37292 - Mathematics

Learning outcomes

At the end of the course, the student will have a basic knowledge of the mathematical concepts and techniques that are of central importance for economics, finance, statistics and econometrics, including elementary functions, linear algebra and matrix operations, geometric sequences and series, derivatives and differentiation techniques, introductory integral calculus. The student will be able, in particular, to apply fruitfully such tools and concepts to a wide range of topics and to a number of linear and nonlinear models in economics, finance and management.

Course contents

Introduction to the course and review of preliminary mathematical notions.

One-variable functions: basic definitions. Elementary functions (linear, quadratic, power, exponential and logarithmic), their properties and graphs.
An intuitive introduction to limits and continuity

Differentiation of one-variable functions: tangents and derivatives, rules of differentiation, chain rule, higher-order derivatives.

Derivatives in use: implicit differentiation and economic examples (including the marginal rate of substitution in microeconomics); concavity and convexity; linear and quadratic approximations; rate of change, rate of growth, elasticity; continuity and differentiability; intermediate-value theorem.

Single-variable optimization: local and global maxima and minima, stationary points and first-order condition, optimization of concave and convex functions, inflection points, study of the graph of a function, asymptotes.

Geometric sequences and series and their application to economics and financial mathematics.

Basic elements of matrix algebra and solution to systems of linear equations. Economic applications.

Introductory integral calculus: the Riemann integral and its geometrical interpretation as area; primitives and indefinite integrals, elementary rules of integration; integration by parts. Integration in economics: integrals over an infinite time horizon and their interpretation; continuous compounding and discounting, present values; 'stock' and 'flow' variables.

Introductory multi-variable calculus: partial derivatives with two variables, geometric interpretation; partial elasticities; differentiation along a level curve; multi-variable optimization; economic applications.

Readings/Bibliography

K. SYDSÆTER, P. HAMMOND, A. STRØM and ANDRÉS CARVAJAL. Essential Mathematics for Economic Analysis, 5th Edition. Pearson, 2016

or:

S. WANER and S.R. COSTENOBLE, Finite Mathematics and Applied Calculus, 8th Edition, Cengage, 2023.

Detailed chapters and sections will be indicated by the instructor.

Teaching methods

Class lectures. During the class lectures, each topic will be illustrated by examples and worked-out exercises.

Assessment methods

Written examination.

The written exam aims at testing the student's ability to understand and effectively apply the concepts and techniques learned in the course to specific mathematical (and economic) problems.

The written exam is based on questions, exercises and problems (of variable level of difficulty) on the course topics. In particular, the written exam consists of:

(a) a set of short routine exercises and questions on basic concepts;

(b) one or two review exercises, or problems on more advanced topics.

A minimum performance level on part (a) must be reached for the exam to be passed (irrespective of the result on part (b)).

Sample exams will be made available on the VIRTUALE platform.

The maximum possible score is 30 cum laude, in case all anwers are correct, complete and formally rigorous.

The grade is graduated as follows:

<18 failed
18-23 sufficient
24-27 good
28-30 very good
30 e lode excellent

 

Grade rejection

Students can reject the (sufficient) grade obtained at the exam once. To this end, students must email a request to the instructor within the date set for registration. The instructor will confirm reception of the request within the same date.

Teaching tools

Slides and graphics tablet. Class slides will be made available on the VIRTUALE platform. However, although class slides are generally very useful, they cannot replace textbooks.

Office hours

See the website of Roberto Dieci