For prospective students | UniBG Economics & Finance

For prospective students

Crash Courses

Among the other extra-curricular opportunities, EDA provides the No One Left Behind activities to help students with a weaker background and to support students with difficulties to attend classes and pass the exams.

Crash courses: 

To help our prospective students with a weaker background in Math, Statistics and/or Economics to fill the gap and conveniently attend classes, we suggest some basic materials to go through during the summer.

Basic Economic Background

The knowledge of basic microeconomic concepts is highly recommended. The reference book is H. R. Varian, Intermediate Microeconomics: A modern Approach (2010), Norton & Company, New York.


  • Consumer Theory (ch. 2, 3, 4, 5, 6, 8, 9, 12, 14, 15)
  • Firm and Market (ch. 1, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28)
  • Welfare and Public Goods (ch. 33, 34, 36)
Basic Mathematical Background

The indispensable background needed to safely start the EF program can be summarized as follows

  • Linear Algebra: vector spaces, vectors, matrices, linear transformations, systems of linear equations.
  • Calculus: functions of several variables, continuity and differentiability. Derivatives and simple integrals. Mathematical programming (maxima and minima of functions). Convexity.Implicit function theorems.

This corresponds more or less to the contents of a first-year course in Principles in a degree in Economics (or Business Economics).

Italian- speaking students may refer to:
Manuale modulare di Metodi Matematici (Moduli 1,2,3,4,5) E.Allevi, M.I.Bertocchi, C.Birolini, G.Carcano, A.Gnudi, S. Moreni, Giappichelli Editore, Torino, ultime edizioni.

A nice book in English instead is:
Sydsaeter et al. “Essential Mathematics for Economic Analysis” Pearson 2016 


Some more advanced or specific  mathematical topics and techniques might emerge early during EF, like for instance:

  • Eigenvalues and eigenvectors
  • Differential and difference equations
  • Intertemporal optimization

If  after covering the more basic material there remains enough time, some of the above topics might be sketched during the introductory course. Materials will be made available in due course.



  • Any student holding a degree in Mathematics, Physics, Engineering can safely assume he /she is in con full control of these subjects; those interested in a preview of the economic applications can refer to the faculty for suggestions on readings. Students with other scientific degrees should evaluate their background against what has been said above and, when in doubt, ask for advice.
  • Students with a degree in Economics might find in the introductory course the opportunity for a useful review and for filling gaps on particular topics. This applies in particular to students with a background  in Business Economics.
  • Students with non-economic and non-scientific backgrounds should definitely care about their mathematical skills and profit of the opportunities to enhance them.
Basic Statistics Background

The following topics are considered part of the background in Statistics of each student enrolling in the master program:

  • univariate descriptive statistics: frequency distribution and graphs, summary statistics (measures of location, variability and distribution shape);
  • bivariate descriptive statistics: double-entry frequency distribution, measures of association between two variables (Chi-squared index, covariance, correlation), simple linear regression;
  • probability: sample space and events of an experiment, properties of probability, conditional probability and independence, Bayes’ theorem;
  • probability distributions: discrete and continuous random variables, expectation, Binomial, Poisson, Uniform and Normal distribution, transformation of random variables;
  • sampling distributions: sample mean, variance and proportion, central limit theorem;
  • estimation: point and interval estimators for the mean, variance and proportion of a population, maximum likelihood method;
  • testing statistical hypothesis: hypothesis tests, first and second type error, p-value, tests concerning the mean, variance and proportion of a population, test for independence in contingency tables.

The following books are suggested if some of the topics have to be recovered:

For more information, please contact Michela Cameletti or Ilia Negri

Basic Econometric Background

Please see Part II, in particular Chapters 4-7 of the Stock & Watson (2019) textbook: