More library books, some unread
Draft of 2017.06.17 ☛ 2017.06.19
May include: readings ↘ mathematics ↗ &c.
Another short stack of overdue library books, some read, some not:
- In Eves’ Circles A rather interesting (and wide-ranging) collection of papers presented in honor of Howard Eves, including one of a number of similar essays I’ve come across through the years called “Reflections of a Problem Editor” (this one by Clayton)
- The Puzzle Universe: A History of Mathematics in 315 Puzzles Bow before the mighty power of Ivan Moscovich. Seriously, this is a heavy, huge, tremendously well-made collection of puzzles and games and what I’m calling “études” (of the form “Hey here’s this thing, which is a large and sprawling branch with numerous people doing fascinating work, but which I will show you the heart of by drawing some lovely regular tessellations involving mixed polygons,” and so on). Every one of the entries has “the stuff”: it’s enough to spark a reachable programming étude, or a genetic programming experiment, or an animation for your web page that you could do in Processing or Quil with very little trouble.
- Old and New Unsolved Problems in Plane Geometry and Number Theory Full of great ideas for genetic programming projects, as well as some classics of mathematical recreations (like the Collatz Conjecture). Some very old ones, like those regarding Egyptian Fractions, still have legs for études and exercises.
- Latin Squares and Their Applications If you’re going to write about Sudoku or Magic Squares, the more general (and practical) notion of Latin Squares—especially when it comes to experimental design applications—are something it feels as though you need to touch on. This monograph touches on lots of adjacent topics, such as graphs and group theory, and since it’s well over 40 years old it’s the sort of advanced mathematics I can actually follow along with.
- Combinatorics, Paul Erdős is Eighty A collection of papers in honor of Erdős’s birthday, mainly approachable and all rather provoking if you take my meaning. For one thing, it’s clear when so many things are spelled out in a row like this, Erdős had a toolkit with a few very heavily used heuristics that he trotted out many times, in many settings. “If I have a bunch of stuff, can I prove that a subset of the stuff has a particular trait 100% of the time?” or “If we have some things on a plane, and we connect them with geometric figures of a particular kind, and count the [pieces] of the resulting figure, what can we say about them?”. See next entry.
- The Mathematics of Paul Erdős II This one is less approachable, but more of an overview. Numerous provocations: Penrose tilings, things about planar arrangements of lines, stuff like that. Also a lot of the analysis stuff I can’t follow personally. Definitely more of a “Springer Yellow” sort of volume.
- Geometrical Etudes in Combinatorial Mathematics There’s a reason I’ve taken to calling my little puzzles and recreations “études”, and it’s this book’s fault. It’s one of the best I’ve seen to date, filled with nice, legible intuitive diagrams, stuff about polyominoes and polyhedra, and while (as with Erdős himself, and most modern mathematical writing) it’s a bit too focused on proofs and too little on exploratory looking-to-see, it’s filled with good ideas and provocations. Would buy, given a chance.
- Magic Graphs A lovely little monograph, with an excellent section near the end with open research problems for the aspiring student and/or researcher. This is the volume that provoked me to order this whole pile, since I was (and still am) following up on an interesting generalization/relaxation of magic squares to something more like “magic arrangements of lines”. As with many such monographs, I had no idea so many of the “but what if” modifications and variations of magic squares had been explored so thoroughly, nor that so much of the “off-label” varieties have been so little touched. For instance, I learned about edge and vertex magic labelings—and also edge-and-vertex magic labelings—here.
- Pearls in Graph Theory: A Comprehensive Introduction Nice little overview of graph theory concepts, using lots of good diagrams and intuitive, readable prose. Colorings, planarity, closeness to planarity, some advanced concepts but all explained quite clearly. Not so many provocations, except by the usual heuristics: If I asked you to count the [X] you can build with [Y], how would you go about doing that algorithmically, without mindlessly copying over an algorithm from some textbook? That sort of thing.
- The Book of Numbers John H Conway explains it for the rest of us. Nice, readable and reachable introduction to some complicated Number Theory stuff. Plus the expected recreational faves, like Fibonacci everywhere and counting in alternative bases. Tucked in amongst them all are some tidbits, and some good (and some illegible) color diagrams apparently made expressly for the purpose of exercising the 3d rendering software.
- Before Sudoku: The World of Magic Squares An excellent overview, better in some ways than Pickover’s related work on the topic of magic squares, probably because it feels better-aimed at somebody like me. Touches on the basics of magic squares, and then in quick succession handles all the nominally “different” magic graph lebelings: circles, stars, cubes, spheres and so forth. But then gets into the “good stuff” (by which I suppose I mean “exotics” that I haven’t run across before) with sections on magic squares that can be squared or cubed, concatenative magic squares (where concatenations of columns and rows, added up, have magic totals), and “magic lightning” figures, which I admit an immediate fondness for.
- Games Ancient and Oriental, and How to Play Them; Being the games of the ancient Egyptians, the heira gramme of the Greeks, the ludus latrunculorum of the Romans, and the oriental games of chess, draughts, backgammon, and magic squares Yeah, well there you go.
- Graph Theory and Combinatorial Biology Collection of papers by Eastern European worthies, with a few of some interest (to me). Specifically, here is where I learned for the first time about competition graphs, a topic I hope to come back to in he context of some other graph applications and analyses of evolutionary algorithms and also attractor basins of cellular automata and their ilk.
- Horizons of Combinatorics Too advanced for me, mainly, except for the question of coloring hypergraphs. I think there’s something there which would be helpful and/or interesting two write about, in the context of some of these études I’ve been doing recently.