Mechanical Systems: Symmetry and Reduction

Reduction theory is concerned with mechanical systems with symmetries. It constructs a lower dimensional reduced space in which associated conservation laws are taken out and symmetries are \factored out" and studies the relation between the dynamics of the given system with the dynamics on the reduced space. This subject is important in many areas, such as stability of relative equilibria, geometric phases and integrable systems

Developing reflection on values as a foundation for a business career

Students can learn to analyse questions of ethics from the philosophical perspectives of duties, consequences and virtues. This includes the development of empathy and moral courage. Our brains respond to the experiences of others using 'empathy neurons'; we are 'hard-wired' for empathy. Developing moral courage can be linked to the development of empathy, drawing on 'ethics of care' theories. Graduates who express empathy for their colleagues and care for themselves are better equipped to act ethically. We show how learning experiences can enable students to develop problem-solving responses as an alternative to 'fight or flight' reactions to ethical problems. We can help students to develop expertise in ethics by providing them with more opportunities to engage rationally and empathically with ethical problems, through active learning experiences followed by critical reflective processes. Discussing moral exemplars in active learning helps to avoid a cynical view that unethical behaviour is normal. Critical reflection encourages students to make more use of their rational and empathic capacities. The theory of cognitive dissonance helps students to become aware of how we tend to seek information that confirms our decisions while avoiding information that would alert us to ethical hazards