Tips for Passing on Your PhD Qualifying Exams: Focus on the Fundamentals

I know that it's been a while since I've last written on this blog. Unfortunately, that's part of life for a PhD student: You get very busy for long periods of time. Although I've written about how to pass your PhD qualifying exams in the past, I want to focus more on a key suggestion that really helped me pass my qualifying exam: focus on the fundamentals!

As a fresh PhD student, it's very easy for one to over do it when it comes to studying for the qualifying exam. I remember preparing for my first qualifying exam. I tried reading up to eleven books by reading a chapter in one book and switching to another book. I also choose my three background papers poorly in the sense that they covered too many topics related to my research in anti-jamming beamforming antenna arrays. In short, I spread myself too thin, and I was unable to focus on the most important topics related to my research.

After failing my first qualifying exam, the Electrical and Computer Engineering (ECE) Department at Carnegie Mellon University changed the rules such that I could have a year to prepare for my second and final qualifying exam. I spoke to my Pittsburgh PhD advisor, and he gave me a very good piece of advice: Select the three most important electrical and computing topics related to my research and focus my studies on those topics. Those three topics would contain the fundamentals related to my research.

Tip: Do more than read books in topics related to your research. Take undergraduate / graduate classes in those areas too!

Because of my research, I realized that the three most important topics for me were electromagnetics, probability & stochastic processes, and optimization. I sat down and thought about this for several days and consulted both of my PhD advisors as part of my decision process. I read plenty of books and research papers on those subjects. There is nothing wrong with reading books and papers. However, you tend to remember the material more if you struggle through end of chapter problems. When you take a class, you are required to do this in order to pass the class. You are certainly welcome to take graduate courses to prepare yourself for your qualifying exams. I would suggest that you at least sit in several undergraduate courses, attend all of the lectures, and do the homework assignments. Undergraduate classes tend to cover more fundamental theories and ideas, and graduate courses tend to focus on more specific (i.e., non-fundamental) topics.

Tip: Be a teaching assistant for an upperclass (i.e., Junior or Senior level) undergraduate course.

Someone once said that the best way to learn a topic is to teach it. When it comes to preparing for a qualifying exam, that's great advice to follow. I gave tips on being an outstanding graduate student previously, and I highly recommend that you re-read that article. Remember that undergraduate courses focus on fundamental topics (such as electromagnetic waves or probability theory) that are important for specialized research. Being a good TA has several benefits when it comes to preparing for your qualifying exam:

1. You must solve fundamental engineering problems because you are responsible for writing homework solutions.
2. If you are assigned a guest lecture, you must read the assigned text and related documents very closely because you will need to base your lecture notes on them.
3. You get practice giving a presentation in front of an audience.
4. Students will ask questions during your office hours. This gives you plenty of practice writing solutions on a white board while clearly explaining how you solve the problems to someone not familiar with that topic.
5.  You are more likely to remember the materials covered during the class because you had a hands on role whether it was teaching lectures, writing homework solutions, and answering students' questions.

In summary, you must know your fundamentals in order to prove to your qualifying exam committee that you are capable of conducting good research. Here's an example to explain this: Suppose that I told you that I could climb all of the floors in the Empire State Building. Now, let's say that the next time you saw me, I was climbing one flight of stairs in a building, and I was completely out of breath by the time I reached the top. Would you believe that I could walk all the way to the top of the Empire State Building? Absolutely not! Why? There's no way I could climb 90+ flights of stairs if it took one flight of stairs to wear me out. In other words, the act of climbing one flight of stairs is fundamental to climbing many flight of stairs. If I can't climb one flight, I certainly wouldn't be able to climb many flights. It's as simple as that.

Sincerely,

Jonathan Becker
ECE PhD Candidate
Carnegie Mellon University

Remember to think about the tips that I gave and
ponder on how they will help you prepare for your qualifying exam.