I have not enjoyed my undergraduate math program, primarily because it is not challenging enough - not enough advanced courses offered, too few research opportunities, classes are just not at the level I feel they should be for junior-senior math majors. I am choosing to apply to grad schools (pure math) which I know have elite and challenging programs. I do not want to spend 5 years repeating this undergraduate experience. In the statement of purpose one is asked to explain why they are applying to the particular program. Should I mention this desire to have a more challenging, competitive environment, as compared to the undergraduate program, as a reason? I do have other substantial things I will write about, but I'm wondering if I should also mention this, as it is one of the main motivations I have for applying to the programs I am applying to.