Evolutionary Theory: Mathematical and Conceptual Foundations, by , tries to not use any more math than is needed. This only holds off the PDEs until the case of multiple alleles at one locus, p. 24.
Theoretical Ecosystem Ecology: Understanding Element Cycles, and , is PDE-free all the way to a concept of substrate quality, page 37. Those aren't bad, actually; the persnickety equations are often just ODEs.
Theoretical... compares its results to quite a lot of empiric data, considering that it's a short book on mathematics. Also, there's some odd, odd Nordic poetry (in translation) and some worked exercises; very useful, and I must get back to it after this quarter's class in PDEs.
Somewhere else asserts nitrogen:food-energy:water::carbon:fossil-fuel-energy:air. In the soil, it's more like potential and ?metabolic? energy, but they're still wonderfully linked.
ISBN: 0521580226 (Theoretical...)
LCCN: QH 344 A35 1996 (Theoretical...)
ISBN: 0878937021 (Evolutionary...)
LCCN: QH 366.2 R523 2004 (Evolutionary...)
Subtitle: Making the Right Connections
The game Hex, which can be explained in a paragraph and played on (say) bathroom tiles, is quite hard despite being perfectly deterministic; like Go. (Not that I can beat the Java applet version; maybe after I read the book, which is mostly about strategy with a lot of alternate versions of the game, including Hex on a torus.)
John Nash was one of the two simultaneous inventors, so in English the game was called "Nash" for a while except when played on those bathroom tiles, when it was called "John".
Odd that two people should have come up with such a simple game at once. (The other is Piet Hein.) Browne points out that it has a little to do with the four-color problem, too, in a metaphorical, simplifying way. It's more directly descended from game versions of maintaining or destroying network (circuit) connectivity.
ISBN: 1568811179
There are little exercises-for-the-reader in the beginning of the book, some dating from the Victorian heyday that produced questions one could illustrate; but as the history progresses more of the book is about the people than about the increasingly abstruse problem. It does all wind towards the political or philosophical question that the long, computer-calculated proof produced; to quote Wilson, half the mathematicians at a conference ...could not be convinced that a proof by computer was correct...[half] could not be convinced that...700 pages of hand-calculations could be correct.
Those are not exclusive opinions, grumps the empiric.
Did discrete math look like one body of inquiry before computers? Was it called something else, or did it suffer from the simplicity with which many of its problems can be stated? I wonder only because, on laughably cursory examination, the discrete section in the math library is short and shiny. Maybe the aged classics are in the computer science library. (Not an explanation I often try, that last sentence. I wonder what the oldest book in the CSci library is.)
A Beginner's Guide to Discrete Mathematics, , has nothing explicit about map coloring but, of course, lots of simple graph theory, Hamiltonian cycles, Boolean circuits. Discrete Mathematics: Elementary and Beyond, , , , does mention the four-color theorem (and lots else, including more crypto). The prose in the latter is distractingly perky and humorous, and it's a bit more mathematical and maybe slightly less aimed at CSci than the former. Both provide the puzzles I missed in Wilson.
Shorter versions of the four-colors-suffice proof are already appearing, but that's not where the glory is.
ISBN: 0691115338 (Four Colors Suffice)
ISBN: 0817642692 (A Beginner's Guide...)
ISBN: 0387955852 (Discrete Mathematics:...)
From Matilde's comment on Invisible Adjunct, I was led to a history and summary of the algorithm used to match residents to hospital slots. Nice to have these things clear - or "Clearing", as the UK system for getting into college seems to call it. The algorithm is easy to understand; the old and basic example is stated in terms of boys proposing to girls who keep an eye out for better engagements. Still, startling to find so blunt a summary of old-fashioned sexual mores and politics:
Gale and Shapley also showed that the match achieved in this manner has a remarkable property: It is "boy-optimal" and "girlpessimal," meaning that each boy is matched to the best girl he can get in any stable matching, while each girl ends up with the worst possible guy. (I leave this as an easy exercise for the reader's morning commute.) Of course, the corresponding algorithm that has the girls proposing achieves the opposite, prompting some reflection on real-life dating conventions.
Another exercise is to show that it's possible for those on the side that's not proposing to "game the system." By lying about her preferences, a girl can do better in the male-proposing algorithm than she would otherwise.
I need to tidy up whatever is preventing this blog from having several categories for one post, because it's not all that often I can categorize something at once as math and 19th c. fiction.
Locksley Hall gave me my title.