Mostly I don’t miss academic math, but sometimes I do

I really haven’t looked back since leaving academic math. For the most part I lost interest in math research in graduate school and took an academic job just to be sure that, indeed, I didn’t want to be in academia.

I definitely enjoy reading about current developments, though sometimes the articles make me happy I found something else to do. Pretty amazing what IMO gold medalists / perfect scorers are doing, though:

Math Quartet Joins Forces on Unified Theory

A Tenacious Explorer of Abstract Surfaces

Working with my kids has reminded me about the joy math brought me when I was younger. Sometimes that work even inches towards questions that you might ask in math research.

This morning my older son and I talked through this problem from the 2015 AMC 10b:

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Here’s that project:

A Challenging Factorial Problem

After finding the four smallest numbers satisfying the conditions in the problem my son wondered how many more solutions there were, and if there would actually be infinitely many.

Good things for a kid to wonder and ponder – it brought me back to my grad school days for just a second 🙂

Looking at Michael Pershan’s subtraction post

Saw a neat post from Michael Pershan last night:

One of the reasons it caught my attention was that my younger son has had to change the way he does subtraction. Sadly the reason for the change is that the standardized testing up here tests borrowing and carrying. Ugh.

Anyway, I thought it would be interesting to hear him work through this problem since subtraction is back to being new to him. Here’s what he did (as well as his explanation of borrowing and carrying):

Next we scrolled through Pershan’s blog post. I wanted to see how my son would react to the different solutions. The solution that used addition rather than subtraction was the one I was particularly interested in him seeing:

So, an interesting exercise – especially viewing and trying to understand the other solutions.

A challenging factorial problem

Yesterday my older son and I worked through a a challenging algebra problem. Today’s challenging problem involved factorials. The problem is #23 from the 2015 AMC 10b:

Problem 23 from the 2015 AMC 10b

Here’s the problem:

Let $n$ be a positive integer greater than 4 such that the decimal representation of n! ends in k zeros and the decimal representation of (2n)! ends in 3k zeros. Let s denote the sum of the four least possible values of n. What is the sum of the digits of s?

We started by just talking through the problem and coming up with a plan:

Next he implemented that plan and did a great job working through to the end of the problem:

Finally, we went to Wolfram alpha and double checked that the numbers he found were indeed solutions to the problem (and sorry for the stumbling around by me in this part!)

So, a challenging problem and a good solution from my son. We continue to work on ideas about problem solving. It is always nice when everything comes together like it did for today’s project!