Academic year
2023/2024 Syllabus of previous years
Official course title
Course code
ET2003 (AF:463540 AR:252382)
On campus classes
ECTS credits
Surnames A-K
Degree level
Bachelor's Degree Programme
Educational sector code
3rd Term
Course year
Go to Moodle page
This course (CTEM) represents a basic subject in the curriculum of any student of ECONOMIA AZIENDALE - BUSINESS ADMINISTRATION AND MANAGEMENT. The course is taught in the third period of the first year of the course of study, so that the student has already attended basic courses of mathematics in the previous two periods. Following the guidelines of basic mathematical courses in the first two periods, the contents of this course are presented in a theoretically correct framework, using a logic-deductive approach. In addition, the main goals of this course are:

1) to provide specific computational tools, in order to solve models elaborated using mathematical language;

2) to apply basic and advanced notions of calculus, financial mathematics and linear algebra.

As a quantitative course CTEM also aims at providing:

(a) better understanding of theory, techniques and problems encountered in math and economic courses;

(b) the ability to "translate" a problem into workable R code, getting a numerical solution and provide insights on the relevant issues of the problem.
Virtually all the models and exercises in students previous quantitative courses can be potentially handled/solved using the techniques studied in CTEM;

(c) practical knowledge of the R programming environment (see also ). Basic programming skills will be acquired, together
with ideas on how to "compute" models with a formal structure, including the use of functions, derivatives, integrals, estimates, graphs, optimization, etc.
The attendance and the participation in the teaching activities proposed in the lectures, together with the individual study, should allow the student to appropriately acquire tools taught in 'Computational Tools of Economics and Management', related to problems that have been formalized in mathematical language. Through the study and discussion of examples and exercises, the student is induced to both contextualize and apply their knowledge in the field of managerial disciplines. Frequency and active participation of students to the lessons, along with the homework, will allow students to pursue the following tasks:

1) Knowledge and Understanding:
(1a) to acquire a basic knowledge of R programming, including some advanced tools for unconstrained and constrained optimization;
(1b) to understand some geometric concepts related to function plots;
(1c) to apply some techniques of calculus using R, using 2 or more unknowns;
(1d) to apply tools for the solution of problems in financial mathematics;
(1e) to properly manipulate advanced matrix operations and solve underdetermined / overdetermined linear systems, using R.

2) Capability to Apply Knowledge and Understanding:
(2a) to generate/manipulate quantitative models for real economics problems, using specific indicators and descriptors;
(2b) to integrate linear algebra with fundamental results of financial mathematics;
(2c) to know and manipulate the relevant operations among matrices, for advanced linear algebra.

3) Capability of Making judgement: using mathematical tools and indicators in order to infer novel information from economics models.

4) Lifelong learning skills:
4a) to enhance the capability of distinguishing problems from their mathematical models;
4b) to enhance the capability of interpreting and validating results obtained from mathematical models.

The course requires a basic knowledge of math (numbers, sequences, linear algebra, calculus with one-two unknowns) as a Prerequisite.
Students should provably know the contents of the MATHEMATICS course. In particular, students must be able to work with the following
concepts: systems of equalities and inequalities, linear algebra for matrices, extreme points of functions, functions with
two or more unknowns, integrals.
The course will cover the following topics:


1) introduction to R, including where to download and how to install the program,
2) graphics, root-finding,
3) computation of derivatives and integrals with R,
4) extremal points, optimization, constrained optimization,
5) state preference model and linear algebra,
6) introduction to random variables, basics on simulation,
7) notes on interfacing Python and R.

Active participation is required to students, and computer experiments are needed to master the material and appreciate
the potential of computational approaches for model analysis.
The next references are advised to better assimilate the contents of the course. These references are all (but the last) available for free. The last reference
can be considered "not essential":

1) afternotes by the teacher, available at and and on
2) additional teaching material (thanks to the kind permit of Prof. Paolo Pellizzari), available on
3) “Using R for Scientific Computing” by Karline Soetaert (ZIP): lecture notes, reference card for R beginners and exercises" available on
4) “The R Guide” (version 2.5)" by Jason Owen, available on
5) “The R book” by Michael J. Crawley, 2007, Wiley.
Each call may include several days for the exam. In particular, students who want to apply for the exam will have to follow
the next rules:

1) joining a/the call by registering (on the standard unive website) for a time slot in one of the days of the call (the first available),
2) each time slot lasts 1h15' - 1h30', which is used in the following way: 50'-60' represents the time for students to solve the exercises, 25' - 40’ are used by the teacher,
3) the exam will include multiple computations and written tests with short answers, to be solved at the PC (exams take place at Palazzo Moro, S.Giobbe),
4) exercises will cover only the current programme of the course. Moreover, each multiple/open choice exercise has the following grading:
i. 1 point for each of the first 3 exercises (2 points for each of the other exercises) in case of correct answer
ii. 0 points if blank
iii. -1 point for each of the first 3 exercises (-0.5 points for each of the other exercises) in case of wrong answer
5) final grades will be communicated by the teacher in the end of the last day of each call, using Moodle platform ,
6) sample exams+solutions are released by the teacher on both and , during the period of lessons.
7) students joining the call must have: their own USERNAME + PASSWORD (by UNIVE) to use the PC at Palazzo Moro, a valid document with photo, and a pen to write.
This is a conventional face-to-face- course which adopts also additional teaching material available on the e-learning platform .
The online teaching material reports the contents of the lessons. Students are required to actively participate, practice and do experiments on a PC, to replicate the results on the used models.
See also and for further info/documents/downloads.

Accessibility, Disability and Inclusion
Accommodation and support services for students with disabilities and students with specific learning impairments

Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding support services and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). If you have a disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services:
written and oral
Definitive programme.
Last update of the programme: 16/03/2023