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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).

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Real analysis and optimization brush-up course for PhD

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