Sunday, September 04, 2005

Some Math One-Liners

From "How to write Mathematics", Steenrod, Halmos, Schiffer and Dieudonne, AMS, (1976). Under the heading "Think about the alphabet", Halmos suggests a couple of helpful ideas when it comes to notation.
A good, consistent notation can be a tremendous help, and I urge (to the writers of articles too, but especially to writers of books) that it be designed at the beginning. I make huge tables with many alphabets, with many fonts, for both upper and lower case, and I try to anticipate all the spaces, groups, vectors, functions, points, surfaces, measures and whatever that will sooner or later need to be baptized....There are...awkward and unhelpful ways to use letters...A related curiousity that is probably the upper bound of using letters in an unusable way occurs in Lefschetz. There x_{i}^{p} is a chain of dimension p (the subscript is just an index), whereas x_{p}^{i} is a co-chain of dimension p (and the superscript is an index). Question: what is x_{3}^{2}?


He becomes more polemical...
As history progresses, more and more symbols get frozen. The standard examples are e,i, and \pi, and of course, 0,1,2,3,..., (who would dare write "Let 6 be a group."?)...A mathematicians nightmare is a sequence n_{\epsilon} that tends to 0 as \epsilon become infinite.


On the dangers of writing instructions for how to write maths, he quotes several collegues...I will post these later.

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Manny Is Here: Some Math One-Liners

Sunday, September 04, 2005

Some Math One-Liners

From "How to write Mathematics", Steenrod, Halmos, Schiffer and Dieudonne, AMS, (1976). Under the heading "Think about the alphabet", Halmos suggests a couple of helpful ideas when it comes to notation.
A good, consistent notation can be a tremendous help, and I urge (to the writers of articles too, but especially to writers of books) that it be designed at the beginning. I make huge tables with many alphabets, with many fonts, for both upper and lower case, and I try to anticipate all the spaces, groups, vectors, functions, points, surfaces, measures and whatever that will sooner or later need to be baptized....There are...awkward and unhelpful ways to use letters...A related curiousity that is probably the upper bound of using letters in an unusable way occurs in Lefschetz. There x_{i}^{p} is a chain of dimension p (the subscript is just an index), whereas x_{p}^{i} is a co-chain of dimension p (and the superscript is an index). Question: what is x_{3}^{2}?


He becomes more polemical...
As history progresses, more and more symbols get frozen. The standard examples are e,i, and \pi, and of course, 0,1,2,3,..., (who would dare write "Let 6 be a group."?)...A mathematicians nightmare is a sequence n_{\epsilon} that tends to 0 as \epsilon become infinite.


On the dangers of writing instructions for how to write maths, he quotes several collegues...I will post these later.

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