Mathematics
Objectives
The goal of this course (*) is to present some mathematical tools and the results that will be used throughout the PhD courses.
(* the updated course’s syllabus will be available to students at the beginning of each academic term)
General characterization
Code
6301
Credits
7
Responsible teacher
Prof Doutor Paulo M. M. Rodrigues
Hours
Weekly - Available soon
Total - Available soon
Teaching language
English
Prerequisites
n/a
Bibliography
TBA
Teaching method
The teaching method is connected to the evaluation method. Both promotes students’ ability to learn promoting research capacity.
Evaluation method
Midterm 40%
Final Exam 40%
Problem set 20%
Subject matter
Introduction to topology
Metric spaces
Continuity, convergence, separability and completeness
Contractions, compactness and connectedness
Correspondences and the maximum theorem
Fixed-point theorems
of Brouwer and Kakutani
Elements of measure and integration theory