# Introduction to DG

Class materials (Fall 2022):

Class materials (Spring 2022):

We are going to use LaTeX typesetting system to prepare the home assignment solutions. Each of you should see the dedicated project shared with you on https://overleaf.com
Please note the submission rules for all home assignments:
Firstly, some technical rules:

• Do not modify the page layout (margins, padding, font size) unless explicitly asked to do so.
• Do not erase, modify or reorder problem statements.
• Write your solution under each problem statement, staying strictly between \begin{solution) and \end{solution}.
• If you do not have a solution for some problem, keep \begin{solution) and \end{solution), do not erase them, but just put an empty line between.

Secondly, stilistic rules:

• Treat the solutions as excerpts from some publishable paper, not handwritten notes or whiteboard dump. All sentences should conform to English grammar, be complete and woven into mathematical discourse.
• In case you use some fact, including some fact from our classes, mention it explicitly. If this is some named theorem, state it in between \begin{theorem) and \end{theorem). Also you can use \begin{lemma}, \end{lemma} and \begin{proposition) and \end{proposition} if you feel that to better fit the context. If that is a really commonly known fact, you can omit the statement, but should still mention it like e.g.: "Due to pigeonhole principle, we have..."
• Do not use quantifiers $\exists, \forall$ and boolean junctions inside general text. For instance, "This happens for all values of $x$" should not be turned into "This happens for $\forall$ values of $x$". Every letter that you use should generally be first introduced. There are really few exceptions to this rule, like $\mathbb{R}$ for the set of real numbers. If you are not sure if something needs to be introduced, then better introduce it than not.
• You can collaborate (discuss homework problems) with your classmate. However, prepare writings independently. We would like to see your individual reflection on the homework problems. For instance, if you just copy-past a solution of your classmate, we will not count almost identical solutions to the problem (that is, yours and your classmate).

These are recommended references for mathematical style:

The following resources may help you with getting into LaTeX (Pay attention to how the problem statements in the assignments are typeset. This you usually gets you half-way there with learning the symbols needed to typeset the solution.)

General "psychological" advise: take it easy if you have lots (I mean LOTS) of corrections from the TA on your mathematical text. Working mathematicians and researchers in general get corrections from the reviewers all the time when submitting papers for publishing, that is normal. Also, if you never wrote in LaTeX, this is going to be time consuming at first, but this period is not long at all, about 1-3 weeks, but only in case you indeed invest your effort into learning the tool and working on the home assignments.