Research Scientist
Department of Mathematics
MIT
Email: dspivak--math/mit/edu
Metric
realization. A short paper (possibly with errors) connecting fuzzy
simplicial sets and metric spaces, by way of adjoint functors.
Smooth
chess. A short, unfinished paper about something I call "smooth
chess," in which the idea is to generalize chess by replacing the set
{0,1} with the unit interval [0,1].
So, on your turn, you can move
fractional pieces adding up to 1. For example .7 white bishop moves to a
square with .4 black queen and thereby captures .1 of the black queen (the
square now contains .7 white bishop and .3 black queen). In the same
turn, white also moves .3 pawn, and thus his total move is .7+.3=1, as
desired. Fractional pieces (e.g. rooks) can move through squares that are
already inhabited by other fractional pieces, so long as they do not
"overflow the square" in doing so.
Stokes Theorem
A look at freshman vector calculus from the perspective of
differential geometry. (Written as a grad student.)
My PhD
thesis. The 150 page version that preceded the current
version.
Grothendieck Topologies Another way to view Grothendieck
topologies.
Box
monads. An unfinished note about two monads I like on the category
of categories.
Presheaf the
cobbler A funny abstract for a talk I gave about presheaves and
sheaves.
Group-ring
calculation program. An object-oriented program I wrote in the
"Scheme" programming language, which solves equations in groups, rings,
group-rings, etc. Very un-user-friendly. Runs in emacs.
Sheaves and
Homotopy Theory Dan Dugger's
unpublished paper on sheaves and homotopy theory.
A quote of Albert
Einstein on the importance of the theory of knowledge. I got this from
Ronnie Brown.
symbols.pdf LaTeX
symbols.
symbols-all.pdf Many more
LaTeX symbols
xyguide.pdf A
guide to using the LaTeX package xymatrix.
Skill
with LaTeX. Includes nice tables.
pgfmanual.pdf
A guide to using tikz.
diagxy.pdf Documentation for a LaTeX program for drawing complicated
commutative diagrams.
multicol.pdf Multiple columns in LaTeX.
PhD
Graduation picture. With Eli Lebow and Johanna Franklin.
This
work by David I. Spivak is licensed under a
Creative Commons
Attribution-Share Alike 3.0 Unported License.