I was taught that you cannot divide by zero and that the answer is undefined. Every explanation I have had since is either a restatement of the rule or a calculator error message. What I do not understand is why the…
This has been running in our group for a week and neither side will move. A player said "this is going to be a 17" and then rolled a 17. I said that was a 1 in 20 event. Another player says no: the guess is one of…
Take a disc, drop n independent uniformly random points into it, and connect each point by a segment to whichever other point is nearest to it. The connections group the points into clusters. For a small example, twenty…
I am a software engineering student and I keep meeting this in hardware courses. A quantity is only defined for whole numbers, how many adder stages, how many pipeline registers, how many parallel units and the analysis…
Probabilities live between 0 and 1, which seems like a perfectly comfortable range to work in. Yet every textbook and every library I open converts to logs almost immediately and then stays there. I can follow the…
A colleague set this as a puzzle: two strings of H and T, 200 each. One came from actual flips, one a student invented while trying to look random. Work out which is which and be able to justify it. I know the counts of…
The statement I have been given is that for a non negative measurable function on a set, and any positive number lambda, the measure of the region where the function is at least lambda is bounded by the integral of the…
The problem is easy to state: visit every city once, return to the start, minimise total distance. Evaluating any particular route takes almost no work add up the distances. So the difficulty is entirely in the search…
The theorem itself follows immediately from the definition of conditional probability. Write the joint probability two ways, divide, done. As a piece of mathematics it is about as deep as rearranging a fraction. Yet it…
Take the curve y = a x², and a point on it at some positive x, so that the arc from the origin to that point has some length L. Now change the coefficient to a different value. I want the point on the new parabola such…
First term of a proof based course. A single exercise ate 40 minutes last night and I still did not finish it, and there are six on the sheet. My classmates all say it took them twenty minutes so I cannot tell if I am…
Across all differential equations, finding an analytical solution is the exception rather than the rule. Even innocuous looking equations built from elementary functions either have no closed form solution or have one…
She brings home ratio and proportion questions and I show her the way I was taught, cross multiply and solve. The answers are right and the working gets a line through it, because the school wants bar models. Now she…
I simulated data from a normal distribution and then computed the likelihood of that data under the very distribution that generated it. The number came out astronomically small. That is what confuses me. This is the…
Three equations, three unknowns, and the determinant of the coefficient matrix comes out 0. My notes say that means no unique solution, but when I row reduce by hand I find solutions that check out when I plug them back…
I start a maths degree in September and the first module is Foundations: logic, sets, relations, proof technique. Everyone in the year above says it broke them, and not one of them can tell me what specifically broke. I…
Working through for a homework set. The first round of parts leaves me with , and the second round hands me back the exact integral I started with. I have done it four times and I keep going in a circle. Is my choice of…
I am 17 and school has started putting me in front of olympiad style papers on Saturday mornings. I enjoy them, but they eat the hours I would otherwise spend on the syllabus, and two people have told me university…
I placed into Calc 1 for the autumn but I last did algebra properly about seven years ago. I have roughly six weeks and can give it 45 minutes a day, not more, because I am working full time. Do I spend that on a…
I can follow epsilon delta proofs when I read them but I cannot produce one. The step where the proof says let delta equal epsilon over five feels like it came from nowhere. How do people actually find that number, and…