Noah Gochnauer assignment 2

Style is an important part of writing. What you are writing should impact how you write it. I was drawn to section 2.2, 2.3, and 2.4 because these sections speak about writing theorems, proofs, and definitions. All three of these things are major aspects of mathematics that do not follow traditional writing form.

The main idea of the sections on theorems and proofs (2.2 and 2.3) is accessibility. The whole point of writing theorems and proofs is to teach people new things. A theorem or proof that is long can be daunting, and the extensive information can make it hard to read and understand. Krantz emphasizes the need to split up the information and signpost the connection between sections. This will direct the reader's learning process in a more constructive manner than simply throwing a wall of information at them. All of the information should still be present in the writing though; the goal is to make the theorems and proofs easier to understand without leaving out crucial information.

The focus of Krantz's section on definitions is consistency. Mathematics has a foundation that has been built on for a long time, leaving many standard definitions. It is important for a writer to be aware of common definitions and the notation that traditionally accompanies them. Using these conventions when possible will help the readers understand the information being imparted, and make the writing more clear. A writer should use a light hand when providing definitions, but still  provide the necessary information. To use an exaggerated example, when writing a paper for graduate students there is no need to provide the definition for fractions.

Summary based on pages 69-76 of Steven G. Krantz's A Primer of Mathematical Writing.