Math 581: Topics in Graph Theory
Graphs and Geometry
Fall 2008

Tips on LaTeX for Course Notes

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Index

Writing

  1. Fill in the missing proofs, as well as missing details. This is especially true if the proof is called "obvious" or "easy"! If you have trouble, try the references, or see me. (I might make exceptions, but I think this is the right way to do the course notes.)

  2. Write text to explain what's going on and to connect your formulas and math statements together. Math writing is in many ways a kind of narrative.
    • In a definition, theorem, or proof, there must be words!
    • Say what you're defining or proving before the formal definition or proof.
    • In a calculation, explain how the steps in the calculation (other than pure rearrangements) are justified.
    • When you write up a theorem, the assumptions must be clearly stated.

  3. I see too much reliance on itemized lists. When you get to a depth of 3 in itemized lists in an exposition (as distinct from an outline), something is very wrong! Even a depth of 2 should almost never appear. How to get around it?
    1. You don't need to bullet everything. You might shoot yourself in the foot! For instance, you can have paragraphs in an \item; that obviates the use of a sublist (see several examples in the notes).
    2. You can use subsections (the \subsection* command so they won't be numbered) for topical subdivisions (see the notes, again).
    3. You can just use paragraphs in the old-fashioned way!

  4. Use the word "that" often. E.g., you wrote "Notice in the above graph ...". That's grammatically incorrect. "Notice" takes a noun as its object (technical term for what follows "notice"). "in the above" is not a noun. You have a clause (embedded sentence) as the object of "notice" and to make that work you must (not optional) have "that" before your clause.

  5. Revising notes: I don't want you to spend too much time on it. I'll do a lot of revision and improvement. You might look to get ideas for better (or worse) writing.

General LaTeX Guidelines

Course Notes Frame

The file "course-notes.tex" automatically includes the header and bibliography as well as the title page. You can use it for yourself by adjusting the "\include" statements.

Header

I have a standard Latex header adapted for our class, which I ask you to use. This will help make the daily notes consistent. I update it now and then, when new needs appear.

You can add any necessary new commands after the header.

Bibliography

I have a Latex bibliography that is automatically included in the "course-notes.tex" file. You can use it separately if you wish by typing
      input{bibliography}

Figures

  1. Figures can be prepared at the office using xfig (I'll show anyone how to use it), or anywhere using whatever you have.

  2. Please make sure to provide PDF figures. EPS is also okay, but I need the PDF because my home Apple can't deal with PostScript. Thanks.

Specifics About LaTeX

On-Line Help

  1. Online Latex explanations, with more depth than most online sites:
          http://www.giss.nasa.gov/tools/latex/
    I found this very useful for subtle details as well as simple ones, and it's easy to navigate. However, it's years out of date.
  2. Places to find Latex downloads, including Miktex:
    • The (La)Tex user's home page with too many links to count:
            http://www.tug.org/
    • The Comprehensive TeX Archive Network is the authoritative collection of materials related to the TeX typesetting system:
            http://www.ctan.org/

Formatting

  1. Please use chapter and section headers following the on-line outline.

  2. \displaystyle is different from a displayed formula. \displaystyle and \textstyle are Latex commands that affect how a formula appears. A displayed formula is something that appears outside your text, as opposed to an inline formula. You can make a displayed formula appear in \textstyle and vice versa, and sometimes this is a good idea, though not usually.

  3. Naming declarations:

  4. Referring to a declaration: To get the right number, type "Theorem \ref{T:MMDDNAME}" (or similarly for anything else).

  5. Referring to an equation: Inside the equation environment type \mylabel{E:MMDDNAME}. When referring to an equation, type \eqref{E:MMDDNAME} (this will automatically insert parentheses around the equation number) or \ref{E:MMDDNAME} (this will not insert parentheses).

Special characters

  1. Abbreviated commands. They are optional, but very convenient. Here are examples:
      \cA for \mathcal A
      \fA for \mathfrak A
      \bbR for \mathbb R
    I defined these for the more common letters in my header; feel free to add more, or not to use them.

  2. Multiletter symbols are similar to \sin, \max, \lim, but not defined in Latex or AMSLatex. I provide many of them, such as:
      \transpose (for a matrix transpose),
      \codim (codimension),
      \sgn (sign of a real number),
    and see the header for more, or make your own. See the header for models for making such a symbol using \operatorname.

  3. \iff and \implies give the double-line arrows you would expect.

Typography

  1. When defining a change of type face, as with \emph, don't leave spaces inside at the ends. Wrong: \emph{ this is emphasized }. Right: \emph{this is emphasized.}

  2. \text{TEXT} gives you text inside a formula. This is especially necessary in displayed formulas. If you want space around the text, you'll need \text{ TEXT }. Try it to see how it works.

  3. For primed math symbols, $V'$. For starred ones, $V^*$. (You'll get used to it.)

  4. For defining a symbol, use :=, not \equiv. (We'll have other uses for \equiv.) E.g., $n := |V|$.

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