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Advice to a Beginning Graduate Student (2001)
Advice to a Beginning Graduate Student
or
What is Research?
or
The 4 R's of Graduate School:
Reading, Rithmetic, Research, and Writing
READING, STUDYING, THINKING,
STARTING OFF on the PhD,
DEEP in the MIDDLE of the PhD,
WRITING it all up.
YOU
READING:
Books are not scrolls.
Scrolls must be read like the Torah from one end to the other.
Books are random access -- a great innovation over scrolls.
Make use of this innovation! Do NOT feel obliged to read a book from beginning
to end.
Permit yourself to open a book and start reading from anywhere.
In the case of mathematics or physics or anything especially hard, try
to find something anything that you can understand.
Read what you can.
Write in the margins. (You know how useful that can be.)
Next time you come back to that book, you'll be able to read more.
You can gradually learn extraordinarily hard things this way.
Consider writing what you read as you read it.
This is especially true if you're intent on reading something hard.
I remember a professor of Mathematics at MIT,
name of BERTRAM KOSTANT,
who would keep his door open whenever he was in his office, and he would
always be at his desk writing.
Writing. Always writing.
Was he writing up his research? Maybe.
Writing up his ideas? Maybe.
I personally think he was reading, and writing what he was reading.
At least for me, writing what I read is one of the most enjoyable and
profitable ways to learn hard material.
STUDYING:
You are all computer scientists.
You know what FINITE AUTOMATA can do.
You know what TURING MACHINES can do.
For example, Finite Automata can add but not multiply.
Turing Machines can compute any computable function.
Turing machines are incredibly more powerful than Finite Automata.
Yet the only difference between a FA and a TM is that
the TM, unlike the FA, has paper and pencil.
Think about it.
It tells you something about the power of writing.
Without writing, you are reduced to a finite automaton.
With writing you have the extraordinary power of a Turing machine.
THINKING:
CLAUDE SHANNON once told me that as a kid, he remembered being stuck on
a jigsaw puzzle.
His brother, who was passing by, said to him:
"You know: I could tell you something."
That's all his brother said.
Yet that was enough hint to help Claude solve the puzzle.
The great thing about this hint... is that you can always give it to yourself
!!!
I advise you, when you're stuck on a hard problem,
to imagine a little birdie or an older version of yourself whispering
"... I could tell you something..."
I once asked UMESH VAZIRANI how he was able,
as an undergraduate at MIT,
to take 6 courses each and every semester.
He said that he knew he didn't have the time to work out his answers the
hard way.
He had to find a shortcut.
You see, Umesh understood that problems often have short clever solutions.
There will come a time when you work on a problem long and hard but UNsuccessfully
:(
And then you learn that someone else found a solution.
See this as the GREAT opportunity it is to learn something important.
Don't let it pass you by.
Ask yourself: "How SHOULD I have been thinking to solve that problem?"
I have found that doing so is a powerful exercise.
Danny Sleator tells me that BOB FLOYD independently recommended exactly
this exercise to his students.
He would lead them into asking themselves:
"How COULD I h