Comments for João Ferreira http://www.joaoff.com Programming, Algorithms, and Mathematics Sat, 04 Jul 2009 01:11:06 +0000 http://wordpress.org/?v=2.6.1 Comment on How to be more confident about your own programs: an example using Perl by How to be more confident about your own programs an example using | debt solutions http://www.joaoff.com/2007/07/26/how-to-be-more-confident-about-your-own-programs-an-example-using-perl/#comment-4334 How to be more confident about your own programs an example using | debt solutions Tue, 16 Jun 2009 01:24:31 +0000 http://www.joaoferreira.org/2007/07/26/how-to-be-more-confident-about-your-own-programs-an-example-using-perl/#comment-4334 [...] How to be more confident about your own programs an example using Posted by root 1 hour 52 minutes ago (http://www.joaoff.com) Indirect equality and the solution to the problem i 39 m aware that although the ceiling and floor functions are widely used in financial applications my previous comment got completely hosed because the blog software threw away a square grid path problem Discuss  |  Bury |  News | How to be more confident about your own programs an example using [...] [...] How to be more confident about your own programs an example using Posted by root 1 hour 52 minutes ago (http://www.joaoff.com) Indirect equality and the solution to the problem i 39 m aware that although the ceiling and floor functions are widely used in financial applications my previous comment got completely hosed because the blog software threw away a square grid path problem Discuss  |  Bury |  News | How to be more confident about your own programs an example using [...]

]]> Comment on How to be more confident about your own programs: an example using Perl by How to be more confident about your own programs an example using | Outdoor Ceiling Fans http://www.joaoff.com/2007/07/26/how-to-be-more-confident-about-your-own-programs-an-example-using-perl/#comment-4036 How to be more confident about your own programs an example using | Outdoor Ceiling Fans Sun, 31 May 2009 09:37:19 +0000 http://www.joaoferreira.org/2007/07/26/how-to-be-more-confident-about-your-own-programs-an-example-using-perl/#comment-4036 [...] How to be more confident about your own programs an example using Posted by root 3 hours ago (http://www.joaoff.com) Jul 26 2007 the problem i am going to deal with involves the ceiling and floor functions my previous comment got completely hosed because the blog a square grid path problem jo o ferreira 2009 powered by wordpress Discuss  |  Bury |  News | How to be more confident about your own programs an example using [...] [...] How to be more confident about your own programs an example using Posted by root 3 hours ago (http://www.joaoff.com) Jul 26 2007 the problem i am going to deal with involves the ceiling and floor functions my previous comment got completely hosed because the blog a square grid path problem jo o ferreira 2009 powered by wordpress Discuss  |  Bury |  News | How to be more confident about your own programs an example using [...]

]]> Comment on A Calculational Proof of the Handshaking Lemma by jff http://www.joaoff.com/2009/04/07/calculational-proof-handshaking-lemma/#comment-2981 jff Thu, 30 Apr 2009 12:26:35 +0000 http://www.joaoff.com/?p=86#comment-2981 Ted, thanks a lot for your comment. Regarding bibliography, I recommend you to take a look at the following webpage: http://twiki.di.uminho.pt/twiki/bin/view/Research/Matisse/MatisseBiblioteca It is in Portuguese, but under the section Livros (Books) you can find several good books. Also, http://mathmeth.com has some very interesting material and if you google "Dijkstra archive" you'll find more than 1000 notes from Edsger Dijkstra. I plan to write a post with some references (as this is a frequently asked question), but I don't know when I'll do it. I don't really know how to answer to your question "Does the calculational proof works in “all” mathematics?". There are areas which are much more suitable for calculation than others; all I can say is that our goal is to reduce the amount of guessing and increase the amount of calculation (that way, we believe we can make the teaching of proofs more systematic). I'm currently working more with number theory. Finally, you wrote that you had problems with the notation. Could you suggest improvements? What was the most difficult notation and why? Thanks again, Joao Ted,

thanks a lot for your comment. Regarding bibliography, I recommend you to take a look at the following webpage:

http://twiki.di.uminho.pt/twiki/bin/view/Research/Matisse/MatisseBiblioteca

It is in Portuguese, but under the section Livros (Books) you can find several good books.
Also, http://mathmeth.com has some very interesting material and if you google “Dijkstra archive” you’ll find more than 1000 notes from Edsger Dijkstra. I plan to write a post with some references (as this is a frequently asked question), but I don’t know when I’ll do it.

I don’t really know how to answer to your question “Does the calculational proof works in “all” mathematics?”. There are areas which are much more suitable for calculation than others; all I can say is that our goal is to reduce the amount of guessing and increase the amount of calculation (that way, we believe we can make the teaching of proofs more systematic). I’m currently working more with number theory.

Finally, you wrote that you had problems with the notation. Could you suggest improvements? What was the most difficult notation and why?

Thanks again,
Joao

]]> Comment on A square grid path problem by jff http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-2980 jff Thu, 30 Apr 2009 12:14:36 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-2980 Mohammad: if you allow movements in all directions, then you have to be careful with loops (Note that RLRLRLRLRLRLRLRLRLRLRLRL maintains your position; you can thus prepend it to any other path.) In that case, I suppose you could reformulate the problem to counting paths of size N that lead you to the bottom-right corner. Mohammad: if you allow movements in all directions, then you have to be careful with loops (Note that RLRLRLRLRLRLRLRLRLRLRLRL maintains your position; you can thus prepend it to any other path.)

In that case, I suppose you could reformulate the problem to counting paths of size N that lead you to the bottom-right corner.

]]> Comment on A square grid path problem by Mohammad Hourani http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-2960 Mohammad Hourani Wed, 29 Apr 2009 21:04:23 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-2960 also, what if we want from down to up path, we just change 2*n to 3*n...?? also, what if we want from down to up path, we just change 2*n to 3*n…??

]]> Comment on A square grid path problem by Mohammad Hourani http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-2959 Mohammad Hourani Wed, 29 Apr 2009 20:51:12 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-2959 great work, but what if i want to include "go to left n positions", what will happen to the formulas?, thx in advance.... great work, but what if i want to include “go to left n positions”, what will happen to the formulas?, thx in advance….

]]> Comment on A Calculational Proof of the Handshaking Lemma by Ted http://www.joaoff.com/2009/04/07/calculational-proof-handshaking-lemma/#comment-2857 Ted Mon, 27 Apr 2009 00:16:18 +0000 http://www.joaoff.com/?p=86#comment-2857 Hi João, I'm a first year undergraduate student of mathematics and computer science. We have just started with graph theory and have been introduced to the handshaking lemma and its corollaries the very first hour. The proof which was presented was pretty much the same as the one you quoted and sadly, your concerns about the "students using seemingly unrelated concepts" are utterly true. On the other hand, the proof you presented looks really neat and convincing although I had a hard time with the notation, since I'm not familiar with it. Does the calculational proof works in "all" mathematics? Also, could you recommend some literature to get a better grasp on the calculational proofs and maybe on the Eindhoven notation too? Thank you and best regards from Slovenia, Ted Hi João,

I’m a first year undergraduate student of mathematics and computer science. We have just started with graph theory and have been introduced to the handshaking lemma and its corollaries the very first hour. The proof which was presented was pretty much the same as the one you quoted and sadly, your concerns about the “students using seemingly unrelated concepts” are utterly true.

On the other hand, the proof you presented looks really neat and convincing although I had a hard time with the notation, since I’m not familiar with it.

Does the calculational proof works in “all” mathematics?
Also, could you recommend some literature to get a better grasp on the calculational proofs and maybe on the Eindhoven notation too?

Thank you and best regards from Slovenia,
Ted

]]> Comment on New domain name (joaoff.com) by Jane Forrester http://www.joaoff.com/2008/02/25/new-domain-name-joaoffcom/#comment-1885 Jane Forrester Fri, 13 Mar 2009 02:10:47 +0000 http://www.joaoff.com/2008/02/25/new-domain-name-joaoffcom/#comment-1885 I really enjoy your brilliant "seemingly-easy" approaches to hard proof problems. However, I have a few dangling doubts in my mind. 1. It seems like your research is about applying formal methods(constructive approach) to programming. Is there any significant result in the industry using that methods? I think Dijkstra's approach(with simple toy problems) resulted (directly) in no fruit in the real world. 2. What do you think about MIT's Alloy? It's kind of a mix between formal and informal proof/check. Some people consider it a somewhat practical approach. 3. What books and materials do you recommend someone who wants to learn your approach? (for undergraduates, and for professionals like me) Thanks as always. I really enjoy your brilliant “seemingly-easy” approaches to hard proof problems.

However, I have a few dangling doubts in my mind.

1. It seems like your research is about applying formal methods(constructive approach) to programming. Is there any significant result in the industry using that methods? I think Dijkstra’s approach(with simple toy problems) resulted (directly) in no fruit in the real world.

2. What do you think about MIT’s Alloy? It’s kind of a mix between formal and informal proof/check. Some people consider it a somewhat practical approach.

3. What books and materials do you recommend someone who wants to learn your approach? (for undergraduates, and for professionals like me)

Thanks as always.

]]> Comment on A square grid path problem by 1234 http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-1711 1234 Tue, 17 Feb 2009 16:55:21 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-1711 Thank you very much for this helpful and clear description. Thank you very much for this helpful and clear description.

]]> Comment on A square grid path problem by Problem 15 | Project Euler http://www.joaoff.com/2008/01/20/a-square-grid-path-problem/#comment-1583 Problem 15 | Project Euler Thu, 05 Feb 2009 17:32:05 +0000 http://www.joaoferreira.org/2008/01/20/a-square-grid-path-problem/#comment-1583 [...] using combinatorics. João Ferreira has a good description of the problem and general [...] [...] using combinatorics. João Ferreira has a good description of the problem and general [...]

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