What is the crowd's opinion of Combinatorial Enumeration (Dover Books on Mathematics)?

From 3.5 billion comments

The exams varied by professor, but for the most part they were very difficult. The professors curved heavily; you weren't intended to get a perfect score unless you were very on the ball. Exams were generally 90% proof, with maybe a computational question. I honestly can't remember a single computation question from any of my exams.

Putnam problems are great. Even when they're computational, they're non-trivial and force you to think logically instead of mechanically.

> Maybe once I get out of the "engineer danger zone" of calculus and linear algebra, later classes will start focusing more on proofs?

Depends on what your major is. In engineering, probably not. In fine arts, if you're incredibly lucky. But depending on how your school feels about letting you take classes outside of your faculty, if you can swing high level math or pure math courses, they will probably be at least decent. In analysis, try to take Real Analysis, Complex Analysis, Topology, Measure Theory, Differential Geometry, and Functional Analysis. In algebra, go for Group Theory, Ring Theory, Galois Theory and maybe some sort of number theory if you can swing it. I recommend these courses because it's pretty hard to approach them from a numerical perspective, and you're more likely to get proof oriented treatments.

Also any sort of combinatorics, graph theory, and advanced statistics will serve you well. Proof oriented pure math can sometimes start to feel very monotonous in terms of the techniques you use and the overall structure of the results. Working on counting problems with generating functions and geometry/group theory using graphs is a nice way to break away from that monotony and keep yourself sharp. It also helps you remember that sometimes deceptively simple sounding problems ("counting") can have very difficult and novel solutions. If you're looking for a compendium of counting style problems, I recommend: http://www.amazon.com/Combinatorial-Enumeration-Ian-P-Goulden/dp/0486435970/ref=sr_1_1?ie=UTF8&s=books&qid=1262965920&sr=8-1

Fair warning: I'm biased. Goulden was my combinatorics professor, and he is awesome ;)

Probability theory and advanced statistics are also very interesting fields that keep you thinking differently, and have great practical applications.

EDIT: The homework was also very difficult. Usually assignments had 5-10 problems with maybe subproblems related to the larger theme of the problem. Most problems took 1-3 hours, but the variance was extremely high. I solved some problems in 10 minutes, I labored all day for two days and still failed on others. The homework was required and usually made up about 20% of your mark. In most classes I get miffed by required homework because I was used to the high school (and crappy university) standard of homework being an easy, boring waste of time intended primarily as busy-work. In UW pure math, homework was a blessing bestowed upon you by the professor. If you didn't do it, it didn't really matter what your homework mark was, because you were definitely going to fail the exam.