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Introduction to transseries

JacquesC's picture
Posted on 2008-02-01 12:15 By JacquesC (Maple Rating 4 1697)
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A long-time member of mapleprimes, Gerald A. Edgar has recently posted a wonderful paper, "Transseries for beginners" up on the arXiv.  It is elementary[1], but not easy, and written in a very engaging style.  For those interested in the mathematics used in some of the darker corners of Maple, this is a great introduction.

[1] Elementary, in mathematics as in Sherlock Holmes novels, is a technical term meaning that very few underlying knowledge is necessary to understand it. 

Comments

Robert Israel's picture

Elementary

Comment on 2008-02-03 01:20 from Robert Israel (Maple Rating 4 1420)

Actually, there are several technical meanings of "elementary" in mathematics (see e.g. eom.springer.de/E/default.htm), and that is not one of them.  The closest is in number theory, where methods that don't involve complex analysis are called "elementary".

 

JacquesC's picture

Indeed

Comment on 2008-02-11 23:11 from JacquesC (Maple Rating 4 1697)

You are quite right that the term 'elementary' is used a lot in mathematics, and that my use is perhaps not the most common.

I should have been more precise and described it more at a meta-mathematical statement.  In other words, it is really about proofs/arguments rather than about a specific piece of mathematics.  This is indeed closest in spirit to the use from number theory.

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