Mathematical Sciences at Oxford

Stephen Drape

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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

Email: stephen.drape@comlab.ox.ac.uk

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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

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Myth 1: Little chance of getting in False!

Statistically: you have a 20–40% chance

Admissions data for 2007 entry:Applications Acceptances %

Maths 828 173 20.9%

Maths & Stats 143 29 20.3%

Maths & CS 52 16 30.8%

Comp Sci 82 24 29.3%

Physics 695 170 24.5%

Chemistry 507 190 37.5%

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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!

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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.

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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.

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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

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The UniversityThe University consists of: Colleges Departments/Faculties Administration Student Accommodation Facilities such as libraries, sports grounds

The University is distributed throughout the whole city

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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

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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

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Colleges

There are around 30 colleges in Oxford – some things to consider:

Check what courses each college offers Accommodation Location FacilitiesYou can submit an open application

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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.

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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

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

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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.

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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

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Mathematical Science Subjects

Mathematics Mathematics and Statistics Computer Science Mathematics and Computer Science

All courses can be 3 or 4 years

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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)

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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

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First Year Maths Course

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

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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

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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

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Computer Science 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

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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

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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

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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

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Useful Sources of Information Admissions:

http://www.admissions.ox.ac.uk/

Mathematical Institute http://www.maths.ox.ac.uk/

Computing Laboratory: http://www.comlab.ox.ac.uk/

Colleges

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Information Days

Oxbridge Regional Conferences Thu 19th March, Walkers Stadium, Leicester Thu 26th March, Emirates Stadium, London

ComLab Open Days Sat 9th May Wed 1st July Thu 2nd July Fri 18th September

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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.

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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, emails, military, etc

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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

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Keys

But how do Alice and Bob agree on which key to use?

How do they stop the pirate getting the key?

Encrypted

File

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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

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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 ga (mod n) Bob sends Alice gb (mod n) The key is gab (mod n) The security relies on the fact that it is

hard to find a from ga (mod n) (called the Discrete Logarithm).

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Using two keys

Alice and Bob have their own locks and keys. How can they send a message?

Instead we could two different keys

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Alice locks

Alice locks using her key and sends it to Bob

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Bob locks

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

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Alice unlocks

Alice unlocks her lock and sends it back to Bob

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Bob unlocks

Bob can then unlock the file and read the contents

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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?

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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?

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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.

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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 = me (mod n) Decryption: m = cd (mod n) Devised by Rivest, Shamir and Adleman

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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?)

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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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