Mathematical Sciences at Oxford Stephen Drape

2 Who am I? Dr Stephen Drape Access and Schools Liaison Officer for Computer Science (Also a Departmental Lecturer) 9 years at Oxford (3 years Maths degree, 4 years Computer Science graduate, 2 years lecturer) 5 years as Secondary School Teacher

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

4 Myth 1: Little chance of getting in False! Statistically: you have a 20–40% chance Admissions data for 2007 entry: ApplicationsAcceptances% Maths % Maths & Stats % Maths & CS % Comp Sci % Physics % Chemistry %

5 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. Most colleges and departments are very close to the city centre – low transport costs!

6 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.

7 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 Look at accommodation & facilities offered. Choose a college that has a tutor in your subject.

8 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. A typical offer is 3 A grades at A-Level

9 The University The University consists of: Colleges Departments/Faculties Administration Student Accommodation Facilities such as libraries, sports grounds The University is distributed throughout the whole city

10 Departments vs Colleges Departments are responsible for managing each courses by providing lectures, giving classes and setting exams College can provide accommodation, food, facilities (e.g. libraries, sports grounds) but also gives tutorials and admits students

11 Teaching Teaching consists of a variety of activities: Lectures: usually given by a department Tutorials: usually given in a college (often 1 tutor with 2 students) Classes: for more specialised subjects Practicals: for many Science courses Projects/Dissertations: for some courses

12 Colleges There are around 30 colleges in Oxford – some things to consider: Check what courses each college offers Accommodation Location Facilities You can submit an open application

13 Applications Process Choose a course Choose a college that offers that course Your application goes to a college rather than the University as a whole since college admissions tutors decide who to admit. You can choose a first choice college – second and third choices get allocated to you.

14 Interviews Interviews take place over 2 or 3 days. Candidates stay within college Mostly candidates will have interviews at the first and second choice colleges For some subjects, samples of written work or interview tests are needed

15 What do interviewers assess? Motivation Future potential Problem solving skills Independent thinking Commitment to the subject

16 Common Interview Questions Why choose Oxford? Candidates often say “Reputation” or “It’s the best!” Why do you want to study this subject? Frequent response: “I enjoy it” It’s important to say why the course is right for you – look at the information in the prospectus.

17 What tutors will consider Academic record (previous and predicated grades) School reference UCAS statement (be careful what you say!) Written work or entrance test (as appropriate) Interview performance

18 Mathematical Science Subjects Mathematics Mathematics and Statistics Computer Science Mathematics and Computer Science All courses can be 3 or 4 years

19 Maths in other subjects For admissions, A-Level Maths is mentioned as a preparation for a number of courses: Essential: Computer Science, Engineering Science, Engineering, Economics & Management (EEM), Materials, Economics & Management (MEM), Materials, Maths, Medicine, Physics Desirable/Helpful: Biochemistry, Biology, Chemistry, Economics & Management, Experimental Psychology, History and Economics, Law, Philosophy, Politics & Economics (PPE), Physiological Sciences, Psychology, Philosophy & Physiology (PPP)

20 Entrance Requirements Essential: A-Level Mathematics Recommended: Further Maths or a Science Note it is not a requirement to have Further Maths for entry to Oxford For Computer Science, Further Maths is perhaps more suitable than Computing or IT Usual offer is AAA

21 First Year Maths Course Algebra (Group Theory) Linear Algebra (Vectors, Matrices) Calculus Analysis (Behaviour of functions) Applied Maths (Dynamics, Probability) Geometry

22 Subsequent Years The first year consists of compulsory courses which act as a foundation to build on The second year starts off with more compulsory courses The reminder of the course consists of a variety of options which become more specialised In the fourth year, students have to study 6 courses from a choice of 40

23 Mathematics and Statistics The first year is the same as for the Mathematics course In the second year, there are some compulsory units on probability and statistics Options can be chosen from a wide range of Mathematics courses as well as specialised Statistics options Requirement that around half the courses must be from Statistics options

24 Computer Science Computer Science firmly based on Mathematics Mathematics and Computer Science Closer to a half/half split between CS and Maths Computer Science is part of the Mathematical Science faculty because it has a strong emphasis on theory

25 Some of the first year CS courses Functional Programming Design and Analysis of Algorithms Imperative Programming Digital Hardware Calculus Linear Algebra Logic and Proof Discrete Maths

26 Subsequent Years The second year is a combination of compulsory courses and options Many courses have a practical component Later years have a greater choice of courses Third and Fourth year students have to complete a project

27 Some Computer Science Options Compilers Programming Languages Computer Graphics Computer Architecture Intelligent Systems Machine Learning Lambda Calculus Computer Security Category Theory Computer Animation Linguistics Domain Theory Program Analysis Information Retrieval Bioinformatics Formal Verification

28 Useful Sources of Information Admissions: Mathematical Institute Computing Laboratory: Colleges

29 Information Days Oxbridge Regional Conferences Thu 19 th March, Walkers Stadium, Leicester Thu 26 th March, Emirates Stadium, London ComLab Open Days Sat 9 th May Wed 1 st July Thu 2 nd July Fri 18 th September

30 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.

31 Information Security Suppose Alice wants to send Bob some information – how can she stop a pirate stealing it? This is a problem faced by internet shopping, banking, s, military, etc

32 Encryption One way to stop pirating is to make the information unreadable by pirate. This process is called encryption When encrypting something, you also need to be able to decrypt it (so that Bob can read it!). So, encryption usually requires a key

33 Keys But how do Alice and Bob agree on which key to use? How do they stop the pirate getting the key? Encrypted File

34 Exchanging Keys Alice and Bob could meet before and exchange a set of keys. But what if Alice and Bob can never meet? (Alice and Bob might be two computers on the internet) There are key exchange methods

35 Diffie-Hellman Key Exchange Alice and Bob agree on numbers g and n but also decide on secret numbers: a for Alice and b for Bob. Alice sends Bob g a (mod n) Bob sends Alice g b (mod n) The key is g ab (mod n) The security relies on the fact that it is hard to find a from g a (mod n) (called the Discrete Logarithm).

36 Using two keys Alice and Bob have their own locks and keys. How can they send a message? Instead we could two different keys

37 Alice locks Alice locks using her key and sends it to Bob

38 Bob locks Bob locks it using his lock and sends it back to Alice

39 Alice unlocks Alice unlocks her lock and sends it back to Bob

40 Bob unlocks Bob can then unlock the file and read the contents

41 Using two keys with Maths In a computer, a lock is equivalent to a function and an unlock is the inverse Suppose that : Alice’s lock is (×2), key is (÷2) Bob’s lock is (+3), key is (–3) Can we use these locks as we did before?

42 Locking has problems in Maths Using Alice’s and Bob’s locks: This is because we must reverse the order when we invert things How can we use a two key system?

43 Public Key Encryption Alice gives everyone her lock (called the public key) and keeps her key secret (called the private key). Alice’s key is never sent so it should remain secret. The challenge is to design an algorithm that is hard to crack without knowledge of the private key.

44 RSA Alice picks two large primes p and q and works out the product n = p×q She picks a private key d and works out a public key e (with a special property). She can send e to Bob. Encryption: c = m e (mod n) Decryption: m = c d (mod n) Devised by Rivest, Shamir and Adleman

45 Breaking RSA The security of RSA relies on how e is computed (based on number theory) If we can find p and q by factoring n then we can find e There is no known “fast” method for computing factors Currently the keys need to be 2048-bit (how large is this?)

46 The future If a fast factoring method can be found then RSA can be broken Fast machines mean we need to keep increasing the size of the keys Quantum computer could provide constant time factoring but may lead to quantum encryption

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