To help our prospective students, enrolled in the a.y. 2024-25, with weaker backgrounds in Mathematics, Econometrics, and/or Economics fill the gap and fruitfully attend the main courses, we offer three crash courses during the period from September 2 to September 13, 2024:

**Introductory Mathematical Methods for Economists****Introductory Econometrics****Introductory Microeconomics and Macroeconomics**

*The crash courses are held both in person and in live-stream mode (hybrid mode). Students can choose whether to attend classes in person or follow them online. The timetable for the crash courses is provided below.*

*Attendance at the crash courses is strongly recommended. All the material covered in the crash courses will be taken for granted in the main courses and will serve as the basis for the more advanced material covered in them.*

**Introductory Mathematical Methods for Economists** (Prof. Alessandro Vaglio) – Link to MS Teams

- Monday, September 2, h. 8:30-10:30
- Tuesday, September 3, h. 14:30-17:30
- Wednesday, September 4, h. 8:30-10:30
- Thursday, September 5, h. 14:30-17:30
- Friday, September 6, h. 11:30-13:30
- Monday, September 9, h. 8:30-10:30
- Tuesday, September 10, h. 14:30-17:30
- Wednesday, September 11, h. 8:30-10:30
- Thursday, September 12, h. 14:30-17:30
- Friday, September 13, h. 8:30-10:30

**Introductory Econometrics** (Prof. Elona Harka) – **Link to MS Teams**

- Monday, September 2, h. 10:30-13:30
- Monday, September 2, h. 14:30-17:30
- Tuesday, September 3, h. 8:30-10:30
- Wednesday, September 4, h. 14:30-16:30
- Thursday, September 5, h. 8:30-10:30
- Friday, September 6, h. 8:30-11:30
- Monday, September 9, h. 10:30-13:30
- Tuesday, September 10, h. 8:30-10:30
- Wednesday, September 11, h. 15:30-17:30
- Thursday, September 12, h. 8:30-10:30

**Introductory Microeconomics and Macroeconomics **(Prof. Salvatore Piccolo and Giampaolo Lecce) – **Link to MS Teams**

- Tuesday, September 3, h. 10:30-13:30
- Wednesday, September 4, h. 10:30-13:30
- Thursday, September 5, h. 11:00-14:00
- Friday, September 6, h. 14:30-17:30
- Monday, September 9, h. 14:30-17:30
- Tuesday, September 10, h. 10:30-13:30
- Wednesday, September 11, h. 10:30-13:30

- Thursday, September 12, h. 10:30-13:30

Basic Mathematical Background

**The indispensable background needed to safely start the EDA 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 EDA, 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.

**Notice: **

- 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 Econometric Background

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

https://www.pearson.com/us/higher-education/product/Stock-Introduction-to-Econometrics-4th-Edition/9780134461991.html

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.

Topics:

- 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)