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The mathematics course is a service course taught by the DAMTP and mainly covers the mathematical methods used in the Physics and Chemistry courses in future years. It closely complements the Physics A and B courses with some topics even being repeated, albeit from a more mathematical perspective. Based on a straw poll done at a lecture this writer was attending, students taking IB Maths also took a variety of subjects, with a very small number also taking a biological subject with Maths. However, the usefulness of the IB Maths course to the Physics A and B course makes it a rather popular combination to take for those wishing to specialise in either Physics or Astrophysics in the third year. Lectures are usually at 11 am on Mondays, Wednesdays and Fridays.
The course begins with a refresher on vector calculus, before ploughing through the rest of the syllabus. In Michaelmas, you will be lectured on Vector Calculus, Green’s Functions, Fourier Transforms, PDEs, Matrices, Elementary Analysis and Series Solutions. In Lent, lectures begin with Sturm-Liouville theory, before continuing with Variational Calculus, Laplace’s and Poisson’s Equations, Cartesian Tensors, Contour Integration and its application to Fourier Transforms. Easter term will see Normal Modes, Group Theory, and Representation Theory being covered.
In general, the format of the lecture notes, either tends to be partially filled or filled. In the case of partially filled notes, the filled notes are uploaded to the portal after the lecture.
You can expect supervision problems to take longer to solve than they have in IA and difficult problems are starred to indicate as such.
One of the benefits of Maths is that there are no practicals. There are about 3 Scientific Computing exercises to complete before the end of Michaelmas and Lent each, but these are relatively doable, if not a little time-consuming. These form about 10% of the total mark.
Revision and Exams
The bulk of the total marks come from two 3 hour written exams at the end of the year. Each paper consists of 10 questions, of which you may attempt a maximum of 6 questions (leaving about 30 minutes for each question). Unlike in IA, the division of the topics across paper 1 and paper 2 is much more consistent across the years, and roughly follows the order in which the topics were lectured throughout the year. In paper 1, you can usually expect to see questions related to Vector Calculus, Green’s Functions, Delta Functions, Matrixes, Fourier Transforms, Elementary & Complex Analysis, Series Solutions, SL Operators and Variational Calculus. In paper 2, it is common to see questions from SL Operators and Variational Calculus as well as Poisson’s and Laplace’s equations, Tensors, Contour Integration, Normal Modes, Group Theory and Representation Theory. These are just rough guidelines and are by no means a guarantee, but in this writer’s experience they have been generally true.
As expected, the time limit can be a challenge during the exam, and the questions can be inherently challenging. The best way to prepare is to work through past papers and refer to worked solutions (some supervisors provide unofficial solutions). There have been years where questions have been repeated without any changes so there is much to be gained through this process. Make sure to schedule timed practice, without referring to any notes, since you won’t have a formula sheet (or less crucially, a calculator) in the exam.
Course Website: https://www.natsci.tripos.cam.ac.uk/subject-information/part1b/maths.