Ngô Quốc Anh

April 6, 2009

The QE – Harvard University, Department of Mathematics

Filed under: Đề Thi — Ngô Quốc Anh @ 9:45

The qualifying exam in mathematics is designed to measure the breadth of a student’s knowledge in mathematics. The exam may identify those areas in which a student’s knowledge is weak. Passing the exam is an indication that a student is ready to begin more specialized study leading to research work.

The exam is given at the very start of each semester. A student may take the exam as often as (s)he likes. There is absolutely no stigma attached to `failing’ the exam. `Failing’ it may well provide more useful information than `passing’ it. `Passing’ the exam early is mainly an indication that a student has been an undergraduate at a university with a broad undergraduate program in mathematics. It is not a good predictor of the quality of the eventual PhD thesis.

Students are strongly encouraged to first take the exam no later than their second semester. Before passing the qualifying exam, students should take three beginning 200 level (or 100 level) math courses each semester. In a semester in which they are teaching they need only take two such courses. After passing the qualifying exam students are usually excused from grades in any math courses they take. Students are expected to pass the qualifying exam by the end of their second year.

The exam consists of three three hour papers on three consecutive days. Each paper typically has 6 questions covering a broad range of mathematics. The questions aim to test your ability to solve concrete problems by identifying and applying important theorems. They should not require great ingenuity. In any given year the exam may not cover every topic on the syllabus, but it should cover a broadly representative set of quals/topics and over time all quals/topics should be examined.

Some Old Qualifying Exams

Some old departmental qualifying exams are available here:

(Fall 1995 pdf) (Fall 2001 pdf) (Fall 2002 pdf) (Fall 2003 pdf) (Fall 2004 pdf) (Fall 2005 pdf) (Fall 2006 pdf) (Fall 2007 pdf) (Fall 2008 pdf)
(Spring 1996 pdf) (Spring 1997 pdf) (Spring 2003 pdf) (Spring 2004 pdf) (Spring 2005 pdf) (Spring 2006 pdf) (Spring 2007 pdf) (Spring 2008 pdf) (Spring 2009 pdf)
Some PDF files of questions arranged by topics.

Collected by Danny Calegari and Tom Coates source.


Leave a Comment »

No comments yet.

RSS feed for comments on this post. TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Create a free website or blog at

%d bloggers like this: