trying to be a mile wide AND a mile deep
Well, not so much “me” as my handwriting. Of course there are deep posts to be had on how the study and practice of mathematics changes one’s approach to all manner of life situations, but the most visible (literally) of the changes it made to me is how it altered my handwriting. Or, more accurately, […]
I had the good fortune as an undergraduate to have a “bridge class” in my math curriculum. We learned basic logic, set manipulation, formal functions and relations, proof structure and induction. In that class our instructor had us read an article by Reuben Hirsch called “Math Lingo vs. Plain English: Double Entendre” (published in the […]
If you disagree, feel free to append “IMNSHO” to each. Respect your students: Learn their names. Start and end on time to the best of your ability. Admit your mistakes and when you don’t know an answer. Answer questions without implying they are stupid ones. Set out all expectations in the syllabus and stick to […]
Theorem: Suppose a, b, c are natural numbers. If a divides b and b divides c, then a divides c. Bad Proof: Suppose the hypothesis. We can substitute a times something for b in the equation b times something equals c. The two somethings together multiply a to c so we’re done.[way too vague; might […]
Proof traits explicit/specific (non-vague) logically sound, including complete lacking irrelevant statements understandable to the reader self-contained (may assume basic things; anything else needs explicit reference to previous work or must be written out in the proof) Proof kinds Direct proof: Assume hypothesis and march to conclusion. Contradiction: If proving a single clause, assume its negation […]
From the Editor in Notices of the AMS Vol 43, Issue 10 (October 1996) was an essay on the need for mathematical literacy in the general public, beginning with Nixon’s use of the third derivative. A beginner’s guide to quadric surfaces (pdf), by me, for my calculus students and intended to supplement the textbook rather […]