 

       • Good: Because x^2 - 1 = 0, it follows that x = 1 or x = -1.

4. Do not use mathematical symbols in place of plain English. Mathematical symbols should appear only in mathematical expressions.

   • • • Bad: Since x and y are =, their square are equal

       • Good: Since x and y are equal, their squares are equal.

       • Bad: ∃ a number larger than x.

       • Good: There exists a number larger than x.

5. Use the active, plural, voice. You and the reader are travelling together through this proof. The actors in your proof are the readers and the mathematical objects. 

   • • • Bad: The value x = 3 is obtained by factoring.

       • Good: By factoring, we get the value x = 3.

       • Bad: Since both sides can be divided by y, we know...

       • Good: Since y divides both sides, we know..

6. Watch out for “it” and “any”, they are ambiguous.

   • • • Bad: Since x < y and 0 < x, we see that it is positive.

       • Good: Since x < y and 0 < x, we see that y is positive.

       • For ‘any’, prefer the more explicit ‘every’ or 'some'.

7. "Since", "because", "as", "for", and "so" are your best friends. They all mean “I am going to give the premise and the conclusion in one sentence."

8. "Thus", "hence", "therefore", and "consequently" are all good ways of to start a sentence  with “Based on what I just said, I’m going to conclude some new stuff.”