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67

I've been spending a fair amount of time editing a journal this year, and it's pretty amazing what different people think of as a "referee report". The first thing you should keep in mind is that the editors will be incredibly appreciative if you look at the paper in detail and send in comments in a timely manner, whatever the comments are. In my mind ...


37

Whenever someone claims a proof (or disproof) of a big conjecture, many people leap to the question of whether the proof is correct. The problem then is it that it takes an enormous amount of work to confirm that a proof is correct. Even a clear mistake in a proof could be reparable. Moreover, attempted proofs have inferences that amount to gaps of ...


28

1) Should you summarize the main results and or the argument? In general, I would say: No. However, for some journals I have come to know the overwhelmed editors who in fact need this summary. So: Write it for the editors, if you write it at all. [But see my acquiescence to Jukka Suomela's compelling point in the comments.] 2) What do you do when ...


17

Suggestion number one: Learn Calligraphy! It's a lot of fun and does mean that you can write the fonts in genuinely nice ways. Books on calligraphy tend to have detailed instructions on how to do at least the basic alphabets: explaining which stroke to do first, and how to hold the pen. Although not all of it transfers to the blackboard, it helps a lot. ...


10

This is sort of goofy, but if you have a tablet, you could try training yourself with Detexify. Try to get it to give you the indended symbol with as good (low) a score as possible. If a computer can read your writing, a human probably can too!


6

This webpage (scroll down to "German") has a nice chart about fraktur letters and how they should look when handwritten. I must admit I don't have enough experience writing fraktur letters, I really should learn to write them properly.


6

The answer is as follows. We need to show that $$I(Z; X)-I(X; Y)\leq H(Z|Y).$$ The left hand side of this is simplified as $H(X|Y)-H(X|Z)$, so we need to show that $H(X|Y)-H(X|Z)\leq H(Z|Y)$. Since conditioning reduces the entropy we have $$H(X|Y)-H(X|Z)\leq H(X|Y)-H(X|Y,Z)=I(X;Z|Y)\leq H(Z|Y).$$


5

The question as stated is not really helpful, but it's worth pointing out that the ADE and other graphs/diagrams evolved over a couple of decades in different countries. The graphs, which encode at first the Coxeter data for finite (or more general) reflection groups, go back at least to Coxeter's 1934 paper. In Witt's 1941 paper these now familiar ...


5

I disagree with the universality of your question, but I agree that the diagrams are often drawn in similar ways. They are drawn that way because they are easy to draw that way, and there isn't a good reason to deviate from what we are taught. I have seen both of your proposed alternatives for the $E_6$ diagram in the literature, and I might even say that ...


4

I've often thought that someone should write a book on mathematical calligraphy. Maybe not a full course on it, but as it stands the symbols we use are so inconsistent and often look little like they should, simply because we all "guess" how to draw them. How did we learn when younger how to write in cursive, or to write in general? We practiced. The ...


3

Although only a minor point, remember that many old fonts were written with a pen or quill. You only get a strong line on a down-stroke. From this you can sometimes work out the best way to draw a character, if you think of think of the rhythm of the character and make the wider stronger lines downward lines. It's almost impossible to get a thick upward line ...


3

I have never heard of anybody teaching how to write on a blackboard. There are a lot of books about calligraphy. You could try finding a calligraphy book with a font close to Fraktur. By the way, you can find tips on how to write greek letters: http://www.ibiblio.org/koine/greek/lessons/alphabet.html


3

I'd prefer to keep the symmetry of $X$ and $Y$ in the argument. Then $$ H(Z|X) + H(Z|Y) + I(X,Y) \\ = H(X\vee Z) - H(X) + H(Y\vee Z) - H(Y) + H(X) +H(Y) -H(X\vee Y) \\ = H(X\vee Z) + H(Y\vee Z) - H(X\vee Y) \\ = 2 H(Z) + H(X|Z) + H(Y|Z) - H(X\vee Y) \\ \ge 2H(Z) + H(X\vee Y|Z) - H(X\vee Y) \\ = H(Z) + H(X\vee Y\vee Z) - H(X\vee Y) \\ \ge H(Z) $$ Several ...


2

If the author finds a mistake (or someone finds and tells to the author) s/he usually publishes a correction in the same journal. If the journal is reviewed by Mathscinet or Zbl, they usually review the correction as well, so you can find it. Papers posted on arxiv are usually corrected, before or after publication. Be sure that you read the latest posted ...


2

Do you know this site from Ecole normale superieur: http://www.diffusion.ens.fr/index.php?res=themes&idtheme=30 almost half of the talks are in french. You can also switch from mathematics to philosophy or history or logic... it's really impressive.


2

Suggestion number two: Get rid of the blackboard. The way to guarantee that the fonts look right is to have a computer display them (either by directly projecting or by printing out slides first). This also means that you can use colour and other fun things. To forestall the deluge of "How can you suggest getting rid of blackboards?" posts, all I'll say ...


1

Concerning the greek letters, it is essential to know the following: there does not exist in the greek language a cursive style (joined-up writing, schreibschrift). To my knowledge, at least. And has never existed. As a further point, the greek z should be written as a 3. It is essentially the same symbol, I should say.


1

I think not only for books, but for published papers etc. also there should be errata lists----these could really save many a hair-pulling moment! Moreover, this will make the errata-fixing process public, and because of that probably faster and more transparent. In fact, it would be great if such a database were created on the stackexchange.com framework, ...



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