trying to be a mile wide AND a mile deep
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 […]
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 […]
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 […]
The three properties of relations learned first are reflexivity, symmetry, and transitivity. Reflexivity is an existence property; a possession property. If you contain this entire particular set of pairs, you’re reflexive. If not, then not. Symmetry and transitivity are implications; closure properties. Now some pairs don’t come for free – they require other pairs be […]
Let A = {1,2,3,4,5}. Define a function f from A to A that is also a transitive relation, but is not the identity function. Answer after the jump.
A professor is writing a multiple choice question. The question will show three graphs and ask which of them are connected, and the answer choices will be of the form “I and II only”, “none of them”, “all of them”, “III only”, etc. The professor uses a program to generate the answer selections, which guarantees […]