I know exactly what I’d like to put out this Monday: 2 small examples of multicollinearity when we try to fit polynomials to data. The mathematics is probably done… but I don’t think I’ve actually written a narrative to accompany it… so what I have is, at best, through stage III. Getting a complete draft will take me through stage IV… transferring it to the blog will take me through stage V… and then it will still need final edits. In other words, I have my work cut out for me.
In the background, I’m working on some posts about group theory. My alter ego the undergraduate went through the group theory in Dummit & Foote “Abstract Algebra”… and I want to talk about a few things in it.
He has since worked his way through Pilkey & Pilkey “Mechanics of Solids” and Stilwell “Naïve Lie Theory”, and he has started an elementary book on electric circuits…. I need to start writing up the nifty examples I’ve seen in all these. (Did you notice the alternation of pure and applied?)
In addition, I still have to write up how to get the final tableau of a linear programming problem, given the solution and the initial tableau. And I still have to write up generalized eigenvectors. And dimensional analysis.
I also found it very interesting collection of reviews of math books, by a handful of undergraduates. Some of their remarks are priceless…. “Spanier is the maximally unreadable book on algebraic topology”…. “It’s [Lang’s Differential and Riemannian manifolds] not really human-readable”…. “[Griffiths/Harris, Principles of algebraic geometry] A huge, sprawling, beautiful, inspiring, infuriating book.”… “[Hartshorne, Algebraic geometry] legendarily difficult”….
It makes me want to write more vivid book reviews myself.
I also came across a thorough link for a problem I had seen and forgotten about. It’s called “the Tuesday birthday problem”… a man tells you that he has 2 children, one of whom is a son born on a Tuesday… what is the probability that his other child is also a son?
This is not a simple question. Rather surprisingly, the information about the Tuesday birthday can affect the answer. To see why, follow the link. (The space of possible events depends on just how one meets this particular man.)
4 books came in last Monday… I’ve looked through one (Steinberg, “Representation Theory of Finite Groups: an introductory approach” – it looks like a fine summary of everything I should have learned by now in my studies, but don’t actually have at my fingertips)… and I have read – not worked! – about halfway through the other 3.
Actually, it introduces some things I haven’t seen – but want to – such as Fourier analysis on finite groups. As with so many other books, I’m looking forward to my undergraduate working through it.
Friedland’s “Control System Design: an introduction to state space methods” looks excellent: well-written, with plenty of examples, and it even has an index to the examples. (Many books do progressively more work on a collection of examples as they provide more tools – I think this is the only book I own that actually has an index showing all the pages where, for example (no pun intended, I swear!), he works on a hydraulically activated gun turret.
It was highly recommended during an acrimonious discussion out on the comp.dsp newsgroup – which is also control theory, despite the name.
Abhyankar “Algebraic Geometry for Scientists and Engineers” – I had to buy it just for that title. Modern algebraic geometry is incredibly abstract (please pardon the understatement) – what the heck can you say about it for non-mathematicians? Well, it reminds me of my own blogging… it’s mostly introductory computational examples. It is far less formal than Bix “Conics and cubics” – which, while formal, is rather down to earth. Both of these are welcome additions to a subject which tends to be marked by extreme abstraction.
Finally, Krömer “Tool and Object: a history and philosophy of category theory”… I wish it had more history and less philosophy, but it still provides desperately-needed context for me… and as a result, I spent some time curled up in a recliner browsing through Rotman “An Introduction to Algebraic Topology” and Osborne “Basic Homological Algebra”. I wish I understood that stuff!
For a break, last night, I started rereading Woit “Not Even Wrong”, about particle physics and string theory. As I said before, he got a PhD in particle physics – and found a home in the mathematics department of Columbia University.
No wonder I don’t actually have a blog post written for this coming Monday!