## Welcome!

Congratulations on receiving a place to study Mathematics, Mathematics and Computer Science, Mathematics and Philosophy, or Mathematics and Statistics at the University of Oxford! We look forward to welcoming you in October.

Your college will be in touch before term starts, but we hope this page will be a useful resource for preparing you for your studies. You may also want to look at the Information for Prelims Students section of the website, as this is specifically for first years and gives key dates, information on finding your way around, and information about exams.

## Pre-reading and summer work

We would encourage you not only to read about mathematics over the summer but also to do some mathematics. Feel free to do any of the practice problems online that seem helpful - these make sure that you are up to speed with all the concepts you need to begin the course. Your college tutors may set you these sheets to do over the summer, but they are good to review even if your tutors don't require it. Additionally, if you've only done A-level Mathematics (or have not studied in the A-level system) you may want to look at the bridging the gap material.

Have a look at the "How do Undergraduates do Mathematics?" booklet which gives you an idea of tutorials, how university-level mathematical study differs from school study, and how to approach problem sheets.

Several of the books in the departmental prospectus are good for bridging the transition from school to university, we particularly recommend:

Lara Alcock - How to Study for a Mathematics Degree

Kevin Houston - How to Think Like a Mathematician: A Companion to Undergraduate Mathematics

Richard Earl - Towards Higher Mathematics

If you've done the online practice problems you might also want to look at NRICH's preparation for pure maths and preparation for applied maths. Underground Mathematics has a lot of problems encouraging you to explore various concepts more deeply. If you didn't take STEP you might also want to read through (and do the problems in) Advanced Problems in Core Mathematics: Preparing for University by Stephen Siklos which is available as a free pdf.

**You are very much encouraged to view the following video which provides guidance on how to make the most of tutorials.**

## Your first year

Terms at Oxford are short (8 weeks) and for most weeks of the first year you'll have 10 hours of lectures a week in term-time, running from 9-11 in the Mathematical Institute (Maths & Philosophy and Maths & Computer Science students will also have some lectures in the University Examination Schools or in the Department of Computer Science respectively). You can find out information about the first year courses in the Information for Current Students section of the website. The handbooks for the different courses also contain lots of useful information - including the structure of the year, a summary of each course, and information about exams.

The three terms at Oxford are called by different names: Michaelmas is the first term and runs from October to December, Hilary is the second term and runs from January to March, and Trinity is the third term and runs from April to June. You can find out when the terms start and finish on the main university website.

At the end of Trinity Term you will take exams - these don't count towards your final degree classification, and are simply graded distinction, pass, partial pass, or fail. You must pass these exams in order to continue with the course. You can find out more in the examinations and assessment part of the website.

Mathematics and Mathematics & Statistics students study all the courses listed below, Mathematics & Philosophy and Mathematics & Computer Science students study the courses indicated as well as Introduction to Logic and Elements of Deductive Logic, and Computer Science courses respectively

## Michaelmas Term

**Introductory courses (Introduction to University Level Mathematics and Introduction to Complex Numbers) - M&P, M&CS**

*The purpose of these introductory lectures is to establish some of the basic language and notation of university mathematics, and to introduce elements of (naive) set theory and the nature of formal proof.*

**Linear Algebra I - M&P, M&CS**

*Linear algebra pervades and is fundamental to algebra, geometry, analysis, applied mathematics, statistics, and indeed most of mathematics. This course lays the foundations, concentrating mainly on vector spaces and matrices over the real and complex number systems.*

**Analysis I: Sequences and Series - M&P, M&CS**

*In these lectures we begin a rigorous treatment of the real and complex numbers, and study their properties, particularly completeness; we define and study limits of sequences, convergence of series, and power series.*

**Introductory Calculus - M&P**

*These lectures are designed to give students a gentle introduction to applied mathematics and at the end of the course, students will be able to solve a range of ordinary differential equations (ODEs). They will also be able to evaluate partial derivatives and use them in a variety of applications. *

**Probability - M&P, M&CS**

*The aim of this introduction to probability is to develop the concept of chance in a mathematical framework. Random variables are introduced, with examples involving most of the common distributions. Probability models considered include random walks and linear difference equations.*

**Geometry **

*The course is an introduction to some elementary ideas in the geometry of euclidean space through vectors. One focus of the course is the use of co-ordinates and an appreciation of the invariance of geometry under an orthogonal change of variable.*

**Computational Mathematics**

*Many mathematicians use general-purpose mathematical software which includes tools for symbolic and numerical computation and other features such as plotting, visualization and data analysis. In this introductory course, students will explore these ideas using the popular specialist mathematics software MATLAB software.*

## Hilary Term

**Linear Algebra II - M&P, M&CS**

*This course is an introduction to determinants, linear transformations, eigenvectors and eigenvalues and the spectral theorem for real symmetric matrices. It covers both theory and applications of diagonalizability amd brings in the geometrical importance of an orthogonal change of variable.*

**Groups and Group Actions - M&P, M&CS**

*Abstract algebra evolved in the twentieth century out of nineteenth century discoveries in algebra, number theory and geometry. The group is an important first example of an abstract, algebraic structure and groups permeate much of mathematics particularly where there is an aspect of symmetry involved.*

**Analysis II: Continuity and Differentiability - M&P, M&CS**

*In this term’s lectures, we study the continuity of functions of a real or complex variable, and differentiability of functions of a real variable. *

**Dynamics**

*The subject of dynamics is about how things change with time. A major theme is the modelling of a physical system by differential equations, and one of the highlights involves using the law of gravitation to account for the motion of planets. *

**Multivariable Calculus**

*In these lectures, students will be introduced to multi-dimensional vector calculus. They will be shown how to evaluate volume, surface and line integrals in three dimensions and how they are related via the Divergence Theorem and Stokes’ Theorem.*

**Fourier Series and PDEs **

*Fourier series are a way of representing functions as sums of trigonometric functions. Students will then be shown how the heat equation, the wave equation and Laplace’s equation arise in physical models.*

**Computational Mathematics**

*In this term you undertake an assessed project using MATLAB and there are drop-in sessions and demonstration sessions.*

## Trinity Term

**Groups and Group Actions - M&P, M&CS**

*Continuation of the course from Hilary Term.*

**Analysis III - Integration - M&P, M&CS**

*In these lectures we define the Riemann integral and study its properties; prove the Mean Value Theorem for Integrals and the Fundamental Theorem of Calculus. This gives us the tools to justify term-by-term differentiation of power series and deduce the elementary properties of the trigonometric functions.*

**Statistics and Data Analysis**

*The course introduces the concept of likelihood for a probabilistic model and its use in estimating unknown model parameters. Techniques for finding structure in datasets are relevant to many parts of applied maths, specifically this course will cover principal components analysis and clustering techniques. *

**Constructive Mathematics**

*This course is an introduction to mathematical algorithms; that is procedures which one can carry out to achieve a desired result. Such procedures arise throughout mathematics both Pure and Applied. *

## Typical Timetable

You can find lecture lists online - Maths & Philosophy and Maths & Computer Science students will attend some of these lectures, but will also have lectures outside of these times.

Tutorials are arranged with your college tutors. You will be asked to hand in work before the tutorial, which will be your answers to problem sheets (which are based on the material you learn in lectures).

It can be a little overwhelming to be in charge of your own timetable for the first time, so the university has produced study skills videos on managing your workload and revising for exams.

## Laptops

If you’re buying a computer for university, please do consider a standard laptop (running MS Windows or MacOS X) over a desktop, Chromebook or tablet etc. as such a laptop will be used for the Computational Mathematics practical sessions and project work in the first year. The Computational Mathematics course uses Matlab, for which the University has a site licence. The software can be downloaded from IT Services and to save time you should install it prior to the first practical session. If you do not have a laptop you will be able to borrow one for the sessions, and can apply for access to the computers in the Undergraduate Study Room to work on your projects, please contact Academic Admin to make arrangements.

## Maths Societies

Student representation is important and to that end the Mathematics Undergraduate Representation Committee (affectionately known as MURC) forwards your views and suggestions to departmental committees. They have produced a Freshers' Guide (Fresher is the name for a first year student) and run an annual bookstall.

Your college is a great place to socialise, but you might also want to socialise with mathematicians from other colleges. There are two societies for mathematicians at Oxford:

**The Oxford Invariants**

The Invariants are the Oxford University student society for Mathematics. They host informal lectures, often given by leading mathematicians, as well as socials and puzzle competitions. They also produce a termly magazine and you can find out more about them on their website.

**The Mirzakhani Society**

The Mirzakhani Society is a society for women studying maths at Oxford - its aim is to support students through providing a space to discuss issues that women may encounter during their degrees. It holds weekly ‘Sip and Solve’ meetings with tea and cake, and other events such as socials and talks. You can find out more about the society on their Facebook page.