PhD – 40th cycle – Thematic fields – Mathematics and Statistics

Mathematics and Statistics

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.   


  • 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. 

The students will be assessed on these prerequisites at the beginning of the course.

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.



  •  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, Dynamical Systems, backward and forward solution (Ch 15, Ch 16, Ch 17, Piersanti Mathematical Appendix A.1)
  •  Multivariate and Dyn. Optimization Ch 12, Ch 13, Ch 14


  •   Basic Probability (Ch 1.1-10**)
  • Random Variables (Ch 2.1-17**)
  • Parametric Distributions (Ch 3.1-2, 3.4-9, 3.12, 3.14, 3.16, 3.18, 3.22**)
  • Multivariate Distributions (Ch 4.1-9, 4.11-12, 4.14-16, 4.20**)
  • Normal and Related Distributions (Ch 5.1-5, 5.7**)

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

(**) B. E. Hansen: Probability and Statistics for Economists (2022).


At the end of the course, students will have an exam consisting of a written part and another part based on research paper reports. After the exam there will be the possibility of a colloquium with the professors of the course during witch students have to explain their exam assessments.

Students that will not pass the exam will resit it later in the year: the resit of the exam will be agreed upon with the professors.


  • Antonio Palestrini
  • Francesca Mariani
  • Maria Cristina Recchioni
  • Mariateresa Ciommi
  • Giovanni Campisi
  • Giovanni Piersanti
  • Paolo Canofari


  • Dadkhah (2011), Foundations of Mathematical and Computational Economics (2nd ed.), Springer
  • B. E. Hansen (2022), Probability and Statistics for Economists, Princeton University Press
  • G. Piersanti (2012), The Macroeconomic Theory of Exchange Rate Crises – Mathematical Appendix

M. Sugiyama (2015) Introduction to Statistical Machine Learnin. Morgan Kaufmann.