Part IB mathematics builds significantly on the material covered in first year. Michaelmas term especially is mainly an extension of the methods taught in Part IA, and you are taught some indispensable results in vector calculus, Fourier transforms, linear algebra and Green functions.
The topics covered in Lent Term will likely be more unfamiliar, and includes solving the Poisson and the Laplace equations, contour integration, tensors, and Fourier methods for partial differential methods. Easter term consists of a few lectures on normal modes, and then the remainder is spent on group theory and its applications.
The coursework component introduces computational methods (e.g. solving ODEs/PDEs numerically), this is done through six projects containing problems which you will solve in Excel. The write-up and taking screenshots for evidence can be a bit tedious, but the methods taught are staples of computational science.
Compared with part IA, problems are far more advanced, though considering this is within a NatSci course the emphasis is still on providing a solution rather than increased rigour.
Mathematics is a popular choice for those taking both or one of the physics options. Some of the topics covered – the method of images, Fourier transforms and vector calculus, are applied directly in IB physics. Others, such as Sturm-Liouville theory and tensors will give a deeper insight into the mathematical foundations of many physical ideas – such as operators in quantum mechanics and elasticity – than the physics courses alone. There is a non-examined mathematics course in Michaelmas for those taking one of the physics options but who don’t take mathematics IB.