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 […]
Far from carefully vetted for accuracy. We must be careful not to confuse data with the abstractions we use to analyze them. William James A judicious man looks on statistics not to get knowledge, but to save himself from having ignorance foisted on him. Thomas Carlyle After all, facts are facts, and although we may […]
This is an exam problem I gave once; you’ll need to know |A| is the size/number of elements of A. Let A and B be finite nonempty sets, and f a function from A to B. Fill one I, for injective (1-1), and one S, for surjective (onto), in each line of the following table […]
Using the ease of moving between geometric series and their sums, plus the fact that for power series the derivative of a series is the sum of the derivatives of each term (and likewise for integrals), we can find a wider range of power series without too much trouble. I like making diagrams so here […]
Break into chunks and then add back together. Break into tasks and then multiply together. Do via the back door – find exactly when you don’t want and what’s left over is what you do want. Combining this with DeMorgan’s Laws can be powerful. Counting: find the total number of ways to accomplish a task […]