If an ape can make a discovery, so can you.
Richard P. Feynman
as quoted in this book
What do you think about this quote?
The Princeton Companion to Mathematics was extensively reviewed, and often praised, all over the mathematical and scientific blogosphere, see e.g. here, here, here and here. Most of this praise is probably well deserved. But where should an interested student (or even a professional mathematician who wants to extend her or his professional range, for that matter) go in order to deepen the knowledge acquired from PCM without getting bogged down into the details of the proofs and other such subtleties that abound in the specialized literature?
Of course, there is plenty of possible answers to this one, and you are welcome to share yours in the comments. However as far as “classical” (basically more or less up to the early XXth century level) mathematics goes, the Oxford User’s Guide to Mathematics appears to provide, at least for me, a reasonable, if not quite perfect, enhancement for PCM.
OUGM has many omissions of its own and certainly could use more editing and proofreading — in particular, in order to make it somewhat more self-contained, but nevertheless this book provides a fairly broad and reasonably deep (for the beginner) panorama of the “classical” mathematics as defined above. For instance, it does not cover category theory and related stuff. However, by and large, OUGM does a quite decent job in helping the beginner to advance her/his understanding of a great number of mathematical disciplines from abstract algebra to probability theory, and I certainly recommend to have a serious look into this book if you really want to deepen your knowledge of the “classical” subjects beyond the PCM level.
P.S. I just cannot miss this opportunity to wish merry Christmas and happy New year to the readers of this blog 🙂
While writing the research papers one quite often needs to get back to the full texts of old (pre-Internet or at least pre-arXiv) references. Of course, having access to a good library and/or the interlibrary loan usually solves the problem but can be somewhat time- and cost-consuming.
It is not that well known, however, that there is a fair chance to find the old paper or preprint you need online for free. Of course, the first thing to try is Google or perhaps another search engine of your choosing. However, if this does not work, you still have a fighting chance, at least as far physics and mathematics are concerned. The places to try are:
All items but KISS are purely mathematical databases (to be precise, MathNet.Ru includes several physics, mechanics and mathematical physics journals as well).
If you know of other similar databases (be it in physics, mathematics, life sciences,…), please feel free to drop a comment with the relevant link(s).
This very interesting and very controversial issue is discussed here, here and here. The discussion was triggered by this post at the YFS blog on the all not-too-nice kinds of people one encounters in science and on losing one’s illusions down the road into the academe (see also here for a related post at the RS blog); for a kind of alternative point of view see here.
Choosing a research problem to work on is a tough decision to make, and the relevant advice is rather scarce.
So far I have found only a handful of reasonably looking tips:
The last three tips are somewhat of a common wisdom and can be found in a number of places; see e.g. the article Choosing a research topic by Richard Reis, which contains some further interesting thoughts on the subject.
Some good advice on the subject is here, here and here (the last two are primarily intended for the mathematicians), here (this one is primarily on giving short talks) and here (this one also contains some helpful links to writing tips). As for the job talks, see e.g. this article by Richard Reis. On a related note, see also his article on getting the most of your conference trips.
Update 1: Presentation Guide for Scientists by Ad Lagendijk
How to Conquer Public Speaking Fear by M. Orman
Update 3: How to Give a Great Presentation at the To Done blog