Hi, I'm applying this semester to get into a Phd program, math or possibly physics and am serious about it, however I have only completed a Bachelor level degree and while I studied very hard and know as much as I can it just keeps on surprising me when I see the level of degree of the work involved at the higher levels. Normally I just do it and don't worry about how hard something is. I solved some very difficult problems in complex analysis one time and that didn't bother me, BUT when I look at this qualifying exam in basic analysis from Duke University. http://www.math.duke.edu/graduate/wqual/analysis_aug2014.pdf [Broken] It just seems as if no matter how much you know you can always find something that exceeds all of your knowledge. Am I wrong in lacking confidence when I see something like this? Is it okay to apply to a program even if you aren't at this level yet? Or am I just supposed to REACH this level once I've been there several years training? Does anyone else ever feel this way?