I passed my math prelim exams at Clemson University in one shot each!

5 min readSep 8, 2023

I passed my Operations Research prelim exam in August 2023 and my Algebra prelim exam in January 2023. I passed both exams on the first try. Here is the story of how I prepare for these exams.

In case you don’t know what is a “prelim”… Within their first 3 years of graduate studies, students in the Ph.D. program at Clemson University need to pass 2 big exams. Each exam is 4 hour long and cover topics from at least 2 classes.

Classes I took

I took Matrix Analysis with Dr. Ryann Cartor and Abstract Algebra with Dr. Matthew Macauley. I was really busy with both classes but they paid off on the prelims. I used Dr. Matthew Macauley’s YouTube videos to refresh during the break(both for Linear and Abstract Algebra). I was so prepared for the Algebra prelim that I finished one hour earlier.

For Operations Research, I only took the Mathematical Programming class with Dr. Cheng Guo. She was really approachable and I learned a lot from the class. Since I did not take the other prelim class in OR, I needed to complete my knowledge from elsewhere.

Coursera

I went to Coursera and took the following free courses:

Operations Research (1): Models and Applications

Operations Research (2): Optimization Algorithms

Operations Research (3): Theory

The instructor for those three courses is very fun to listen to. He presented the materials very clearly. I also like the fact that I can rewatch the videos again and again. The courses also come with assignments that are graded automatically and there is a student forum to talk about the assignments. The webpage of the instructor can be found here.

Discrete Optimization:

This class covers materials that are not in the prelim but you can find useful techniques.

YouTube series

I also watched most of the videos in the following YouTube series.

APP MTH 3014/4114/7072 Optimisation

ISEN 320: Operations Research I

ISEN 622: Linear Programming

Convex Optimization by Ahmad Bazzi

Optimization Algorithms by Ahmad Bazzi

Books

For Algebra, I mostly used the textbook that we used in class. That is

Linear Algebra and Its Applications by Lax and the Visual Algebra book by Dr Mathew Macauley(I do not think he published it yet).

For Operations Research, I used Operations Research: Applications and Algorithms. I did not read all the chapters, only the ones that are in the prelim.

Kahoot quizzes

I took Abstract Algebra and Mathematical Programming at the same time. I was thinking about making flashcards (I love them and I used them a lot in primary school!) I decided to use Kahoot because of the gamification. With the student plan(costs money), I can use my Kahoot as flashcards or I can do some Kahoot games with bots. I use topics from classes as questions and screenshots of lecture notes as answers.

You can see my Kahoot games in the following link. Feel free to use them if you would like to.

Anki Universal

I heard about Anki Universal from Dr. Bazett’s YouTube channel and I tried it. Using Anki Universal has been a game-changer for me. This app is developed so that you will only see a “flashcard” when you need to review it. I set up my Anki app so that it gives me a reminder in the morning to practice my cards.

The app itself is very straightforward. Once I open it, it shows me how many cards for each topic I should review for the day. I can also choose to review ahead or increase the number of cards by clicking on the arrows.

As with Kahoot, I use the titles of sections for the front card and a screenshot of the lecture notes as the back of my cards. I can use the tools to write on the cards while I am reviewing them. The annotations are not saved!

I am free to decide if I consider the card “easy”, or “good” or if I need to review it “again”. It shows me when I will see the card again after my choice.

Anki Universal is available for free on the Microsoft Store.

Past prelims

I trained myself to solve the prelim exams for the past 10 years. Some senior graduate students told me that only the last 5 years are relevant though! Since prelim questions are only available for Clemson Students, if you would like to have my work(Only for Clemson Graduate Students) on GoodNote and on Overleaf, you can email me and I will be happy to share it with you.

Other solved exams from other institutes

I also read a lot of homework and solved exams from other institutes. I usually just search the topic and read the ones that pop up first.

Timed practices

When the dates of the prelim approached, I made some timed attempts on past prelims I did not see yet. It helped me know how far can I go in 4 hours.

My schedule during Prelim preparation

Do my morning routine (wake up, etc..…)
Review Flashcards from Anki Universal and Kahoot

While not sleep time:
    Attempt past prelims
    If I find myself in trouble:
       watch YouTube/Coursera videos on the topic.
    If I feel I need more information:
       read the book.
    Do work (TAing,…) and social responsibility,
    If breakfast time or lunch time or dinner time:
       Eat 
    Two days in a week:
       Exercise 
    Do my evening routine
    If midnight or really tired:
       Sleep time
Go to line 1

If my story helped you, email the link to your friends! (and leave a comment!)

Antsa