<p>To me, the emphasis on math and physics makes a lot of sense for a research career. To be an engineer, all you need is the "shortcut to the solution" that's already been solved, but to do research and solve new problems, being able to "derive all of the relationships" is indispensable. Maybe this is why most engineers opt for a non-research master's.</p>
<p>As a researcher, you're expected to learn the details of your subfield on your own. The grad program preps you with all of the background theory, and then you apply it to experimental design and interpretation on your research project. The other students shouldn't be expected to know the details of your subfield (in many cases it would not help them in their own work), so the grad program doesn't require all of the students to take courses in all of the subfields of the department. This is why your whole cohort has to take lots of math and physics background theory, but each student takes only a few courses in materials science.</p>
<p>It's the same in my field (biology): everyone takes core + the physical chemistry series, and thus multiple terms of quantum and thermodynamics. But I don't have to take physiology or microbiology, and a physiologist wouldn't have to take structural biology or comparative/evolutionary biology, and a structural biologist wouldn't have to take genomics or immunology. Quantum/thermo is relevant to all of us as researchers, but only the immunologist needs to know the details of immunology, and so on.</p>
<p>At the undergraduate level, exploring and sampling within your field is encouraged, and you can take a variety of courses in order to discover what you like. It sounds like you did this in your undergrad matsci program, taking crystallography and microstructural evolution and the like. But by the grad level, your research interests should be narrowed, and it is no longer the time to study all forms of materials science. It's time to prepare yourself for a specific research project of your design, and so your courses will mainly teach you how to design experiments and interpret results, which is where the proof-based math and physics comes in.</p>
<p>How do you see yourself using a Ph.D. in Materials Science? Engineering or research? Industry or academe? I think Caltech's approach is great if you ultimately want a research faculty post, but if you want to be an engineer, or go into industry, it's probably overkill. What made you choose Caltech? Were you aware that the requirements are very different from Berkeley, Stanford, etc.?</p>
<p>Also, I'm a little surprised that there are "fundamental materials science" questions on the quals here. In bio, quals are mostly a defense of your research proposal, and there is nothing "fundamental" about the questions you'd be asked. At some schools a paper exam is also administered, but it's usually a paper review or somesuch, never with short-answer questions like "In which vascular tissue can sieve tube members be found?" What's the format for your qualifier?</p>