Harry Altman at the University of Michigan

This website is no longer maintained. Please see instead my new website.
My name is Harry Altman. I recently completed my PhD in mathematics at the University of Michigan, studying under Jeffrey Lagarias. Recently I've been studying some combinatorial number theory involving the complexity of computing natural numbers in some simple computational models.

Some recent updates (I appear to have missed some):
2017 October 30 -- Intermediate Arithmetic Operations on Ordinal Numbers is now published!
2016 June 24 -- Integer Complexity: Algorithms and Computational Results is now on arXiv.
2016 April 10 -- Added more images.
2016 March 22 -- "Integer Complexity: Representing Numbers of Bounded Defect" is on arXiv.
2015 September 9 -- Published version of "Integer Complexity and Well-Ordering"
2015 July 1 -- More questions about Snake.
2015 January 26 -- The super-Jacobsthal exponentiation paper is now on arXiv!
2014 September 9 -- Added more images.
2014 September 8 -- The addition chain defects paper is on arXiv!
2014 May 27 -- My dissertation can now be found below, along with the corresponding code!
2014 January 8 -- Minimum and maximum possible scores in Space Alert
2013 December 29 -- Two more words for the Co-files.

I can be reached via email at . (If you can't see my email address, that's because it's been Javascript-obfuscated to fool spammers, but you can deduce it from this page's URL.) My PGP public key can be found here.

Papers and drafts

Published papers




Polished drafts, should be readable

Nothing to go here at the moment.

Old drafts, may be incomprehensible and out of date

"Problem dump"

Informal bloggy writing on problems I don't necessarily know much of anything about.

Other stuff

Here are miscellaneous files I wish to put in public view:

Here are some drawings that people have given me which I have bothered to scan:

And here are some assorted other images.