Thursday, June 28, 2012

Back from NASSLLI

NASSLLI2012 was great, too many great courses to follow, too many interesting people to chat to, too little time to do everything.

Now I realize that I haven't been paying any attention to recording/collecting stuff that I have been doing and, age being what it is, I forget what I have done. and also what I have not done yet...

so I will try another round of blog-post-its, in the hopes that when I finally get my Bham account unlocked and my G'sites account working, life will be easier.

First off: Jean-Yves Beziau and Marcelo Coniglio organized a book in honor of Walter Carnielli's 60th Birthday. I did manage to get a paper on constructive modal logic in, yay!

Monday, June 18, 2012

Homework 2?

Check this short homework out. Slides after the class.

Category Theory for all, June 18, 2012



The slides for today's lecture are here.

Hopefully a not-crazy-jumping pdf, but instead one that you can go up and down, at your leisure.

Thanks for the patience with the scrolling issues!
And  thanks for the expert diagnostics after the event.

Please do take a look at the post on  references for introductions to Category Theory, if you can. 

Sunday, June 17, 2012

Categorical Proof Theory and Linear Logic

These are some very, very old notes from a course I gave in Prague, at  ESSLLI 1996.

The idea was to present enough basic category theory and enough basic proof theory to discuss the categorical modelling of Linear Logic and ... drum roll...introduce  Dialectica Categories.

(and yes, I also had high expectations of understanding enough about models of Linear Logic to be able to discuss them all and write a book, ha...)

 Now I have reduced my expectations and I simply would like to introduce enough category theory to make the categorical modelling of Intuitionistic Logic plausible (before I wanted to do both intuitionistic and linear logic).

But in compensation I would like to do this in four lectures only, as I wanted to keep the 5th lecture to introduce Glue Semantics,  in the style that a linear logician, especially  a budding one, would understand it. At least this is the plan.

Homework for Cat Theory Day 1: why not?

So you know, I hope, that mathematics is not an spectator's sport.
You need to do the calculations, otherwise the stuff doesn't work.

The good news is that no one will come after you, asking for your grades or anything like it. And that you can come and ask  me questions, if you feel like it.

The bad news is that, if you don't do them (the exercises) you'll end up thinking that you've learnt and sometimes you haven't. Your call, of course.

To sweeten the pill, there's a reading for each day, just for the fun of it.
For the exercises, there are answers on the web, but you should really try to do it, first.

The first treat is “The aims of Education” by Andrew Abbott of the University of Chicago. Only 5 pages and (I find it) a different take on why do we go to college.

Thursday, June 14, 2012

Mathematics as we know it...

Frank Quinn had a very interesting article entitled "A REVOLUTION IN MATHEMATICS? WHAT REALLY HAPPENED A CENTURY AGO, AND WHY IT MATTERS TODAY", in the Notices of the AMS, January 2012. You can find it it in his education webpage.

Living and Learning?

Category Theory requires exercises, so I'm trying to organize homework sheets. But I want to add some treats to the homework, a bit like I a did for Phil50/COEN260.

The first treat is “The aims of Education” by Andrew Abbott of the University of Chicago. Only 5 pages and (I find it) a different take on why do we go to college.

The second treat is Lockhart's Lament, check this old post.

The third treat is Quinn's Revolution, published by the AMS, January 2012.

The fourth treat is  Anonymous in Quora on  "What is it like to have an understanding of very advanced mathematics?"

We end with something different, Eli Pariser on "The Filter Bubble", TED talk, May 2011.

And yes, I feel sorry not to include Wigner's `The Unreasonable Effectiveness of Mathematics in the Natural Sciences'. Nor Hamming's ``The Unreasonable Effectiveness of Mathematics" and perhaps the unreasonable effectiveness of data should be mentioned too...

Oh well too many treats might make us sick...
But keeping links in store is not so bad, shame I don't seem to find "The Canon of Technology" anymore.

Category Theory introduction? yeah, sure...


MacLane
Eilenberg













There is plenty of material on category theory around. Collecting here some old favorites and some newer stuff that I haven't checked out,  yet.

The familiar:
S. Mac Lane, Categories for the Working Mathematician (1971, 1998)

R. Goldblatt, Topoi, Dover reprint and online (1979, 1984, 1986, 2002).

J.-Y. Girard, Y. Lafont, P. Taylor, Proofs and Types (1989) online 

V. de Paiva, Categorical Proof Theory and Linear Logic, ESSLLI, Prague (1996) google doc sideways(!) available

D. Crouch, J. Genabith, Linear Logic for Linguists, ESSLLI (2000), notes

J. Gallier, Constructive Logics. Part I: A Tutorial on Proof Systems and Typed lambda-Calculi, paper

Then some traditional fare:

R. Blute P. Scott, Category Theory for Linear Logicians (2003)

F.W. Lawvere, S.H. Schanuel, Conceptual Mathematics (1997)

S. Awodey, Category Theory, (2010)

H. Simmons, An Introduction to Category Theory, CUP, (2011) online version

Adámek, Jiří, Herrlich, Horst, & Strecker, George E.; (1990). Abstract and Concrete Categories Originally publ. John Wiley & Sons. ISBN 0-471-60922-6. (now free on-line edition). 

M. Barr, C. Wells, Toposes, Triples and Theories, 1983, now online.


Then more adventurous (perhaps??) stuff:


M. Johansson, Category Theory and Functional Programming, Stanford FALL 2009 course and St. Andrews 2012 notes   (99 pages)

also Chalmers discussion group

Abramsky and Tzevelekos, "Introduction to Categories and Categorical Logic" (2010)
G. Hutton, Introduction to Category Theory, Midlands Graduate School notes, 2012.

D. Verity, An Introduction to Category Theory - FP-Syd talk.

E. Cheng, The Catstars, YouTube channel.

J. van Oosten, Basic Category Theory, 2002, notes

L. Maertens, Category Theory for Program Construction. ESSLLI notes (1995)

S. Easterbrook, An introduction to Category Theory for Software Engineers, slides

Further afield:

  • Sets for Mathematics by F. W. Lawvere & R. Rosebrugh.
  • Topoi: The Categorical Analysis of Logic by R. Goldblatt.
  • Abstract and Concrete Categories: The Joy of Cats by J. Adamek, H. Herrlich, G. Strecker.
  • Categorical Logic by A. M. Pitts. 
  • Stone Spaces by P. T. Johnstone.
  • Sheaves in Geometry and Logic: A First Intorduction to Topos Theory by S. Mac Lane & I. Moerdijk.
  • Handbook of Categorical Algebra (three volumes) by F. Borceux.

Sunday, June 3, 2012

Categorical Logic Lab? Yes!!!

The bit I saw of the Logic, Rationality and Interaction meeting was excellent.
Love the idea of logical labs:  I want a Categorical Logic Lab!
How do I go about getting one?...

Saturday, June 2, 2012

March was Qualis Time

no, not quality time. (haven't had that for ages...)

QUALIS is the system CAPES (a Brazilian funding agency) uses to measure the quality of pos-grad programmes. Since they classify journals, it ends up being an unofficial yardstick to measure all research produced in the land. Some Brazilian logicians realized that the classification was very arbitrary and we had a petition to try to influence the official arbiters.

Getting a petition going and some small amount of consensus on the classification of journals was very hard.

XV Simposio Latino Americano de Logica Matematica (SLALM2012)

Going to Bogota, Colombia today for the 15th Latin American Symposium on Mathematical Logic.
A bit worried as I don't know many people in this community, but looking forward.