I recently added two new pages to the blog: a bibliography for listing references I cite on multiple occasions, and a suggestions and requests page. The bibliography is likely to soon contain citations for at least some of the following books which have recently come into my possession:
- Introduction to the Theory of Computation, Sipser
- Lectures on Quantum Mechanics, Faddeev, Yakubovskii
- Representation Theory: a First Course, Fulton, Harris
- Conceptual Mathematics, Lawvere, Schanuel
- Concrete Mathematics: a Foundation for Computer Science, Graham, Knuth, Patashnik
I haven’t looked at 2 or 4 very closely yet, but so far I find 1, 3, and 5 to be among the best written textbooks I have ever read. Sipser’s book, in particular, strikes me as having found a perfect balance between brevity and clarity. His tone is conversational but finely polished, and I rather like his habit of summarizing the basic strategy of a proof before actually writing it down. Generally I am finding the book an absolute pleasure to read, which I can’t say for most of the math textbooks I’ve seen. You will likely see me blogging a little about languages and automata once I finish up my current series (right now I’m stuck on what should be a trivial proof).
Why don’t more mathematicians write like Sipser?