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Foundations of Computer Science

i.stanford.edu

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Re: Foundations of Computer Science

#33

Post by shva »

thisisdallas wrote: post #32

Would this be a good resource for someone who doesn't have a CS degree and who doesn't necessarily know the foundation of CS?

After skimming through it a bit, and as a CS student, this looks like an excellent introduction to the theory of computer science, especially for someone with no background in it. It corresponds with what I would expect a first or second year university course on Computer Science would cover. After reading some of this, if you're still interested in this sort of thing, the rather infamous Introduction to Algorithms published by MIT press may be a good next step. PDFs can be found online with a bit of digging.

Re: Foundations of Computer Science

#34

Post by signa11 »

jorgeleo wrote: post #28
dschiptsov wrote: post #17

1992 - a world without Java... And, you know, the book about foundations is... SICP.) OK, this is C Edition .

if "computer science is a science of abstraction — creating the right model for thinking about a problem and devising the appropriate mechanizable techniques to solve it" then language is of no importance

> language is of no importance

well, you are just being facetious, and i guess you know it too. languages are part of 'devising the appropriate mechanizable techniques to solve it' as well as algorithms & data-structures which support the abstractions that you just came up with...

Re: Foundations of Computer Science

#35

Post by eru »

hackinthebochs wrote: post #30
chas wrote: post #27

Earlier quoted context omitted.

Homotopy type theory[1] is essentially working to show that math is (or can be viewed as) an interesting application of computer science. [1] http://homotopytypetheory.org/2013/06/20/the-hott-book/

Very interesting! I've often got into nasty arguments with people online when I dared to say that Computer science (Computing) was not a subset of math, but rather could be viewed more naturally as a superset. It is good to see serious academic work being done along these lines.

You can have the same debate about logic and mathematics, or to some extent philosophy and mathematics.

Re: Foundations of Computer Science

#36

Post by decasteve »

chas wrote: post #27
statik_42 wrote: post #21

Earlier quoted context omitted.

So true. People at my school don't always realize that computer science isn't just about programming, it's truly a subset of mathematics.

Homotopy type theory[1] is essentially working to show that math is (or can be viewed as) an interesting application of computer science. [1] http://homotopytypetheory.org/2013/06/20/the-hott-book/

HoTT even more than that. Type theory does what you describe without the "homotopy".

See: http://golem.ph.utexas.edu/category/2013/06/the_hott_book.ht...

Re: Foundations of Computer Science

#38

Post by davorak »

hackinthebochs wrote: post #30
chas wrote: post #27

Earlier quoted context omitted.

Homotopy type theory[1] is essentially working to show that math is (or can be viewed as) an interesting application of computer science. [1] http://homotopytypetheory.org/2013/06/20/the-hott-book/

Very interesting! I've often got into nasty arguments with people online when I dared to say that Computer science (Computing) was not a subset of math, but rather could be viewed more naturally as a superset. It is good to see serious academic work being done along these lines.

I did not get the impression, from the blog posts, that HOTT was putting forth that CS could or is a super set of math just that it can be used as a foundation for all mathematics, just like set theory or category theory can be.

Re: Foundations of Computer Science

#39

Post by hackinthebochs »

davorak wrote: post #38
hackinthebochs wrote: post #30

Earlier quoted context omitted.

Very interesting! I've often got into nasty arguments with people online when I dared to say that Computer science (Computing) was not a subset of math, but rather could be viewed more naturally as a superset. It is good to see serious academic work being done along these lines.

I did not get the impression, from the blog posts, that HOTT was putting forth that CS could or is a super set of math just that it can be used as a foundation for all mathematics, just like set theory or category theory can be.

I think this is where terminology breaks down a bit, but my reading of "basis of" is taken as being loosely equivalent to saying a superset of. In this same sense, logic can be seen as the basis for all mathematics. Anything that is math is also strictly logic, hence math is a subset of logic.
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