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

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