Mathematicians Bridge Finite-Infinite Divide

[michel paul]

This seems like it might be important: https://www.quantamagazine.org/20160524-mathematicians-bridge-finite-infinite-divide/

Note that in the article is this illustration of Ramsey's theorem for triples.

Note that the example they chose

​for this illustration ​

is

​essentially ​

the Collatz conjecture.

I used to have

​my

 students code Collatz

​:

 

• Write and test a function that will return the
  ​Collatz sequence for a given input.
  
  
• ​W
  rite and test a function that
  ​ given an interval 
  will return the number in
  ​that​
   interval that produces the longest Collatz sequence.

​Using list comprehension

​s and generators, 

coding something like that

​is a wonderful

​little exercise

.

​ Very, very doable at a high school level. Maybe even before with highly motivated kids.​

Yep,

​that is the kind of stuff we did, and I'm glad we had the opportunity.

​ 

Simultaneously, I understand that learning how to use a graphing calculator is much more important than being able to study the Collatz conjecture through code you've created. Yeah, I completely understand - choices have to be made.

--

​ Michel

​

===================================
"What I cannot create, I do not understand."

- Richard Feynman

===================================
"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
===================================

[kirby urner]

On May 26, 2016 09:20, "michel paul"

> Simultaneously, I understand that learning how to use a graphing calculator is much more important than being able to study the Collatz conjecture through code you've created. Yeah, I completely understand - choices have to be made.
>
> --
> ​ Michel

Learning what every button does on a scientific calculator is good review, like exploring math and cmath modules in Python standard library.

However holding kids back with 1900s tools is no solution to the "left behind" crisis.  But was solving that ever the goal?

I understand the US at least is really just wanting to give the rest of the world more of a chance to get ahead. It's all about altruism and helping the disadvantaged doncha know. 😋

I sure hope students agitate for a true "lambda calc track" (whatever we wanna call it). They stand to lose the most if we settle for adults' collective inertia. They should know when they're being bilked in exchange for all that precious chair time.

Fortunately, history suggests enlightened self interest is a real motive, despite neuroscience evidence that we're often irrational in how we pursue it.  Trial and error works, provided people are allowed to address past mistakes honestly and learn from them. 

Kirby