Mathematics is the language of science and logic the language of argument. Science students are often surprised, and sometimes daunted, by the prevalence of mathematical ideas and techniques which form the basis for scientific theory. The more abstract ideas of pure mathematics may find fewer everyday applications, but their study instils an appreciation of the need for rigorous, careful argument and an awareness of the limitations of an argument or technique. A mathematics degree teaches the skills to see clearly to the heart of difficult technical problems, and provides a “toolbox” of ideas and methods to tackle them.

The Mathematics degrees can lead to either a BA after three years or an MMath after four years, though you will not be asked to choose between these until your third year. Both courses are highly regarded: the employability of graduates of both degrees is extremely high, and BA graduates can still go on to second degrees, Masters or PhDs. For the BA, a final classification (First, Upper Second, Lower Second, Third, Pass, Fail) is based on second and third year assessment. MMath students receive this classification and also a similar assessment separately on the fourth year.

Second year

In the first term of the second year there are currently three compulsory courses totaling 64 lectures:

Linear Algebra
Metric Spaces and Complex Analysis
Differential Equations I

Second year students must also take five or six of the following long options (16 lectures):

Rings and Modules
Integration
Topology
Differential Equations II
Numerical Analysis
Fluids and Waves
Quantum Theory
Probability
Statistics

Students also take three of the following short options (8 lectures):

Number Theory
Group Theory
Projective Geometry
Introduction to Manifolds
Integral Transforms
Calculus of Variations
Graph Theory
Special Relativity
Mathematical Modelling in Biology

At the end of the year, each student sits three core papers and six or seven optional papers.

http://www.maths.ox.ac.uk/study-here/...