Monday, October 03, 2005

Another week in books

  • Adventures of a Mathematician (S. Ulam)

    Did I finish this two weeks ago? In any case, it was interesting to read. In addition to the autobiographical and historical comments, Ulam says a great deal about mathematics and mathematical ways of thinking. Though he sometimes mentions specific technical areas, almost all of the book is accessible to a general audience.

  • Fool's Errand (R. Hobb)

    The books in the Farseer trilogy kept me up past when I should have gone to sleep. This one did, too. But I think I will postpone picking up Golden Fool, the second book in this new trilogy. I think the bleakness of the characters is a bit overdone.

  • Forty Signs of Rain (K. S. Robinson)

    I can't think of any books by KSR that I haven't enjoyed (although Icehenge wasn't as much fun as Years of Rice and Salt, for instance). I have a few quibbles, mostly involving his description of the idea of an algorithm, but I like his cast of characters and of ideas, and I really like the writing style. There wasn't much plot, yet, but it didn't feel like a deficiency; and anyhow, I expect the plot will develop further in the other books.

    I do not think the similarity of the events in the book to current political and meteorological events is particularly coincidental.

  • The Education of Henry Adams (H. Adams)

    I haven't gotten more than thirty pages into it, but so far I've enjoyed it. There's a dry humor there that appeals to me.

  • Best American Science Writing 2005 (Edited by A. Lightman)

    Haven't started it yet, but I'm looking forward to it. I usually enjoy anthologies of popular science writing.

  • Fundamentals of Electroacoustics (Fischer)

    A short, plainly written description of different types of electromechanical interactions, and of circuit-style models of coupled electrical and mechanical systems (speakers and microphones, mostly). Translated from the German original. Why couldn't I have found this book a couple years ago? But it's on my shelf now.

  • Mathematics of Classical and Quantum Physics (F.W. Byron and R.W. Fuller)

    A Dover reprint with two volumes bound as one. Includes sections on variational calculus, Hilbert spaces and spectral theory, analytic function theory, Green's functions and integral equations, and symmetry groups. I have other books that treat most of these topics in greater detail, but many of those books make little or no useful mention of physical applications or motivations. At the same time, Byron and Fuller have written an essentially mathematical book: there are no rabbit-from-a-hat tricks (or when there are, they are preceded by an apology and a reference), and certain details which seem subject to frequent abuse in physics and engineering texts -- like the treatment of the Dirac delta -- are handled with appropriate rigor.

    An aside: I'm much better as a mathematician than as a physicist. When I think about physical effects, I tend to think of them as concrete approximations of certain mathematical abstractions; and for the most part, my intuition for the mathematical things is better than my intuition for the physical things. This is a constant source of frustration for me when I'm learning about physics, since hand-waving appeals to physical intuition generally confuse me more than they help, at least initially. Nonetheless, I like learning about physics, and about connections between mathematics and physics. Furthermore, I like to learn about mathematical and scientific history, and a great deal of mathematics has historically been inspired by descriptions of physics: the calculus of variations coming from classical mechanics, many ideas in functional analysis coming from quantum mechanics, many ideas in group theory coming from mechanical symmetries, many ideas in graph theory connecting to circuit analysis, and so on.

  • Modulated Waves (Ostrovsky and Potapov)

    I've mentioned this book before. I read the first several chapters over the course of a couple weeks a while back (early summer), and since then I've been re-reading chapters or reading new chapters as the whim or the need takes me. This, too, is a mathematical book; but like Byron and Fuller's book, it contains a nice infusion of physical ideas and applications. I picked up my copy of Ostrovsky and Potapov this weekend to compare their presentation of dispersion relations to the corresponding presentation in Byron and Fuller.