Math 448 (Expectations)

# Special Hints for this Course

In addition to the homework hints and exam hints, math students should consider the following:

• Outline your proofs before you write them. You should work out the details of your proof before you write up your final version; don't just start writing. This is the same as it would be in any writing that you do: you should know where you are headed and what you plan to say before you start. In class, I may write proofs directly at the board without showing you an outline, but that's because I've already done the thinking that goes into the process. In many ways, however, the thinking that comes before the proof is the most important part -- the proof simply codifies this thinking. You can't skip right to the proof without doing the preparation. Remember that you can work both from the beginning (the information that you know) and from the end (the place you are trying to get to).
• You should be able to interpret new definitions on your own. As you gain experience in mathematics, you should be able to figure out the meanings of, and prove things about, definitions that you've never seen before, even without examples in class. Your goal should be to be able to read and understnad new mathematics on yuor own. The definitions are findamental to that, and you will find yourself going back to them over and over as you work with new theorems and need to understand the details precisely.
• Translate between notation and words and vice versa. If a definition or theorem is given in terms of words, you should try to rewrite it in terms of the associated mathematical notation. Conversely, if a definition includes mathematical notation, you should translate it into the corresponding concepts in words. (And I don't mean just a symbol-by-symbol transliteration, but a concept-based conversion.) Most students find the translation between the ideas in their head and the mathematical notation on the page to be a difficult one, and this is one that you need to practice carefully.

 Math 448 (Winter 2007) web pages Created: 01 Jan 2007 Last modified: Jan 2, 2007 2:58:52 PM Comments to: `dpvc@union.edu`