Computer Science at Oxford Stephen Drape Access/Schools Liaison Officer (Adapted from Mike Spivey’s slides)

Four myths about Oxford There’s little chance of getting in It’s expensive College choice is very important You have to be very bright

Myth 1: Little chance of getting in False! Statistically: you have a 30–50% chance Logistically: it’s never been easier

Myth 2: It’s very expensive False! Most colleges provide cheap accommodation for three years. College libraries and dining halls also help you save money. Increasingly, bursaries help students from poorer backgrounds.

Myth 3: College Choice Matters False! If the college you choose is unable to offer you a place because of space constraints, they will pass your application on to a second, computer-allocated college. Application loads are intelligently redistributed in this way. Lectures are given centrally by the department as are many classes for courses in later years.

Myth 3: College Choice Matters However… Choose a college that you like as you have to live and work there for 3 or 4 years – visit if possible. Look at accommodation & facilities offered. Choose a college that has a tutor in your subject.

Myth 4: You have to be bright True! We find it takes special qualities to benefit from the kind of teaching we provide. So we are looking for the very best in ability and motivation.

Our courses Computer Science Mathematics and Computer Science Computer Science firmly based on Mathematics Mathematics and Computer Science Closer to a half/half split between CS and Maths Courses can be for three or four years

Computer Science Year 1 Year 2 Year 3 Year 4 Mathematics Computing Project work

Computer Science Core CS 1 (75%) Core Maths (25%) Core CS 2 (50%) Year 1 Core CS 2 (50%) CS Options (50%) Year 2 CS Options (25%) Advanced Options (50%) Project (25%) Year 3 Advanced Options (66%) Project (33%) Year 4 (optional)

Mathematics & Computer Science Year 1 Year 2 Year 3 Year 4 Mathematics Computing Project work

Mathematics & Computer Science Core 1 (100%) Year 1 Core 2 (58%) Maths Options (17%) CS Options (25%) Year 2 Maths Options (25-75%) CS Options (25-75%) Year 3 Maths Options (25-75%) CS Options (25-75%) Optional Project (33%) Year 4 (optional)

Some of the different courses Functional Programming Design and Analysis of Algorithms Imperative Programming Digital Hardware Calculus Linear Algebra Logic and Proof

Useful Sources of Information Admissions: http://www.admissions.ox.ac.uk/ Computing Laboratory: http://web.comlab.ox.ac.uk/oucl/ Mike Spivey’s info pages: http://web.comlab.ox.ac.uk/oucl/prospective/ugrad/csatox/ College admissions tutors

What is Computer Science? It’s not about learning new programming languages. It is about understanding why programs work, and how to design them. If you know how programs work then you can use a variety of languages. It is the study of the Mathematics behind lots of different computing concepts.

Finding the Highest Common Factor Example: Find the HCF of 308 and 1001. 1) Find the factors of both numbers: 308 – [1,2,4,7,11,14,22,28,44,77,154,308] 1001 – [1,7,11,13,77,91,143,1001] 2) Find those in common [1,7,11,77] 3) Find the highest Answer = 77

Creating an algorithm For our example, we had three steps: Find the factors Find those factors in common Find the highest factor in common These steps allow us to construct an algorithm.

Creating a program We are going to use a programming language called Haskell. Haskell is used throughout the course at Oxford. It is very powerful as it allows you write programs that look very similar to mathematical equations. You can easily prove properties about Haskell programs.

Step 1 We need produce a list of factors for a number n – call this list factor(n). A simple way is to check whether each number d between 1 and n is a factor of n. We do this by checking what the remainder is when we divide n by d. If the remainder is 0 then d is a factor of n. We are done when d=n. We create factor lists for both numbers.

Function for Step 1

Step 2 Now that we have our factor lists, which we will call f1 and f2, we create a list of common factors. We do this by looking at all the numbers in f1 to see if they are in f2. We there are no more numbers in f1 then we are done. Call this function: common(f1,f2).

Function for Step 2

Step 3 Now that we have a list of common factors we now check which number in our list is the biggest. We do this by going through the list remembering which is the biggest number that we have seen so far. Call this function: highest(list).

Function for Step 3 If list is empty then return 0, otherwise we check whether the first member of list is higher than the rest of list.

Putting the three steps together To calculate the hcf for two numbers a and b, we just follow the three steps in order. So, in Haskell, we can define Remember that when composing functions, we do the innermost operation first.

Problems with this method Although this method is fairly easy to explain, it is quite slow for large numbers. It also wastes quite a lot of space calculating the factors of both numbers when we only need one of them. Can we think of any ways to improve this method?

Possible improvements Remember factors occur in pairs so that we actually find two factors at the same time. If we find the factors in pairs then we only need to check up to n. We could combine common and highest to find the hcf more quickly (this kind of technique is called fusion). Could use prime numbers.

A Faster Algorithm This algorithm was apparently first given by the famous mathematician Euclid around 300 BC.

An example of this algorithm hcf(308,1001) = hcf(308,693) = hcf(308,385) = hcf(308,77) = hcf(231,77) = hcf(154,77) = hcf(77,77) = 77 The algorithm works because any factor of a and b is also a factor of a – b

Writing this algorithm in Haskell

An even faster algorithm hcf(1001,308) 1001 = 3 × 308 + 77 = hcf(308,77) 308 = 4 × 77 = hcf(77,0) = 77

Algorithm Design When designing algorithms, we have to consider a number of things: Our algorithm should be efficient – that is, where possible, it should not take too long or use too much memory. We should look at ways of improving existing algorithms. We may have to try a number of different approaches. We should make sure that our algorithms are correct.

Comments and Questions If there’s any comments or questions then please ask. There should be staff and students available to talk to Thank You