This is a long overdue update on my math learning project. The short of it is that I’ve mostly been using Math Academy to fill in gaps in my background. I’ve also been following Terence Tao’s book Analysis I. This post is about Math Academy. I’ll plan to write about what led me to Tao’s book in a future post.
Happy 15th anniversary to tau!
The Art of Problem Solving, affectionately known as “AoPS” for short, is a math program offering books and courses covering high-school mathematics from an advanced and challenging perspective. The heart of AoPS is a two-volume set of books, mentioned before in “Resources for Math Learning (Intro to Math)”: The Art of Problem Solving, Volume 1: the Basics by Sandor Lehoczky and Richard Rusczyk…
Happy Half Tau Day, everyone! Today on 3/14 we celebrate the halfway point ’round the unit circle, \( \tau/2 = 3.14159\ldots \)
How to Prove It: A Structured Approach (3rd Edition) by Daniel Velleman is one of the main resources I’ve been using for the intro to math phase of my math learning project . It’s an excellent “intro to proofs” book suitable for self-study or for a course aimed at math majors making the transition to higher mathematics. How to Prove It is challenging enough—especially the many excellent…
It’s that time of year again: the summer (or winter!) solstice, high school graduations, college commencements, and of course Tau Day!
I’ve mentioned a couple of times before that contest math is forming an important part my personal goals for math learning. I previously posted the solution to a challenging contest math problem, which showed how to use some clever algebraic manipulations to significantly simplify a particular sum. In this post, I solve another problem from the same resource (The Art of Problem Solving, Volume 1,…
Happy Pi Day—or, as I prefer to call it, Half Tau Day!
I was recently at a party that involved a discussion of physics (no, I did not initiate this discussion), including various aspects of Einstein’s relativity. This led a friend of mine to lament that, due to the limit imposed by the speed of light, the dream of exploring the galaxy—à la Star Trek—could never be realized. As an ardent Trekkie, she said, this really bummed her out.
In Personal Goals for Math Learning, I mentioned that contest math is a great way to practice problem-solving skills while also reviewing the high-school curriculum from a challenging perspective. Among other things, I mentioned a particular problem (together with a hint) that shows just how challenging “high school” mathematics can be in the context of contest math. This post contains a full…