MATH0004 continues the study of a function of a real variable initiated in MATH0003. The main aim of the course is to develop a rigorous theory of integration and develop further the theory of sequences and series.

Starting only with the basic properties of real numbers, rigorous proofs are given of the main results in elementary differential calculus. Topics covered...

Starting only with the basic properties of real numbers, rigorous proofs are given of the main results in elementary differential calculus. Topics covered include sequences, series, continuity and differentiability of functions and the properties of the exponential function. This course has two main aims: (a) To begin the study of analysis, continued in MATH0004 and MATH0013. Mathematical analysis is one of the most important and well-developed strands of pure mathematics with many elegant and beautiful theorems, and also with applications to many areas of mathematics and mathematical physics. (b) To introduce students to the ideas of formal definitions and rigorous proofs (one of the fundamental features of modern mathematics, and something that is not familiar from A-level), and to develop their powers of logical thinking.

In this module you will study the legal constitution and regulation of personal relationships, and how that regulation affects individuals’ relationships...

In this module you will study the legal constitution and regulation of personal relationships, and how that regulation affects individuals’ relationships with each other and with the state. We look at the problems people encounter in those relationships and the legal responses to those problems. We are as concerned with what actually happens in practice and the policy behind it as with the law as stated in the books.

We will explore law’s role in constituting, regulating and dissolving family relationships, including those between adults, between adults and children and between families and state institutions. You will be asked to think about financial issues, family violence and the care of children. 

We will look at families and family law in their social and cultural contexts. We consider not just what the law is but why it is what it is and what significance, if any, attaches to this. The following texts are recommended: J Miles, R George and S Harris-Short, Family Law: Text, Cases and Materials (OUP, 2019) and J Herring, Family Law (Longman, 2019). To get to grips with the social and policy implications of the subject, though, you’ll be directed also to a range of reading beyond cases and textbooks.

This module should engage you with current controversy and give you an insight into state policy, the position of women and children and the state of the contemporary family.