Resources and Tips for taking any prelim exam at Clemson (Ph.D. program in Math only)
This is a work in progress! The tips can be applicable right now, so I let myself publish them! If you have other documents you want to add, leave me a private note, and I’ll add them.
Table of contents
When should you take a prelim exam?
Tips to help you study for any prelims
Resources to help you with the prelims
If you are an international student, read this first.
What is a prelim exam?
As a Ph.D. student in Mathematics at Clemson, passing your two prelim exams is the first milestone. You have to pass 2 of them within your first 3 years of graduate studies without accumulating 3 fails. They're a major deal! A prelim is a very long exam (A big take home computation exam or a 4 hour exam). They cover at least 2 graduate classes. Depending on how many people register for the specific prelim, you may take them alone or with a few students. For each of my two prelim exams, there were 4 other graduate students. Once you register for the exam, you will get a random identification code. That’s the identification you put in the exam sheet, not your name. The grading process is anonymous. Teachers won’t know whose paper is it (Unless it’s your teacher, and you always submitted handwritten assignments during the semester. Or you always solve problems in a very specific style … I do that! Any linear algebra problem I have, I always attempt to solve using induction …)
When should you take a prelim exam?
When you are ready! Really! You can check the list of prelim preparation classes, topic covered and past exam repository here. No, you don’t have to take the prelim class before taking the exams. You can take them in your first semester if you’re confident about it! I took my first one (Algebra) at the beginning of my second year and my second one in the middle of my second year.
Tips to help you study for any prelims
Watch all the lesson videos at 2X speed at least once
I specifically did it for algebra, even though Dr Macauley told me I shouldn’t! I just felt getting a full refresh of all the course is good before getting deep into a specific topic! Without taking any notes, I simply watched and listened to the videos. I took Matrix Analysis one semester before Abstract Algebra so I didn’t see the materials in a while. I spent a full week on Prof Macauley’s linear Algebra series on YouTube before starting focusing on past prelims.
Attempt all past prelim exams
Don’t care who wrote it. Even if the professor who wrote the questions is not at Clemson anymore, attempting to solve that question will equip you with more experience. Knowing a bit more that you need to will not hurt you when taking the prelims.
Work backward:
Each day, I took one past prelim exam and make a goal to solve it. I go through all the questions and take notes on
- what I already know how to do,
- what I may be capable of solving,
- topics that are unfamiliar to me,
From these notes, I go to a textbook or a YouTube video and learn only the specific topics I need to solve each problem. I keep doing it until I know how to solve the whole prelim.
If your answer is too long, you may be on the wrong path
The preliminary questions make you think deeply and challenge all your knowledge, but the answers are always brief. If your calculation are longer than one page, you may be doing extraneous work. If your proof needs multiple paragraphs, something is wrong! Read the question again and see if there are other alternative to solve it!
Timed practice
Two or three weeks before the exam, make sure you do a timed practice at least twice. Take a past prelim you never attempted before. Remove any distraction and go to a place where nobody can bother you. Put a 4 hours countdown and work!
Don’t write full sentence!
You’re not taking an English exam! Teachers want to know your math skills. Use keywords! Of course you need to have a readable handwriting, but as long as your point goes through, that’s all you need.
I have a whole blog post on taking exams! It’s targeted at undergrads but it applies to any math exams. Mostly in the prelims where you don’t have enough time to do all the questions. You can read it here.
Resources to help you with the prelims
Click this to see the repository of past prelim exams.
Algebra and Operations research
I wrote a whole blog post about my experience with these two prelims. You can read it here.
Freeman Slaughter’s algebra documents are here.
Analysis
Clemson alumni Walton Green has this GitHub repository for old analysis prelims. This is a 5-year-old repository so the exams are not up to date. It may still help you, though!
Freeman Slaughter’s analysis documents are here.
Stochastic
Applied Statistics
Computational Math
If this post helped you, share the links with your friends. I want my posts to help as many students as possible. If you have more links or tips to add, send me an email and I’ll add your tips here!
