# PhD - 37th cycle - Thematic fields - Mathematics and Statistics for Economists

Mathematics and Statistics for Economists
Doctoral school in Economics
Department of Economics and Social Sciences, Marche Polytechnic University

The course aims at providing the Ph.D students the advanced statistical and mathematical skills needed in order to analyze economic models. The use of such advanced methods implies to think critically about the mathematical representation of social phenomena and the limit of a model; i.e., ability to simplify reality focusing only to relevant aspects to the analyst, and to analyze the range of conditions under which the model gives reasonable answers.

Prerequisites:

• Importance of Mathematics and Statistics in Social Sciences (Ch 1)
• Basic Mathematical Concepts and Methods (Ch 2)
• Basic Knowledge of vectors (Ch 5.1)
• Basic Calculus (Ch 8.1-5, Ch 11.1-2)

The above parts of the textbook are considered, during teaching and for the final exam, in the knowledge of an undergraduate student. Please, refresh them before the beginning of the class.

Learning Outcomes:

• Developments of abilities to translate an economic problem into a mathematical problem.
• Knowledge of important analytic methods in continuous and discrete time (Calculus, Linear Algebra, Statistics and Optimization) to solve economic problems.
• Ability to analyze critically how the mathematical model is able to capture relevant economic problems and to have in mind the conditions under which the mathematical model is a good representation.

Syllabus:

Math

•  Linear algebra  (Ch 5.2, Ch 6, Ch 7)*
•  Multivariate calculus (Ch 8.6-7, Ch 9, Ch 10, Ch 11.3-6)
•  Differential, Difference equations, and Dynamical Systems (Ch 15, Ch 16, Ch 17)
•  Multivariate and Dyn. Optimization Ch 12, Ch 13, Ch 14

Stat

• Basics in Probability and Statistics  (Ch 4 )
• Some probability distributions. Sugiyama (2016) Ch. 4-5, Palomba (2015) Appendice A

(*) When there is only a chapter indication we mean K. Dadkhah (2011).

Exam:

At the end of the course, students will be assigned a take-home exam on the second and the third blocks (60% of the final grade) and there will be an open-book written exam on the first block (40% of the final grade) on Tuesday 14 January 2020. After the exam there will be a colloquium with the professors of the course during wich students have to explain their solution to the take-home exam.

Students that will not pass the exam will resit it later in the year: the resit will be an open-book written exams on all the program.

Lecturers:

• Francesca Mariani
• Antonio Palestrini
• Cristina Recchioni

Textbooks

• Dadkhah (2011), Foundations of Mathematical and Computational Economics (2nd ed.), Springer
• G. Palomba (2015), Elementi di Statistica per l'Econometria, Edizioni Clua
• M. Sugiyama (2016) Introduction to Statistical Machin