My name's Gavin Lowe, I'm a tutor and director
of studies for Computer Science at St Catherine's
college Oxford. This video is going to be
a demonstration admissions interview, we're
going to try and show you how we run our undergraduate
admissions interviews for Computer Science
and in particular how we run them using online
technology. So with me I've got Alastair Janse
van Rensburg who's another tutor at St Catz
and Tom Aston who's an undergraduate at St
Catz. Tom's just about to enter his second
year. So in a moment we'll be into giving
a demo interview to Tom, see how he gets on.
First of all let me just say a little bit
about how we run interviews. I normally start
interviews by a little bit of general discussion
... try and get to know the candidates a little
bit better, find out what motivates them,
sometimes at that point I'll ask a question
about something on their personal statement,
sometimes I won't, I won't do that today.
However most of the interview is made up of
technical questions, some mathematical problems
or puzzles, to try and assess the candidates
technical ability that how will they help
cope with the Computer Science degree at Oxford.
So for online interviews we use an app called
Miro we'll use it, we'll see it in a bit,
it's an online whiteboard app, ... my experience
is that most candidates get on fairly well
with that ... but it's the sort of thing that
if somebody messes up we're not too worried
about that, we're more interested in how good
candidates are technically. So we want to
see ... how well they cope with the problems
that we give them ... whether they think logically
and come up with good ideas for tackling the
problems. Also are they able to explain their
thinking reasonably, of course we don't expect
a perfect explanation in real time, but I
hope we can have a conversation where we get
to understand what the candidate is thinking.
And also the other way around, can the candidate
pick up hints from us, ... well really we
want to assess whether candidates will cope
well with the interactive style of teaching
that we have at Oxford, so we want to see
that they actually will learn from what we're
saying. At the end of the interview ... we
normally give the candidates a chance to ask
their own questions if they have any, but
we won't be doing that today. Okay so we're
going to do a 20-minute sample interview,
that's a bit short really normally we actually
allow 30 minutes ... for an interview but
it's gonna be a little bit shorter today.
Okay so let's see how Tom gets on.
Hello Tom, so thanks very much for coming
for interview, ... perhaps we can start can
you just tell us why do you want to study
computer science? I study computer science
because I find it incredibly interesting how
an inanimate device like a computer which
fundamentally like built out of silicon, can
sort of work from the very smallest elements
like transistors all the way up to like for
example Teams that were doing this interview
over, ... and how that can also be abstracted
out from like small logic gates up to adders
up to like applications and operating systems.
Okay can you tell us about something interesting
you've done in the area of computer science
maybe an interesting program that you've written?
Although it's quite simple probably my favourite
program that I've ever written was just a
small mini max algorithm for ... noughts and
crosses. It's like yes it's quite simple and
the implementation wasn't too hard but I found
really neat how like an algorithm like that
can be implemented and how like you can basically
create an unpeaceable AI for a game as simple
as noughts and crosses. Okay that sounds interesting,
thanks. Okay so let's move on to some technical
problems ... so for the purpose of the recording
I'm going to share my screen looking at Miro
Okay so there's a question here ... so let
me read the first bit through to you Tom and
then you can have a go at it. So Alice plays
a game with her friends Sam and Pam. In each
of the scenarios below she chooses two positive
integers x and y, so one less than or equal
to x, x less than or equal to y, and she whispers
the sum s which is x plus y to Sam and whispers
the product p which is x times y to Pam. Sam
and Pam have to try to work out what x and
y are. They're all expert logicians and they
always tell the truth. Okay so part one Alice
chooses two positive integers x and y as I
just described, and whispers the sum to Sam
and the product to Pam. Sam says I know what
x and y are, what can you say about x and
y? Okay so for Sam to know what x and y are,
then x plus y must ... well s must specify
two distinct integers. I think the most obvious
or the most obvious initial case is if s is
two because then that that just gives x is
one and y is one. Would there be any cases
beyond that .. I think if s is three then
that also precisely specifies x and y so we
have x is one and y is two. Yeah that's right.
So two equals one plus one three equals one
plus two but then beyond I think those are
the only cases because four could be either
one and three or two and two so it doesn't
give us the exact. Yeah we'll be able to work
out in that case and for larger values of
s? That would hold me on because ... any large
number of s can be one plus ... actually s
minus one or. Or similarly with two. Yeah
or similarly with two yeah exactly. Okay good
let's have a look at part two then ... so
Alice now uses new values for x and y and
whispers the sum to Sam and the product to
Pam. Pam says I know what x and y are what
can you say about x and y?
So in this case we have x and y as precisely
precisely specifying p, which means that p
must only have two factors because otherwise
we don't know what x and y are, which tells
us that p must be prime ... and if p is prime,
because we have x as less than ... well x
has to be ... well less than or equal to y,
but since it's prime we know x is less than
y, so we know that x well x must be one, and
y must be the value of s that Sam is told.
You mean the value of p that Pam's told? Yeah
the value of p that Pam's told, sorry, which
means that the value that Sam is told is p
plus one
Right so. So does Sam now know what x and
y are?
Yes so Sam knows that x equals one, and y
is s minus one. Yeah that's right, you actually
missed a little bit with Pam ... normally
the number one is not considered to be a prime
number. Yeah sorry. So okay so if actually
p is one then x is one and y is one fairly
obviously, okay good. Part three Alice again
chooses new values for x and y and whispers
the sum to Sam and the product to Pam. Pam
says I don't know what x and y are, Sam then
says I know what x and y are but I didn't
know before Pam said that. Okay so first of
all can the sum be less than four?
No the sum can't be less than four because
in part one, ... like the minimum sums got
to be two, and in part one we solve for both
s equals two and s equals three that tells
Sam precisely the values of x and y i.e. that
he knows he knows values of x and y before
Pam says that they don't know what x and y
are. Yeah that's right if the sum is less
than four then Sam would know immediately.
Okay part b, suppose the sum is four, what
are x and y? So if this sum is four then that
either gives x equals one y equals three or
x equals two y equals two ...
so Pam doesn't know what x and y are ... if
however, well, in the case that x equals one
y equals three then Pam knows that p equals
three, and in the other case ... Pam has p
equals four. If p is three then Pam has been
given the prime number which means that ... she
knows the values of x and y, however since
she doesn't know what the values of x and
y are, we must therefore have that x equals
two and y equals two. Right so by the fact
that Pam doesn't know what x and y are we
can eliminate x equals one y equals three
and in the case of ... so how does Sam now
know what x and y are? Well Sam knows that
sum is four so in effect before Pam says anything
Sam knows that so either ... x equals one
and y equals three or x equals two y equals
two and in this case, when Pam says that I
don't know what x and y are, that gives us
the additional knowledge that therefore p
cannot be three. Right. Because in that case
... she'll know therefore we know that must
be p equals four so x equals two y equals
two. Yeah good. Okay ... part c, can the sum
be five?
So if we consider s equals five then that
would give
x one y equals four or x equals two y equals
three as the only cases to consider themselves
must be, well, less than or equal to y ...
so
is that yeah ...
So you consider those two possibilities ... are
they consistent with the story? So with, so
in both cases, well, first one has gives p
equals four the second gives p equals six
... if p equals four then Pam doesn't know
why x and y are, again because we also have
x equals two y equals two ... and then if
p equals six then Pam also doesn't know y
x and y are because we could alternatively
have x equals one y equals six. Right. So
Sam doesn't gain any information from that.
Yeah that's right so ... in both cases Pam
would say I don't know what x and y are so
Sam doesn't learn anything from that. Okay
part d then, can the sum be more than five?
Okay ...
so if this sum was more than five, then we
would have at least three ... pairs of x and
y to consider. Right. So... s equals let's
say six as an example but it will hold then
we have x equals one x equals two x equals
three all to consider ...
so when Pam
yeah that would work for x, s equals six so
no I'm sorry ... y equals five, y equals four,
y equals three, which gives p equals five,
p equals eight and p equals nine
so in this case
... actually yeah in this case the additional
knowledge that ...
Pam doesn't know where x and y are doesn't
actually help
because if if Pam knows what x and y are we
have that x equals one and y equals five because
five is prime, however the other two possible
values aren't prime, so that doesn't actually
tell us anything additionally. So at least
those latter the case of x equals two x equals
three Pam wouldn't know what x and y are,
so
so
Pam only knows what x and y are when without
any additional information when x is one ... however
since x is less than y x is one only occurs
once so the additional knowledge that Pam
Pam doesn't know where x and y are only eliminates
the x equals one case every time, however
for s equals 6 and above we always have at
least two further cases to consider, so it
doesn't actually yeah it doesn't tell us sufficient
information to figure out x and y. Yeah that's
right so in each case it'd be at least two
possibilities where Pam doesn't know what
x and y are and Sam won't be able to tell
the difference between those. Okay so to actually
summarize question three the only solution
we got there was x equals two y equals two
happens to be the only solution to that. I
think what I want to do now is skip part four
because we we're actually quite tight on time
but we can go on to question two and I'll
hand over to Alastair ...
you all need to advance on the pdf so Alastair
if you want to take over. Okay .. Tom can
you see the second page of questions there
starting with consider the following list?
Yes, I can now. Excellent okay I'm going to
read that out for you and then we'll talk
about the questions below. Consider the following
list of five numbers: one, three, two, four,
nine. For some numbers one less than equal
to a, less than equal to b, less than equal
to six, we're going to define the sub list
from a to b to be the consecutive numbers
from the list starting at position a and up
to but not including position b, so for example
if we wanted the sub list from two to five
that would be three to four and the sub list
from four to six is four, nine, and so that's
the six going off the edge there but we're
just ignoring that there, because we want
up to the last one, and then the sub list
from one to two is it's just the element one,
and then finally just as a convention we're
going to say the sub list from from x to x
from for any x there is defined to be just
the empty list there. We're also going to
say that s of a b is going to be the result
of adding up all the elements of the sublist
from a to b. So the first question I want
you to answer here is ... how many sub lists
are there that start from the first element?
Starting from the first element there would
be five sub lists. Okay can you just go through
which what those would be? Sure so you have
a first one is going to be the empty list.
Okay. Then just the first element itself,
first two elements
first three elements so one three two and
finally first four elements one three two
and four
Okay well why do we stop there?
so if you just look at the definition. Yeah
we can go ... up to the last one sorry. Exactly
but so you have spotted that the empty list
is one of those lists so that's good, okay
so now how many sublists are there starting
from any element, not just from the first
one?
so from any elements in this list if we
from any elements in this list it would be
well for the ... first element we have ... six.
Yep. Six sublists. From the second element
we'll have an empty list, list of one, a list
of two, lists of three of length three, and
a list of lengths four, but not the list length
five. Yeah. So in this case it would the total
number of sub lists from any element would
be seven minus n where we let n to be the
position or index. Okay so if you add all
those up you're gonna get some some number
there. Have you double counted any lists there
so do you have any lists in those set of lists
that would be the same?
... when you say in that set of lists what
do you mean by that? So for instance your
list starting from the first element there
you have the empty list and then one and then
one three etc, ... what are your elements
starting, sorry what are your sub lists starting
from the second element? From the second element
the empty list will obviously be the same
... but then otherwise there wouldn't be any
overlap with the elements in the first one,
so we'd have empty list.... So can you spot
the duplicate there where you have two, two
lists that are being counted, or whether one
is being counted twice? Yes so the empty list.
Excellent okay yeah so we can count that and
get rid of that, but okay so moving on to
question two here then, ... can you tell me
what the value of s two six is that's the
sum of the elements of the list two six, sublist
two six
the sub list two six involves ... starts from
index two so that would be so three plus seven,
two plus the fourth element plus the fifth
element which works so three plus two plus
four plus nine is eighteen. Excellent okay
... so now what we wanna do is do a bit of
manipulation with that so I've got an expression
there in part three there, says there's s
of a b is s of one b minus s of one a. Can
you explain to me why that expression is true?
Okay so
okay ... I think I want this
right so if we have
oh okay ... so in fact the value of s of a
can be if we just draw a list currently from
one three
two four nine ... if we let ...
but basically the sub list, well the value
of s from one to b .... well obviously includes
all the values from one to b and yes these
... sublist the value of s records 1 comma
a includes with values from 1 to a, which
means that all the values less than a of so
all the values of index of less than a are
included but in both the summation from one
to b and also the summation of one to a. Yeah.
Then as a result they get
like this the subtraction effects removes
them. Yeah exactly. So yeah the only values
that aren't then eliminated are the values
that occur from index a onwards in the expression.
Yeah up to b. Yeah that's good all right.
That's why they're equal. Yeah excellent okay
so ... part four... I'm sorry I'm going to
just pop in at this point ... I'm afraid we're
basically out of time at this point we've
had our 20 minutes and ... we never get through
all the questions so don't worry about that
but but thank you very much Tom for that ... bye
for now. Bye thanks.
Okay so I think Tom did very well there generally
... I sort of expected that ... Tom's already
been interviewed once and he got a place on
the basis of his interview so he's already
shown that he is very good, has the sort of
skills that we're looking for. In addition
he's now about two years older and has two
years more experience than when we first interviewed
him and hopefully he's learned some things
in that intermediate time. He didn't answer
all the questions in the time available but
we pretty much expect that ... anybody, in
addition we only gave him 20 minutes whereas
normally we'd allow 30 minutes for an interview
like that, so ... anybody who gets about that
far in 20 minutes is almost certainly going
to get a place, so he did very well and we're
not really expecting all candidates do that
well. In particular one thing he did work
very well was just not to get muddled. It's
quite common, particularly the first question
we asked there, for candidates to just get
completely stuck for a bit or to spend time
going around in circles ... a common thing
that people do is actually repeat the earlier
parts forgetting that they've already solved
a particular sub problem and go back and solve
it again ... even though effectively they're
just repeating an earlier part. One thing
with hindsight I should have stopped him doing
is that he rubbed out his answers to each
of the individual parts, actually it would
have been a better tactic for him to have
left those there so that you could refer back
to earlier parts when answering later parts.
Yep so generally he did very well ... understood
all the questions well, thought very clearly,
... there were a couple of bits where he was
just a little bit slower ... he was in the
second question with Alice he was a little
slow to spot that the the empty list was repeated
but we expect the odd oversight like that
and his final explanation might have been
a little bit clearer ... I think it's the
best way to answer that question is to draw
a picture highlighting the different regions
that different parts of the equation represented,
but these sort of minor criticisms and and
overall that was a good performance, that's
the sort of performance that would normally
get somebody a place in Oxford. Okay so I
hope this video has been useful and interesting
to you and helpful to show you how we run
these sorts of interviews.