I can’t believe how late it is as I start this draft… but I am determined to put out a diary post today.
Not much is happening, and that’s the problem.
Most of the time, I have a project… I am focused on something… I am posting mostly about whatever it is. And minor, interesting things happen and they are noteworthy largely because they add spice to whatever I’m working on.
Right now, however, I have no mathematics project in hand. Yes, I expect to put out more posts on logic. Yes, I can put out a few posts on regression (ordinary least squares).
I know the mathematics for both of those subjects… more importantly, I know the specific topics I wish to address… I just have to crank out the posts themselves.
This is not a bad state of being. In fact, it is a very good one: I am under no immediate pressure to find topics for the blog. I like that.
I just can’t decide which of a zillion mathematical things to do. (Interplanetary orbits are a very likely candidate, but we’ll see. And some small topics — how about the Fast Fourier Transform? — might show up.)
Okay, there are two more mathematical topics in color theory — one of which I haven’t tried yet, and the other of which I have tried several times. In neither case do I actually know that the mathematics will work out. Still, this means that these are “mathematics” rather than “blogging”.
We’ll just have to see what I end up doing.
In the meantime, I have reorganized “the small desk”, that collection of books I want to study. The next project may come out of one of these, but I won’t know until and unless that happens.
The pile is down to 13 books (only 5 of which were on the very first list). These are books I want to work through in their entirety. (I may change my mind about a book as I progress through it, but for now, this is the plan. Just don’t ask when, or in what order.)
- Armstrong, “Groups and Symmetry”.
- Arnold, “Mathematical Methods of Classical Mechanics”.
- Asselmeyer-Maluga & Brans, “Exotic Smoothness and Physics”. (OK, this one I’m just reading, as an overview and preview of things to come.)
- Baker, “Matrix Groups”.
- Blakelock, “Automatic Control of Aircraft and Missiles” (biblio).
- Fulton, “Algebraic Topology” (biblio).
- Griffiths, “Introduction to Elementary Particles” (biblio).
- Guckenheimer and Holmes, “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields”.
- Hadlock, “Field Theory and its Classical Problems”.
- Priestley, “Spectral Analysis and Time Series”.
- Swallow, “Exploratory Galois Theory”.
- Thomson, “Theory of Vibration with Applications”.
- Vetterli and Kovačević, “Wavelets and Subband Coding”.
The following were removed and returned to my shelves:
Gardner’s “Statistical Spectral Analysis” — because I decided that I couldn’t see how to apply what I was reading. (I wasn’t happy about that, but I have plenty of alternatives, and I chose Priestley.)
Mermin’s “Quantum Computer Science” (biblio) — because it just didn’t look as interesting as the other selections beside it.
Skogestad & Postlewaite’s “Multivariable Feedback Control” — because I am determined to do aircraft first.
Sethuraman’s “Rings, Fields, and Vector Spaces” — because I finished it; and Hadlock is my follow-up. (Yes, that makes me happy.)
Five of the following, which used to be on the previous list, were transferred to another small table. These are books in which there is only a specific chapter, give or take, that I want to read. I also added one other book to this new pile.
- Aris’ “Mathematical Modeling Techniques” — choosing dimensionless parameters for a model.
- Birkhoff and MacLane, “A Survey of Modern Algebra” — for ideals (sad but true: I just don’t grok them).
- Bloch’s “A First Course in Geometric Topology and Differential Geometry” (biblio) — you know, to summarize chapter 3.
- Dean’s “Classical Abstract Algebra”, for modules.
- Nash & Sen’s “Topology & Geomety for Physicists” — for bundles.
- Stillwell’s “The Four Pillars of Geometry” — for the projective plane.
Yes, I know that an entire book needs to be read one chapter at a time… but it still seemed psychologically valuable to separate the books for which I needed to read one chapter from those for which I wanted to read every chapter.
There is also a third pile, for casual reading. This distinction seems far more important than the previous one. I expect that every book in this pile really does qualify as easy going (for me) except for the Mathematica book, which is just difficult to take seriously until I have a specific question.
My casual reading pile, then, at present, is:
- Hair et al., “Multivariate Data Analysis” — because I like its meta-statistics, the things it says about statistics.
- Copi & Cohen, “Introduction to Logic” (biblio) and
- Gensler, “Introduction to Logic” (biblio) — because they both look fascinating.
- Barnes and Fulford, “Mathematical Modeling with Case Studies” — because I like its elementary (ODE) real-world examples, but they’re not at my fingertips.
- Ruskeepää, “Mathematical Navigator” — because I won’t study it, but I might browse it.
Let me close with an explicit invitation. I haven’t said very much about most of these books. Relatively few of them are already in the bibliography. If you have a question about any of them, feel free to ask.