The Art of Computer Programming Volumes 1-3 Boxed Set Book

Perfection itself. Every few months I have to go back to my Knuth for some forgotten analysis or modeling, and it's always a savory treat -- I know no other books so dense and overflowing with rare and obscenely useful tricks, so immense in their scope and successful in coverage thereof; there's really nothing approachable in computer science or, so far as I know, in any field (the Hilbert-Courant volumes or Thorne's Gravitation might compare, if their subjects weren't so much vaster than computing, now in only its seventh or eighth decade as a proper discipline).

Don't bother with editions other than the magisterial Third (I've collected three editions, although I've only studied the most recent) -- remember that Knuth took ten years off to develop TeX as a response to the misery of preparing and printing the First. The Third is a beauty, some of the best-bound books in my library and practically indestructible to boot (note that Volume 3 is in only its Second Edition).

Don't get me wrong: TAOCP is not an introductory guide to programming by any means, and it'd have been fantastically difficult (although possible, in a Ramanujan-like way) to learn from these books alone (try Structure and Interpretation of Computer Programs, or A Discipline of Programming, for that). Indeed, I purchased them before I could put them to full use (and while mathematically, abstractly and computationally underexperienced at 18, I wasn't a tremendous dumbass or anything). Knuth demands, requires, and with epic results justifies a fair level of mathematical sophistication (indeed, the greatest value of early exposure to these classics might be the immediate and forceful demonstration of the absolutely critical role mathematics, abjured by all too many undergraduates brought up on cheesy web programming and mind-rotting video games, plays as a Real Programmer's cynosure and primary tool). Both continuous and discrete analysis are required for following along with the text or solving most of the elegant, absolutely stunning problem sets (Knuth has put more effort into his problems than any author I know, hands down). The sedulous reader will be rewarded many times over.

I've heard complaints about Knuth's use of assembly language; I'm bewildered by these objections and find them fatuous in the extreme. A well-defined assembly language (especially on the MIX/MMIX machines, intended as they are for abstraction) is surely much simpler than the majority of high-level languages, if rather more obscure in its mnemonics. I learned assembly languages for the MosTek 6502 (used in my ATARI 400) and Intel 8086 at the tender ages of 7 and 10, respectively, and found the former a far more sensible and reasonable (not to mention powerful) ontology than an ATARI BASIC that served primarily to eat from your precious 16K of RAM. Let's face a hard truth, gentlefolk: if you can't figure out freakin' assembly language, you'd be better giving up those dreams of code and sticking to blue shirts, smiles and Best Buy's stereo department.

Just as two quick examples of Knuth's power and reach: about a year ago, I needed to set up a multisite scanning platform driven by modular FSM's, designed to perform varied scans of the IPv4 space with an eye towards isotropy. I sought to offer several different targeting schemes, and opened volume 2 wondering semi-absentmindedly "how might one enumerate 2^32 elements in a pseudorandom fashion on a 32 bit architecture?" Simply, and in O(1) state -- iterate through a linear congruence having period 2^32. The necessary constraint equations were there on page 20 or so. I coded up the generating function before lunch that day, turned it into my (awestruck) boss, and it continues even now to form the heart of our active search operations. Secondly, for a recent analysis of a multicore sort viz various cache setups, I was struggling to properly model the transactions -- I opened up Volume 3, and was blinded by 5.3.2 "Minimum-Comparison Sorting", a section I swear I've read multiple times but never thought to apply. My analysis, much finer than it could have been otherwise, was completed within the hour.

Finally, they're uproariously funny at times. Knuth's is an understated and erudite humor, but every few dozen pages he'll toss a riotous throwaway, often two or three levels of reference deep, into the middle of a pile of equations.