If your team qualifies to give a presentation, you will have a few minutes (the actual time will be determined based on the number of qualifying teams) to present your web application in class Monday. You should email a zip file of all the files in your project site to me before class Monday. Teams that make presentations do not need to turn anything in on paper for PS9. If your team does not make a presentation Monday, you need to submit a final project report by Wednesday, as described in the PS9 handout.
Final Exam
The final exam will be handed out in class on Monday, 30 April, and due before 5pm on Monday, 7 May. The final will cover the entire course (roughly 40% on material from Exam 1, 40% on material from Exam 2, and the remaining 20% from the rest of the course).Complexity Classes
Why is it easier to establish an upper bound (O) for a problem than a lower bound (Ω)?
Class P: problems that can be solved in polynomial time on a
deterministic Turing Machine. (Polynomial means O(nk) for some constant k.)
Class NP: problems that can be solved in polynomial time on a nondeterministic Turing Machine.
A problem is in Class NP if we could try all possible solutions at once, we could identify the correct solution in polynomial time.Class NP-Complete: problems that are as hard as the hardest problem in Class NP.A problem is in Class NP if we had a magic guess-correctly procedure that makes every decision correctly, we could devise a procedure that solves the problem in polynomial time.
If a problem is NP-Complete (such as the Pegboard Problem), finding a polynomial time solution for it would mean that there is a polynomial time solution for all problems in NP, and P = NP.What would it mean if you proved that the Pegboard Problem is in Ω(2n)?
What would it mean if you found a procedure that solves the Pegboard Problem in
Θ(n150)?
Link: P
vs. NP, Clay Mathematics Institute, Millenium Prize Problem.
Commencement Address
University of Virginia
May 20, 2001
President Casteen, Professor Ackerly, distinguished faculty of this
great University, graduating students of the Class of 2001 and
especially parents, families, spouses and significant others who have
sweated, slaved and sacrificed to make this day
possible... Congratulations to all of you.
Remember, parents: the best revenge is to live long enough to become a
problem to your children.
It is a great honor to be your commencement speaker today. As you have
heard, I sat in your seat thirty-one years ago today, here on the
Lawn. I experienced a remarkable depth and breadth of an education here
at Mr. Jefferson's university. I first learned to love scientific
research a few hundred yards from here under the able and patient
mentorship of Professor Carl Trindle, now of your Brown College. Glad to
hear that you are represented here. That is great.
This is also a family event for me as it is for many of you because, as
you heard, I grew up not far from here in Staunton. My parents still
live there. My mother is here today as are my three brothers. And two of
my three brothers are UVA alumni. And the third was, for a time, on the
faculty. Perhaps most importantly, my niece, Ruth Collins, is in the
graduating class today. Yeah, Ruth!
So, Class of 2001, you enter a distinguished cadre of UVA alumni today:
senators, governors, writers, scientists, business leaders, artists, and
athletes. Here at UVA you have learned the truth of William Butler
Yeats' words, 'Education is not the filling of a pail, it is the
lighting of a fire.' And I suspect, later on today, your fires will all
be well lit.
But who are you, class of 2001? Well, I have spoken to your senior class
president, Drew Davis. And he tells me that you care profoundly about
your university, your country, and your future. That you have high
ideals, but that you know how to have fun. That you have been actually
sobered by the recent revelations of honor code violations, but proud of
the honor system and confident in the integrity it represents, as am I.
I have read about the 'goings on' around the University in the Cavalier
Daily. The concerns about graduate student health care, the athletic
triumphs and heartbreaks, the Dave Matthews concert. I sort of wondered
should he be your speaker. He seems to be a pretty popular fellow around
here. But, I am glad I had the chance instead. And I even read about the
UVA law student who played tempter on Temptation Island, my goodness.
A lot has changed since I was a student here going to eight o'clock in
the morning classes on Saturday wearing a coat and tie. Which is what we
did in 1966. But, yet so much is still the same. Which reminds me of the
famous observation from Clark Kurt, 'The problems of the university are
universal and timeless: sex for the students, athletics for the alumni,
and parking for the faculty.'
So, recognizing that so-called wisdom imparted in commencement addresses
tends to have a half-life measured in milliseconds, what can I say to
you this morning that will matter? And how can I, a scientist and
professor, do this without slides or Power Points, overheads or
handouts? Well, I have actually tried to remember the dozen or so
commencement addresses that I have sat through. And I regret to say that
only one of them leaves the faintest memory of what was said. But that
one, which was actually my high school graduation, still stays with me
to this day. So, with gratitude and apologies to the Presbyterian
minister who delivered it, I am going to adopt his theme.
So, this speech consists of an exhortation, supported by a focus on four
decisions that I would like you to think about.
The exhortation: Seek a balanced life. Sounds good, but what does that
mean? I suggest that this could perhaps be achieved by arriving at
satisfactory conclusions to four life decisions. You can think of these
as the four food groups of a balanced life, if you wish.
Decision number one: What will be your life's work? Put another way,
what will you contribute? What will you leave behind? It has been said
that the purpose of life is a life of purpose. What will be yours?
Here on graduation day, many of you already have a clear picture of
this. Many of you don't. That is okay. Some of you think you do. And
five years from now, you will have completely revised it.
Sitting in your seat thirty-one years ago, I was sure I knew what I
wanted to do. I wanted to be a physical scientist working in quantum
mechanics. And I went off to get a graduate degree in physical chemistry
at Yale. But along the way I discovered molecular biology. Something
that I wasn't that aware of because it was just beginning to spring out
of the research and biology of the previous few years. And discovering
that it was headed for a genuine revolution that would have profound
consequences for our understanding of ourselves, I changed fields. I
went to medical school and found my passion in medical genetics. A field
which as I was here as an undergraduate, I didn't even know existed. So,
keep loose. You can't be confident that your plans will be quite as
linear as perhaps they seem today. But that is a wonderful privilege to
have the chance to make those changes when they come along.
I now have this remarkable job of standing at the helm of the Human
Genome Project. This effort, an international effort, to map and
sequence all of the letters of our own DNA code, to read our own
instruction book. And what an instruction book it is. Inside each cell
of your body you have 3.1 billion letters of this DNA code. If I decided
because it would make a nice commencement speech to read them for you,
and I would read at an average pace of 'a, c, g, g, t, a, c, c, g, t, a,
c, c...' and asked you to stay here because it is such an important day
and this is such an important reading, while I hope you would have
brought along a little refreshment because we would be here for
thirty-two years. And you have all that information inside each cell of
your body. And guess what, ninety-five percent of that is now on the
Internet for you to go and look at, and try to help us figure out what
it means. Because just in the space of the last year, we have crossed a
threshold that is of historic significance in our history as to human
race. We now have read our own instruction book.
And that was done by a cohort of sixteen centers in six countries that I
have had the privilege to lead. And it has been an extremely
exhilarating experience. In no small part because it involved physics,
chemistry, biology, ethics, and theology and a whole host of other
disciplines. So, would I have predicted that when I sat in your seat?
No, and the same will happen to you.
I also find I spend a lot of my time worrying about the ethical
implications of this. Will, for instance, if you decide to find out what
you are at risk for (because we can now read your DNA sequence) will
that information be used to take away your health care or your jobs?
That is unjust. That is something that we should put a stop to, but that
requires the legislative process to kick in.
So, when I go to Congress to talk about that, I find myself quoting
Thomas Jefferson who said, 'Our laws and institutions must go hand in
hand with the progress of the human mind.' Yet rapid advances in medical
technology of this sort must not be allowed to displace the human touch
of medicine. Albert Schweitzer said, 'Our technology must never exceed
our humanity.' And we must not forget in these exhilarating days where
so many unknowns become knowns, that the way we touch lives is one at a
time. I tend to forget that sometimes. I get carried away with the
excitement of the moment.
And it always helps me to go back to a day about ten years ago when I
spent three weeks working in a missionary hospital in West Africa. If
you have not been to the Third World, I strongly encourage you to do
so. It will change your life.
I went there with my medical student daughter. And I had grand ideals
about how in those three weeks, I was going to change the course of
health care in Nigeria and those 93 million people who live there would
never be the same because I had been there for my three weeks. And I got
there working in this very crowded little hospital, surrounded by people
with terrible illnesses. And I began to feel pretty discouraged. Because
while I could help one or two of them, I knew they would go back out to
the same environment. And the same conditions that caused them to be ill
would still be there.
So, I was feeling pretty low about this and wondering, 'Why am I here?'
And on rounds one morning, a young farmer who had been admitted almost
dead the night before with fluid around his heart from tuberculosis that
we were able to draw off and bring him back to at least temporary
health. He stopped me and said, 'You know, you are different. I have the
sense that you haven't been around here very much. And I have a sense
that you are wondering why you are here at all.' I was a little taken
aback. I didn't know it was quite that obvious. And he said, 'I want to
tell you something. You came here for one reason. You came here for me.'
And that occurred to me that that is all it ever is about. To reach out
to one person, to make a difference in one life, that is really what we
are here for. So, have your grand dreams. Have your great plans for what
your professional life will be, but don't forget that it is one person
at a time where we really leave a legacy.
Decision number two: Well, this is the one that makes people
squirm. What are you going to do about faith? Uh oh, not that one. But
can there be any more important questions than these: How did we all get
here? What is the meaning of life? How is it that we know deep-down
inside what is right and wrong and yet rarely succeed in doing what is
right for more than about thirty minutes? What happens to us after we
die?
Surely these are among the most critical questions in life. And ones
which a university should carefully consider. But how much time have you
spent on them? Perhaps you, like I, grew up in a home where faith played
a significant role, but you never made it your own. Or you concluded it
was a fuzzy area that made you uncomfortable. Or even concluded that it
was all superstition, like Mark Twain's schoolboy, who when requested to
define faith said, 'It is believing what you know ain't so.' Or perhaps
you simply assumed that as you grew in knowledge of science that faith
was incompatible with a rigorous intellect and that God was irrelevant
and obsolete. Well, I am here to tell you that this is not so.
All of those half-truths against the possibility of God have holes in
them big enough to drive a truck through, as I learned by reading
C.S. Lewis. In my view, there is no conflict between being a 'rigorous,
show me the data' physician-scientist and a person who believes in a God
who takes a personal interest in each one of us and whose domain is in
the spiritual world. A domain not possible to explore by the tools and
language and science, but with the heart, the mind and the soul.
Yet, it is remarkable how many of us fail to consider those questions of
eternal significance until some personal crisis or advancing age forces
us to face our own spiritual impoverishment. Don't make that mistake.
Decision number three: What are you going to do about love? Well, first
love for another. Listen to Jefferson's words, 'Nature implanted in our
breasts a love of others. A sense of duty to them. A moral instinct, in
short, which prompts us irresistibly to feel and suffer their
distresses. The creator would indeed have been a bungling artist had he
intended man for a social animal without planting in him social
dispositions.' Listen to those dispositions. Act on them, to all your
brothers and sisters.
Sadly, prejudice still abounds in our society. Though genetics is
teaching us that there is no scientific basis for drawing sharp
boundaries around ethnic or racial groups, we still focus on physical
differences of skin color, facial features, and hair texture. As if they
meant something biologically profound. They do not. At the DNA level, we
are all 99.9% the same. All of us.
And what of romantic love? That enduring, glowing fire! I don't agree
with the wag who wrote, 'The trouble with loving is that pets don't last
long enough and people last too long.' Yet our fast-paced and material
world places romantic love at risk all too often. So, whether you have
found your life's partner or still looking, make this a priority of the
highest order.
So, these three decisions so far: work, faith and love. What of the
fourth one? Well, maybe it doesn't quite belong on the same plane, but I
think it is important too.
Decision number four: How will you keep fun in your life? Yes,
fun. Seems to be resonant chord here this morning. Life is full of
enough sobering and tragic moments, don't forget to exercise your sense
of humor, you are going to need it. Listen to Winston Churchill, 'You
cannot deal with the most serious things in the world unless you also
understand the most amusing.'
Now, I admit, fun is a difficult subject to lecture on. So, with
apologies to President Casteen for springing this on him, I would like
to conclude with a tongue-in-cheek exhibit. A song actually about the
university experience, adapted from a little noticed group from the
1980s, Bright Morning Star. The first two verses of this song are for
you, the last is mine. Instrument please.
So, congratulations and Godspeed, Class of 2001. We'll send you off with
a little music:
I learned so many things, although I know I'll never use them.
Not yet...
Well, wait, wait, wait...
I came, I bought the books, I stayed in the dorms, followed directions.
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I worked, I studied hard, made lots of friends that had connections.
I crammed, they gave me grades, and may I say, not in a fair way.
But, I am a good Wahoo, I did it their way.
The courses that I took were all required. I didn't choose them.
You'll find that to survive, it is best to play the doctrinaire way.
And so, I knuckled down, and did it their way.
Well, yes there were times I wondered why
I had to cringe when I could fly
I had my doubts, but after all,
I clipped my wings and learned to crawl.
I learned to bend and in the end, I did it their way.
Now, this is my verse:
And now, my fine young friends,
Now that I am a full professor, where once I was oppressed,
I have become the cruel oppressor.
With me, I hope you will see the double he-lix
Is a highway and yes, you will learn it is best
To do it my way.
Well, I am just a man, what can I do.
Open your books, read chapter two.
And if it seems a bit routine,
Don't talk to me, go see the Dean.
Just start today, dear UVA
And do it my way.