<p>I thought you were asking a different question, so I typed a long response that makes no sense now, lol.</p>
<p>The answer is that the rigor of two different degrees is not necessarily the same - even at the same school. For example, a math major at my current institution (Columbia) could choose to take easier applied classes because they like math but want to take it into industry and don’t really care about the advanced stuff, whereas a serious math student who wants an MA or PhD can take the more rigorous research-related courses or even some graduate courses to satisfy degree requirements.</p>
<p>I can see the differences. My mid-ranked LAC had a small math major and I took some classes; the classes went more slowly than the math classes here, with more questions and class discussion and more time spent in recitation. My LAC prided itself on group-based learning, so people studied in pockets and much of the learning happened in class. On the other hand, I took a cal II class here at Columbia and had to drop it because it was too fast-paced and I wasn’t prepared for that (I was studying for my PhD quals and doing research at the same time).</p>
<p>Here, they expect most of the learning to happen at home. The professor comes in, lectures in a mildly disinterested tone, and leaves. You then have a monster problem set to do at home, and if you need help you go to the math help room where graduate students and advanced undergrads help you figure stuff out. You don’t go to the professor (who might be an adjunct). The 2-hour lecture may have 2 or 3 questions, mostly for clarification, whereas a 1 hr 15 min class at my undergrad could have 5-10 or more depending on the subject, some of them discussion-oriented. And at my undergrad, if you needed help you went to the professor and asked, or maybe a senior math major you knew.</p>
<p>But at the end, you still know the same math. It’s just taught in a different way. And honestly, a math major from my undergrad who persisted and took some graduate classes at a nearby university (Georgia Tech and Emory were in short driving distance) and did research with professors might be better prepared for a PhD than a math major at Columbia who maybe had a higher aptitude at the beginning, but chose mostly applied classes, no grad level courses and did no research.</p>
<p>That’s why top grad programs will have students from a range of different schools - from Ivies and top LACs to places of which you have never heard. The students all do different things. Maybe a lower-ranked place requires more effort on the part of the student, but they can still adequately prepare themselves for grad school.</p>
<p>To answer your last question - one of my colleagues went to Michigan, and I went to my mid-ranked LAC. Another colleague four years behind me went to Harvard. However, all of us will have a PhD from Columbia. We may have had different preparatory backgrounds to get into Columbia. Let’s even say that I was less prepared than my friends from Michigan and Harvard (which I don’t think I was at all, but for hypothetical’s sake). We still have to complete the same work, so if I’m less prepared I need to work real fast and real hard to get up to speed to complete the work that they may have been better prepared to do.</p>
<p>However - in the end, if we all get the same PhD - it’s because we had to complete the SAME work. If I finish, that means I was just as capable as they were of doing it, and thus probably just as capable of doing whatever work required the degree in the first place, all other things being equal. That’s why undergrad doesn’t matter once you have the grad degree.</p>