PhD-mathematics-brush-up
Lecture notes - Mathematics PhD Brush-up course
This repository contains a set of lecture notes for an introductor course in Real Analysis and Optimization, plus two homeworks.
The whole text is divided into six sections, covering
- basic topological analysis (metric and normed spaces, sequences and convergence, notion of open and closed sets, boundedness and compactness) in Ch.1
- notion of continuity (and related theorems) in Ch.2
- notion of convexity in Ch.3
- differentiability (and related theorems)in Ch.4
- solution of optimization problems in Ch.5
- basic integration in Ch.6
These lecture notes were used for a PhD brush-up course at the Universitat Autonoma de Barcelona (UAB).