The course should provide a coverage of the basic mathematical concepts students should know before entering the coursework of the doctorate. Furthermore, they will be exposed to some proofs where they will learn proof techniques and mathematical methods.
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• “Advanced Mathematical Economics”, Rakesh V. Vohra.
• “Mathematical Methods and Models for Economists”, Angel de la Fuente.
• “Apuntes de matemáticas para economía” [Lecture Notes], Jorge Rivera. (*)
• “Mathematics for Economists”, Carl P. Simon and Lawrence E. Blume.
• “Introduction to Analysis”, Maxwell Rosenlicht.
• “Introduction to Probability”, Dimitri P. Bertsekas and John N. Tsitsiklis (*)
The content and exercises are based mainly on those two references (*). However, if you want to go deeper, with the topics of the first 4 days, I suggest Simon and Blume’s book. If you want to see the advanced level of mathematical economics (specially the theoretical ground of optimization) I suggest Rakesh V. Vohra’s book, their exposition and simplicity for complex issues is beautiful.
During the lecture students will be exposed to a series of fundamental definitions and propositions over each of the topics of the course. Furthermore, some proofs will be provided. For the sake of
time (or the lack of it) most of the proofs and exercises will be part of the problem sets, with selected solutions and explanations provided online in Moodle.
The password for Moodle is: mathenomics
There is no assessment for this course. Students will have problem sets that they can solve alone or in groups. These problem sets are useful to get familiarized with the proof techniques used later during the doctorate.
Introduction to Sets, Introduction to Functions, Introduction to Linear Algebra, Introduction to Topology and Continuity, Differentiation of Functions, Convexity, Static and Dynamic Optimization, Introduction to Probability Theory.
Programs where the course is taught: