# Subject Summary: Part IB Mathematics

This course is especially useful for students intending to study Physics or Chemistry in Part II. It is also occasionally attended by students taking other courses. The following topics are included: introduction to group theory; more advanced matrix theory; Cartesian tensors; more advanced theory of differential equations (including solution in power series and expansions in characteristic functions); Fourier transforms; calculus of variations; functions of a complex variable; calculus of residues. Some continually-assessed practical work is associated with particular topics in the course. This involves the use of computers to illustrate and exploit numerical techniques. No candidate may take Mathematics unless they have read Mathematics in Part IA, unless they have been placed in a class not lower than the second class in Part IA of the Engineering Tripos, or unless they have been classed in Part IA of the Mathematical Tripos, or is an Affiliated Student.

# Programme Specification: Part IB Mathematics

This course is taught by the Department of Applied Mathematics and Theoretical Physics.

In order to take this course, it is highly desirable to have obtained at least a second class (upper or lower division) in NST Part IA Mathematics for Natural Sciences, course A or B. The material from course A is assumed.

## Aims

- to provide a course on advanced mathematical and computational techniques that are used in the physical sciences courses of the Natural Sciences Tripos;
- to develop mathematical skills and methods appropriate for students in the physical sciences. A detailed syllabus is determined by a committee which has input from the physical science subjects in the Natural Sciences Tripos.

## Learning outcomes

At the end of the course students should:

- have a knowledge and understanding of a range of more advanced mathematical techniques;
- be able to solve mathematical problems based on the course material;
- be able to use several computer and numerical methods related to the course material.

## Teaching and learning methods

These include lectures, supervisions, practical work on a computer and occasional examples classes.

## Assessment

Assessment for this course is through:

- two unseen written papers each of three hours (for aims 1 and 2 and learning outcomes 1 and 2);
- six assessed computer practical exercises (for aims 1 and 2 and learning outcome 3).

## Courses of Preparation

**Essential:** NST Part IA Mathematics, course A or B; *or *Part IA of the Mathematical Tripos

**Recommended:** NST Part IA Physics

## Additional Information

Further information is available on the Course Websites pages.