|Module title:||Real Analysis|
|Module lecturers:||Prof Nigel Byott|
Infinite processes appear naturally in many contexts, from science and engineering to economics. From solving the equation that finds the wave function of a quantum system in physics, processing sensor data in engineering, to calculating prices for options in economics, at the foundation of all of these are infinite processes and the pure mathematics developed to rigorously and correctly handle these processes. That field of pure mathematics is called analysis, and the central object of study in analysis is the limit which further extends to the notions of convergence, continuity, differentiation, and integrability. In this module, you will be introduced to the pioneering work of Cauchy, Riemann and many other notable mathematicians. By building on material from the first year, we will carefully and rigorously develop notions first in the context of real variables. In particular, we will develop how to rigorously handle real-variable differentiation, Riemann integration, power series, and basic notions of point set topology.
The material in this module is a prerequisite for the study of Complex Analysis (MTH2009 ), Topology and Metric Spaces (MTH3040 ), Integral Equations (MTH3042 ), Fractal Geometry (MTHM004 ), Functional Analysis (MTHM001 ), and Advanced Probability (MTHM042 ). It is recommended for those studying Dynamical Systems and Chaos (MTHM018 ), and is the basis for applications in economics, science, and engineering. Pre-requisite modules: MTH1001 ; MTH1002 (or equivalent)
Please note that all modules are subject to change, please get in touch if you have any questions about this module.