MATHEMATICS
Instructional goals
The course aims to provide first-year economics students with the main
mathematical tools that are used to analyze and solve a wide range of
problems in applied in economics, business, finance and insurance. This
will be their first step towards achieving a broad training in quantitative
disciplines, as well as a good methodological training for the analysis and
critical interpretation of economic and business dynamics. This will allow
them to acquire the useful tools for the formulation, implementation and the support to the decisions in the professional context.
Intended learning outcomes
Knowledge and understanding:
By the end of the course, students will have acquired a wide range of
mathematical tools and will be able to understand and solve numerous
theoretical and applied problems in economics, business and finance.
Ability to apply knowledge and understanding:
By the end of the course, students will be able to apply quantitative tools
to business decisions, to the analysis of economic phenomena and to the
resolution of economic and business problems in the work contexts in
which they will operate.
Autonomy of judgment:
By the end of the course, students will be able to develop a critical
capacity in identifying the most suitable solution to the proposed
problem, even in highly innovative contexts.
Communication skills:
By the end of the course, students will be able to develop communication
skills through written papers and oral interviews and to highlight the
relationships between the theoretical concepts and the most important
economic and managerial applications.
Learning ability:
By the end of the course, students will be able to stay up to date and
improve their skills in examining the quantitative aspects of economics
and management.
Course Contents
The mathematical analysis for functions of a single variable allows the
students to introduce the fundamental mathematical tools (limits,
derivatives, integrals) for the definition and study of the mathematical
models in economics.
The functions of several variables make it possible to develop models
that are closer to economic reality. To this aim, the tools already
introduced for the functions of single variable are suitably adapted to the
new context.
The study of vectors, matrices and linear systems then allows the design
of models capable of including large amounts of data.
The explanation is accompanied by economic examples to illustrate the
importance of the acquired tools in the context of the study program.
Reference Books
Textbook:
(AG): Angelo Guerraggio, Matematica (seconda edizione), Pearson Italia.
Additional material on the website. Learn.luiss.it
Teaching Methods
Teaching will include the following activities:
- In presence and online teaching
- In presence and online exercise sessions
- material for in-depth study available on the learn.luiss.it page of the
course.
The details will be published before the start of the course in accordance
with the most up-to-date anti-covid provisions.
Assessment Method
The exam includes a compulsory written test and an optional oral test.
The written tests are made up of open-ended questions and exercises, divided into several points.
The written test is considered passed with a grade of at least 18/30. The student who does not take the oral test can verbalize a maximum grade of 24. The oral test can confirm, increase or decrease the grade of the written test.
The written test can be replaced by passing two intermediate tests. Each test is considered passed if a grade of at least 18/30 is obtained. The mark for the written test is obtained by taking the arithmetic mean of the marks obtained in the two intermediate tests.
See details on learn.luiss.it - Mathematics course (F)
Thesis assignment criteria
Interview with the teacher after the exam.
Week 1
Introduction to the course. Natural numbers, integers, rationals and reals. Some set theory. Vectors: definitions, operations, geometric representation, vector spaces, linear combination. Dependent and independent vectors, rank. (Chap. 15) Exercise sessions on the topics of the
week and description of economic applications.
Week 2
Matrices: definitions. Determinant, Sarrus rule, algebraic complement and general formula. Minors, rank and characteristic. Matrices operations, inverse matrix. (Chap. 15 and Chap.16). Exercise sessions on the topics of the week and description of economic applications.
Week 3
Linear equations, systems of linear equations, Cramer theorem, Rouchè-Capelli theorem Systems with parameter. (Chap. 16). Exercise sessions on the topics of the week and description of economic applications.
Week 4
The notion of function (Chap. 2) Elementary functions and first properties:
linear, quadratic, hyperbolic, power, exponential, logarithmic and
trigonometric functions (Chap. 3). Exercise sessions on the topics of the
week and description of economic applications.
Week 5
Limit of a function: An informal definition. A unitary (formal) definition,
from the general definition to particular cases. Left and right limit.
Week 6
Sequences and limit of a sequence. (Chap. 5 only Sections 1 and Chap.
6). Exercise session on the topics of the week and description of
economic applications.
Week 7
Continuous functions and the computation of limits (Chap.7) Derivative
of a function: Definition, geometric and economic interpretations.
Computing of the derivative. (Beginning of Chap.8). Exercise session on
the topics of the week and description of economic applications.
Week 8
Differentiability and continuity, higher derivatives (End of Chap.8). Rolle,
Lagrange and Taylor theorems. De l'Hopital's theorem and indeterminate
forms. (Beginning of Chap.9). Exercise session on the topics of the week
and description of economic applications.
Week 9
Search for the maxima and minima of a function. Optimal problems.
Convexity and concavity of a function, inflection points the study of a
function (End of Chap. 9) The anti-derivatives of a function: immediate
and quasi-immediate cases (Beginning of Chap. 10). Exercise sessions on
the topics of the week and description of economic applications.
Week 10
Integration by parts and by substitution (End of Chap.10) The definite
integral: Construction, definition, main properties, existence and
computation (Chap.11). Exercise session on the topics of the week and
description of economic applications.
Week 11
Functions of two variables: Introduction, continuity, partial derivatives
(Beginning of Chap.14). Exercise session on the topics of the week and
description of economic applications.
Week 12
Functions of two variables: Introduction, continuity, partial derivatives
(Beginning of Chap.14). Exercise session on the topics of the week and
description of economic and sustainability applications.