Where am I?
Let epsilon be positive is unsurprisingly a blog about math. Probably about undergraduate math, for now. Yet, it does not aim at giving another explanation of the chain rule, Gauss reduction, or the binomial distribution; there are already plenty of good resources online already. But it does aim at showing everything your math teacher should have told you.
Who are you?
I am Raoul Normand, a clinical assistant professor of math at New York University. I got my a PhD in France in 2011 in probability, did postdocs in Toronto and in Taipei, after being an invited Assistant Professor at New York University Shanghai from 2016 to 2019. This blog reflects only my opinions and is not affiliated with NYU or other organization.
What is going on here?
As university instructors, we have to contend with many imperatives in the design of our classes: university rules; other courses; tradition; peer-pressure; other departments; time; available resources; etc. Naturally, we also all have our own ideas of what is the most important to teach our students and what is best for them overall. So a certainly more honest albeit protracted subtitle for this blog ought to be “A very biased collection of facts and opinions I would tell my students had I unlimited time, freedom, resources, and no shame at all”.
Notwithstanding, I will attempt to present some useful techniques that, in my experience, are very valuable yet not mastered or known by most undergraduate students of math. I shall also discuss sundry topics that I often find overlooked or poorly understood. I also want to bring different areas of math together, like calculus, linear algebra, algebra, geometry, probability, etc. As these are often taught in separate classes, it is often delicate to show the connection, and it is too bad: that is when math becomes really awesome! A side quest will be to show that rigor in math matters, and that some some things should not be trifled with.
This is of course very influenced by what I observe in my own classes, most of which taught in the American system. On the other hands, the topics of choice are the fruit of my own education in France, and my own tastes as a probabilist.
Betraying the original goal, my fancy may take me to discuss sundry subjects which I deem worthwhile, or merely entertaining. Applications to real life problems, beautiful proofs, mind-boggling counterexamples… And I may rant, will probably rant a smidgen too much about what I think goes wrong in math education. However you feel about this, the comment section is open!