Pictured: Killian Court in springtime
If you’re a new student, you may be wondering a lot about the written diagnostic exams for the core courses. (These exams are sometimes referred to as the written exam, Part 2, the written qualifier, quals, etc. by various people. They’re all the same thing.) You have come to the right place!
At MIT, all graduate students are required to take four core courses, two or three courses in their area of research, and two breadth courses. The four core courses are:
- Classical mechanics
- Electricity and magnetism
- Quantum mechanics
- Statistical mechanics
There are two ways to meet the core requirement: either by passing the relevant course with a grade of B+ or by testing out via a corresponding exam. It’s not a qualifying exam. It’s just a way to see where you’re at and potentially test out of courses.
PGSC strongly urges all first-year students to make an attempt at all four written exams in their first August, no matter how you think you’re going to do. There are three reasons for this: (1) it’ll serve as a good diagnostic to help you see where you’re at, (2) no matter how you think you’ll do, you might get lucky and get a question you know how to do, and (3) it’s good practice for the next time around, when you’ll have to take the exam. There is absolutely zero penalty for taking the exam, no matter how you do, and the exams are anonymous so the graders won’t know who you are.
Students come to our program from a wide variety of academic backgrounds and life experiences, and every year there are diagnostic exam results ranging across the entire spectrum. Yes, it is not uncommon at all that a student won’t pass any on their first try — and there are even some who don’t pass until the last try! – and there is nothing wrong with that! The exam helps serve as a diagnostic to help you and your advisor figure out what material you need to learn or review, and to help you devise a coursework plan for your first few semesters at MIT. Written Exam scores are not indicative of academic potential or future performance; students beginning from all starting points in their first August go on to complete the Ph.D. program, do groundbreaking research, and have successful career.
Let’s say you want to brush up on basic physics, though, or maybe even prepare for one or more of these exams. Perhaps you’re super rusty and haven’t taken any physics courses in a long, long time; whether you’ve been out in the workforce, taking a gap year, or doing a research master’s on string theory, classical mechanics now looks like a foreign language. Or maybe you made some coursework choices your first year at MIT that you might not have made with 20/20 hindsight, and your deadlines for finishing these requirements are coming up. Perchance you don’t have (m)any friends or family members who have gone to grad school in the sciences before, and you’re realizing that you have no idea what you’ve signed yourself up for. Don’t worry. You’re not alone.
But where do you begin?
There are a few different approaches you can take to learning the material, depending on what suits your learning style best:
- Watching videos and working through a formal course
- Reading notes or textbooks,
- Reviewing and memorizing relevant formulas
- Working through old problems alongside their solutions,
or some combination of the above. Here are some tips!
One of the great things about MIT is they put a lot online through OpenCourseWare. You can find class notes, videos, homework, exams, and sometimes solutions to all of the above without every having to show up to a class. Here are all the relevant core courses and their numbers, from intro undergrad all the way up through the hardest grad classes. (One small note about the grad courses: usually they cover some topics beyond what could be tested on the written exam.)
Sometimes you can also find archives of old classes on MIT’s old class site Stellar, or you can ask senior graduate students in your division or UROP friends to send you lecture notes or old problem sets from classes they took. Do not underestimate your professors’ willingness to find you course materials as well.
Don’t be embarrassed about going all the way back to the beginning, if that’s what you need. It’s perfectly fine.
- 8.01 – introductory mechanics
- 8.223 – intermediate mechanics
- 8.09/8.309 – classical mechanics III (graduate)
Electricity and magnetism
- 8.04 – quantum physics I
- 8.05 – quantum physics II
- 8.321 – graduate quantum mechanics
- MIT also offers additional quantum courses like 8.06 and 8.322, but the ones we’ve listed above are the traditional sequence to prepare for the exam
- 8.044 – statistical mechanics I
- 8.08 – statistical mechanics II
- 8.333 – graduate statistical mechanics
- MIT also offers another statistical mechanics course, 8.334, that is the sequel to the core course
If you’re coming straight from college, generally whichever textbook you used in your core classes there probably will suffice for preparing for MIT’s exams and coursework. If you don’t remember what you used, the Physics Department offers a set of textbook recommendations.
Back to square 1?
If it’s been a long while since you’ve taken any undergrad-level physics courses — whether you’ve taken a gap between undergrad and grad school, or you’ve been focused on a master’s project and settled into a rhythm of just looking up the basics when you need them — and you find yourself needing to go all the way back to the beginning on a lot of topics, we find that a good place to start is the Feynman Lectures on Physics. You can usually find a cheap copy on the internet, or if you’re already enrolled at MIT, there are plenty of copies in the library. The Feynman Lectures are notoriously difficult to learn from as a new physics student, but if you’re going back to review, they might very well be perfect for you. They’re entertaining, and unlike a standard textbook, you won’t have to spend too much time trying to dig up the pertinent facts from a mess of examples and instruction on how to do math; the lectures are pretty streamlined. Landau and Lifshitz also have a very thin and very good book on classical mechanics.
Many thanks to Bob Jaffe for making these recommendations initially.
Maybe you’re at the point now where you have the concepts down pat, or you only have a couple days to go before the exam, and you want to brush up on all the relevant equations and make yourself a formula sheet. Here are some ideas.
These sheets don’t necessarily have everything you need, but they are at least a good place to start!
- CM: AP Physics formula sheet; equations from Iain Stewart’s review notes about Lagrangian and Hamiltonian mechanics
- E&M: AP Physics formula sheet, Alan Guth’s long formula sheet for 8.07
- QM: Barton Zwiebach’s formula sheet for 8.05
- SM: formula sheets embedded in the final exams for 8.044. It’s not enough, but it will get you started.
As you’ll hear from many an MIT professor, there is absolutely no difference between a student who “knows physics” and a student who learns how to do the few dozen or so problem types that can come up on an exam of a certain subject area. So one way to tackle an exam is just to make sure that (1) you’ve seen a good smattering of problem types, (2) you have a general idea about how to tackle each one, and (3) you’ve worked through as many as you can (either alongside the solutions or not, depending on how much you’ve had time to review).
You’ll notice as you start working through problems that they get reused a lot, both within our own department and across different institutions! So where do you find these problems?
Old MIT qualifying exams
- The department posts a number of recent exams and solutions online
- The PhysREFS have even more exam scans on their webpage
- There are more old problems (and sometimes solutions) in the Physics Reading Room from the 80’s and 90’s
- Senior graduate students often have scans of old qualifying exams (and course exams!) as well (or remember what questions they got on their exams) — just ask! If nobody you know knows things, hit PGSC or PhysREFS up and we can try to connect you with resources.
- There are even books online with sets of old problems from MIT (and other institutions) — particularly the Problems and Solutions in Physics Series of books. These were originally published in the 90’s, so they have lots of older problems as well
Qualifying exams from elsewhere
You can find lots of old problems online from other places. Many of these same problem types may appear on MIT exams. (Though be aware that difficulty level and material covered may vary between institutions.)