I took (and passed!) my qualifying exam in October 2021. My topics were Algebraic Number Theory (major), Probability Theory (major), and Complex Analysis (minor). You can view my official syllabus and a full transcript from the exam.
Preparing for the Qualifying Exam can be a stressful and scary time. In talking to my advisor and other graduate students and thinking about my own process I collected a lot of good (in my opinion) advice on how to prepare for quals and compiled these thoughts into a short article of advice in the hopes that they may be useful for future students preparing for their quals. My preparation process is by no means the ‘right’ one, as everyone’s background and topics are different. However in presenting my process I hope it will help others get started or feel more confident in their own quals preparations.
The document contains some general advice for the exam itself, a list of types of quals questions to prepare for, details about how I studied for my quals (again, not the only way), and a detailed list of resources you can use for planning and studying for your qual. My advice is far from exhaustive and I highly recommend talking to your advisor and older grad students to learn from their experiences.
Sample Study Materials
Below are the study materials that I created in preparation for quals. Most of the value in these study materials is in creating them yourself. For this reason I highly recommend that if you are studying for quals you create your own study guides. This will also allow you to tailor them to your own topics and understanding, but more importantly is a far more effective study method than reading someone else’s materials.
How NOT to use these materials (for quals preparation)
- Read them over and think “Yeah all this makes sense, I’m ready for my exam!”
- Get a question (online, textbook, etc) and immediately look up the solution here
- Re-write/type them word for word for your own study guides
How TO to use these materials (for quals preparation)
- Look over the typed study guide to get a sense of scope for preparation
- Read the list of quals questions at the beginning of the typed study for ideas about types of questions to consider while reviewing material
- Come up with your own list of questions for a topic and only then comparing with these lists for any more questions
- Download and modify the python script with your own questions to randomly quiz yourself
Typed Study Guides For each topic I created a TeXed study guide which had two sections: ‘memorization’ and ‘questions’. ‘Memorization’ contained terms, theorems, examples that I might want to memorize for the exam. ‘Questions’ is a list of a potential quals questions with solutions. For both, I marked the most important terms/questions in pink and created a table of contents of just the terms/questions.
Handwritten Review Notes During the later stages of reviewing I wrote out hand written review guides for each subject, organized by topic. This is a more condensed and selective version of the material, with an emphasis on how the material fits together.
- Number Theory Handwritten Notes
- Probability Theory Handwritten Notes
- Complex Analysis Handwritten Notes
Python Quizzing Scripts Finally, to practice going through questions and common theorems/proofs I wanted to create a script that would randomly generate a few questions. I wrote one in python for each subject, with questions stored by the chapter/topic and optional flags for focusing on particular potions of the material. To use these, download them and run
python [topic]_practice_Qs.py in the terminal. You can also modify the questions or use the template for another subject entirely. [If you are worried about downloading python files directly, I have included txt versions as well which you can copy/modify as python files yourself]
- Number Theory Python Script [txt]
- Probability Theory Python Script [txt]
- Complex Analysis Python Script [txt]
- Grad handbook - The department maintains a graduate student handbook with a section on the qualifying exam, including logistics details regarding scheduling, filing, committee requirements, and syllabus approval.
- Quals Syllabus Database - The department also keeps a Google Drive of previous students Quals syllabi. When creating your syllabus, use this to find examples for your intended topics. Feel free to trim down from previous syllabi!
- requires a Berkeley email to access
- MGSA Wiki - Complementary to the official handbook is the (possibly outdated) MGSA Wiki which has a Qualifying Exam page that contains information about what to expect and prepare as well as links to previous questions listed by topic (again, possibly outdated).
- Deparmtent Quals Questions Database - During 2021 the department launched an official collection of previous quals questions (filling a management gap from the former MGSA collection). In the spreadsheet, there are questions by topic/subtopic, student and faculty names for each questions. There is also a collection of student advice compiled here.
- requires a Berkeley email to access