This module focuses on advanced measurement techniques that are routinely used in industry, government, advocacy and academic research. The module builds on...

This module focuses on advanced measurement techniques that are routinely used in industry, government, advocacy and academic research. The module builds on the material in the second year Data Analysis module and covers theories of quantitative measurement as well as practical measurement strategies involving data reduction techniques and latent variable modelling. Examples are taken from the wide variety of social science fields that use these methods. The module provides hands-on training in the application of these measurement strategies in to real data sets.

The module falls into 2 parts.
Part I – (first 3 lectures) is a continuation of Part II of PLIN0045. It looks in more depth at pragmatics:
the nature of...

The module falls into 2 parts.
Part I – (first 3 lectures) is a continuation of Part II of PLIN0045. It looks in more depth at pragmatics:
the nature of communication, the relation between language and communication, and some recent approaches to
the study of communication.
Part II – (last 7 lectures) is project-based and looks in depth at some current topics in the study of meaning.

LAGRANGIAN AND HAMILTONIAN MECHANICS|NONLINEAR DYNAMICAL SYSTEMS|CHAOS

Outline:

This module aims to provide students with an introduction to advanced mathematical treatments of deterministic dynamics. The topics include...

Outline:

This module aims to provide students with an introduction to advanced mathematical treatments of deterministic dynamics. The topics include Lagrangian and Hamiltonian dynamics, for both particles and for fields, non-linear systems and solutions to equations and the approach to chaos.

Aims:

Stretch mathematically inclined students by presenting advanced material on the dynamics of classical systems. The second-year modules MATH0043 and PHAS0026 would be an advantage but not a prerequisite;
	Develop Lagrangian and Hamiltonian mechanics;
	Foster an understanding of the role of non-linearity in discrete and continuous equations of motion, particularly through the development of phase space portraits, local stability analysis and bifurcation diagrams;
	Show how non-linear classical mechanics can give rise to chaotic motion, and to describe the character of chaos.
Teaching and Learning Methodology:

This course is delivered via weekly lectures supplemented by a series of workshops and additional discussion.

In addition to timetabled lecture hours, it is expected that students engage in self-study in order to master the material. This can take the form, for example, of practicing example questions and further reading in textbooks and online.

Indicative Topics:

Continuous Dynamical Systems [18 hrs]: Hamiltonian dynamical systems; Symmetry and conservation laws in Hamiltonian systems; Liouville’s Theorem; Local stability analysis; Linearisation theorem; Bifurcation analysis for one and two-dimensional systems, including Hopf bifurcation; Characteristics of chaotic systems with examples.
	Discrete Dynamical Systems [12 hrs]: Iterated maps as dynamical systems in discrete time; The logistic map as main example; Equilibria, cycles and their stability; Period doubling; Bifurcations.