Sean Grate Assignment 2

Chapter 2 of Steven G. Krantz's, "Being a Disquisition on Having Your Ideas Recorded, Typeset, Published & Appreciated," discusses the details and methods of writing a mathematics paper. He goes through the different processes for how to organize and present information. Krantz also discusses some common mishaps some authors make and how to avoid them. For example, when presenting a theorem and its hypotheses, the author should try to make it digestible, but still full of impact. So if there fifteen hypotheses to a theorem, it might be helpful to the reader to break those hypotheses into groups and form definitions from them. Then when those definitions have been formed, this allows the reader to associate more easily the hypotheses with the conclusion of the theorem.

Definitions also serve a purpose. They are extremely helpful in providing a rigorous proof, but they should not be overused because too many can irritate the reader and be cumbersome. Definitions can also introduce new notations. Krantz suggests trying to stick to the already established notations and conventions used if possible as this gives more accessibility and comprehensibility to the paper. Another expert in the topic will be more susceptible to reading the paper if they can also understand it, so the easier it is for them to read, the more likely they are to read it.

Krantz then discusses references and the bibliography. There are many ways to introduce references in the text of the paper and then even more ways to format the bibliography. He suggests trying to give meaningful nicknames to the references or at least having it clear what is being referenced with as little cluttering of the page as possible. When making a reference, he notes that the author should also strive to mention where to find the theorem or text being referenced, e.g. giving a section number of a book. This allows the reader to more readily access any source that the paper is using.