<p>One little point that I found helpful to think about myself was what I really wanted out of classes. Depending on this, I may or may not want exceptionally rigorous courses. I guess I tend to prefer a relaxed atmosphere, and find that my understanding at the end is just as formidable as (if not sometimes more so than) someone who slaved through a rigorous course, because learning math is an ongoing process, and things tend to solidify as you keep seeing them over and over in various settings. A professor told me that this is his style, yet many others have said that highly rigorous course offerings help them master material very well. </p>
<p>And seriously, I wouldn’t worry about rigor of program when thinking about schools like Caltech or Chicago, I’d worry about the style of instruction and things like that. I think one thing to take from happyentropy’s post is that some schools offer more topics courses, and this has little to do with how big the department is. This could be nice, though reading about them in a reading group could be fun too. Depends on style. I’m sure phuriku is right and that Chicago’s classes are very rigorous; in fact, I know a professor who I think got his undergraduate and graduate degrees at Chicago, and funnily enough, he runs extremely ridiculously heavy workload courses.</p>