Re: How to prepare for the Oral Qualifer

On Wed, 28 Nov 2007 02:39:05 -0500, Kira Yamato
<kirakun@xxxxxxxxxxxxx> wrote:

Is the following statement a good advice on how to prepare for the oral
qualifer exam?

Take a recent article in a math journal [in the topic of your
qualifer]. If you can follow it and be able to "fill in between the
lines" with rigor, then you're ready.

This statement tells me that the qualifer is about understanding the
basics of your subjects and be able to prove them. For the more
advanced theorems, only examples (and counterexamples where the
theorems fail) are needed to know.

Is this sound advice?

No -- a waste of time.

Many articles are incomprehensible even to professors.

Instead, formulate simple questions (on index cards perhaps, but to
save time, just the question -- don't bother writing the answer on the
back) which ask for:

--- definitions

Informal, but capable up being formalized, if challenged.

--- prototype examples

Prototype examples of objects with given properties, objects not
having a given property, objects having some properties but not
others. On this last aspect, keep it simple -- it's just an oral exam,
after all, so they can't expect you to produce obscure examples off
the top of your head.

--- statements of theorems

Informal versions of statements of key theorems, omitting all the
details of the hypotheses (unless the full statement is sufficiently
simple to say comprehensibly in words), but be willing to supply the
additional hypotheses (on a blackboard or whiteboard), if challenged.

How a theorem is typically used.

The dependency tree -- which key theorems need (in the usual proofs)
which other key theorems.

--- sample problems

These should be easy problems, ones that you can almost do in your
head, or with a few lines of work on the board. In other words,
problems that could be asked in class, but for which only an A+
student would be able to answer them all quickly, Thus, you are
demonstrating that you are that A+ student.

The problems should be taken over a wide range of the subject, but
always take the simplest problems. Include a lot of true/false,
prove/disprove type problems. Definitely include truly standard
problems -- in other words, problems that tend to be present in almost
the same form in lots of textbooks.

--- diagrams

Practice drawing nice, reasonably clear diagrams -- but quickly. A
picture really can be worth lots words -- maybe not 1000, but still
lots. What you want is quick, easy graphics which dramatize key
connections. This demonstrates your ability to teach.

Mastery of a subject means you can teach it back.

Good luck.

quasi
.

Relevant Pages

  • Re: How to prepare for the Oral Qualifer
    ... qualifer exam? ... theorems fail) are needed to know. ... On this last aspect, keep it simple -- it's just an oral exam, ... The dependency tree -- which key theorems need ...
    (sci.math)
  • Re: How to prepare for the Oral Qualifer
    ... qualifer exam? ... theorems fail) are needed to know. ... On this last aspect, keep it simple -- it's just an oral exam, ... The dependency tree -- which key theorems need ...
    (sci.math)