During courses on geometry it is sometimes necessary to draw a triangle on the blackboard that can easily be recognized as a general triangle. It must not be rectangular and must n …

I'm going to have a one-hour lecture for middle school students next Monday. It will be about fractals. The students know virtually nothing about this subject. I'll show some frac …

I am trying to prepare a "mathematics talk" for five year olds from my daughter's elementary school. I have given many mathematics talks in my life but this one feels very tough to …

The chaos game is a way to construct (an approximation) of Sierpinski triangle. It's clear (using Thales' theorem!) that if we begin with a point on the sierpinski triangle, then w …

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but w …

I'm teaching axiomatic linear algebra again this semester. Although the textbooks I'm using do everything over the real or complex numbers, for various reasons I prefer to work ov …

Every real symmetric matrix has at least one real eigenvalue. Does anyone know how to prove this elementary, that is without the notion of complex numbers?

No less an authority than Gilbert Strang frames "row rank equals column rank" (and a couple of other facts) as "The Fundamental Theorem of Linear Algebra." I'd simply like to asse …

For the purposes of teaching my elementary course in algebraic geometry I am looking for a reference (or notes) that contains a complete proof of a higher-dimensional weak Bezout t …

By Classical I mean something that could have been found before 1900 (say). A well known consequence of Bezout's theorem for plane curves is Pascal's theorem http://en.wikipedia. …

Are their simple/natural examples of real-valued Borel-measurable random variables whose image is not a Borel set? Something that occurs "naturally"? I am teaching Doob's lemma (f …

I have been chosen by my university to give a 1 hour public research lecture. Every year a researcher is chosen for this honour. Traditionally people explain their own research a …

At the end of this month I start teaching complex analysis to 2nd year undergraduates, mostly from engineering but some from science and maths. The main applications for them in fu …

Thought Experiment Consider a 2-sphere, $S^2$, and let $p$ be a point at the equator. Case 1 Let us parallel transport a vector, $V$ from $p$ using the recipe: Move one unit o …

I'm not teaching calculus right now, but I talk to someone who does, and the question that came up is why emphasize the $h \to 0$ definition of a derivative to calculus students? …