Mathematics
Commonly referred to as "Mathmo"
The first year maths course consists of seven lecture courses, all of which are compulsory. There are twelve one-hour lectures a week and two one-hour supervisions a week. The seven courses are:
Michaelmas term:
Algebra and Geometry
Differential Equations
Numbers and Sets
Lent term:
Analysis
Vector Calculus
Probability
Dynamics
Algebra and Geometry
This is a 48-lecture course (twice as long as the other six, which are 24 lectures long).
It assumes no knowledge of A-level further maths but the material on complex numbers is lectured
very quickly so it would help to do some reading on this before the first lecture if you have
not studied complex numbers before. It also covers vectors, matrices, linear maps, möbius
transformations, group theory and eigenvectors.
Differential Equations
This course does not assume any previous knowledge of differential equations.
Numbers and Sets
Numbers and Sets provides an introduction to rigorous proof and includes elementary logic,
number theory, set theory, modular arithmetic, and countability (this is about measuring the
size of infinitely large sets).
Analysis
A very pure course that proves in detail a lot of results you will already know as well as
introducing methods for determining whether sequences converge.
Vector Calculus
This extends the calculus you studied at A-level to two and three dimensions, so you will
learn to use integration to find the volume of objects and the lengths of lines in three
dimensions and differentiation to find the gradient of a surface in different directions.
The course also covers vector fields and scalar fields, using gravitational fields as an
example of vector fields.
Probability
The probability course starts from scratch, building up the theory of probability from a
few axioms and so no A-level knowledge is required.
Dynamics
This covers a lot of the material in the A-level mechanics course but in more detail,
so you will find this course easier the more mechanics you have done. Orbits, the motion of
charged particles in electric and magnetic fields, systems of particles, collisions, energy,
dimensional analysis, moments of inertia, and the motion of objects in a rotating reference
frame are all covered.
Exams
At the end of the first year you will have four exams with each exam containing questions
on two courses (algebra and geometry appears twice).
There are four second-year courses in the Easter term. These are special relativity, metric
and topological spaces, optimization, and numerical analysis. These do not appear on the first
year exams but it can be helpful to go to some of these courses to take notes in the first year.
The most valuable source of information you will have for answering questions and for revision
will be your lecture notes - you do not need to buy any textbooks.
© 2003 The Danby Society of Downing College, Cambridge