69213 - MATHEMATICS FOR SOCIAL SCIENCES

Conoscenze e abilità da conseguire

This course is designed to review students' knowledge of elementary mathematics and to expose them to some of the mathematical concepts and techniques that are required to study mathematical models in the social sciences. Upon completing this course, students should be able to identify, sketch and analyze functions; to solve several types of equations and systems of linear and quadratic inequalities; to know the basic theory of matrix algebra; to explain the concept of a derivative and to differentiate single variable functions using different rules of differentiation.

Contenuti

 

• Linear Algebra: matrix algebra, gaussian elimination, determinants, inverse of a matrix, solutions of a linear system.
• Real function of a real variable: definition, graph of a function, elementary functions, injective and surjective functions, compound functions, invertible function.
• Differentiation: definition, tangent and derivatives, rules for differentiation, higher order derivatives, implicit differentiation, Taylor's formula, De l'Hopital's rule. Concave and Convex functions
• Limits: function's limit definitions, infinitesimal order and infinite order, operations with limits; continuous functions.
• Optimization: local extreme points and global extreme points.
  
• Qualitative analysis of the graphs of simple functions.
• Integrals: definition, integration of elementary functions, integration rules
• Functions of many variables: partial derivatives, level surfaces, linear approximation, differential, unconstrained optimization, constrained optimization (the lagrange multiplier method)
  

During the study of any of the above topics, examples of applications to economics and social sciences problems will be analyzed. 

 

In order to be able to attend the course it is required a basic knowledge in high school mathematics consisting in: polynomials algebra, roots, exponential and logarithmic functions (and related properties), equations and inequalities involving polynomials, roots, exponetials and logarithms.

Testi/Bibliografia

Students notes together with teacher tablet notes class by class uploaded on Virtuale are enough to overcome the exam, obviously provided they are correct and complete.

Lecture notes with lists of exercises for every topic will be provided by the professor.

For further reading it is suggested book:

K. Sydsaeter, P. Hammond, A. Strom "Essential Mathematics for Economic Analysis", Pearson

 

Metodi didattici

Traditional classes using the blackboard or a tablet

Due to the different mathematical backgrounds and knowledge of the students, a crash course is organized before the start of the lectures. Attendance is strongly recommended to all students.

 

Modalità di verifica e valutazione dell'apprendimento

The assessment is made through a written exam.


The full exam is made by a multiple choices quiz and by a part with open exercises. The total maximum score in the written exam is 33 of which at most 18 reacheable in the quiz.


A mid-term written exam is scheduled between the two sub-cycles based on around half of the program. Students that achieve a score of at least 15 out of 33, can take a final exam focused on the topics of the second part of the course: the final exam is scheduled simultaneously to the full exams sessions in January and February calls. Mid-term and final exams are made of a multiple choices quiz and open exercises too and the final grade is given by the arithmetic average of the two single scores.

Moreover,

- the final exam can be taken only once and as first with respect to the full exam. More precisely, if a student sits the full exam, the midterm grade expires and he will never be allowed to sit the final.
- if a student sits the final on the first call and he fails (or he refuses the grade), he is not allowed to sit the final on the second chance and he will necessarity sit the full exam.
- if a students skips the first call, he is allowed to take or the final or the full exam on the second call.
- on summer call, it is possible to sit only the full exam.

Strumenti a supporto della didattica

Blackboard and tablet

Orario di ricevimento

Consulta il sito web di Sabrina Mulinacci