69213 - MATHEMATICS FOR SOCIAL SCIENCES

Learning outcomes

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.

Course contents

• 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.

Readings/Bibliography

Some lecture notes will be provided by the professor on specific topics and with exercises. However all topics can be found in the book

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

Teaching methods

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 for all students.

Traditional classes using the blackboard or a tablet

Assessment methods

Mandatory written exams and optional oral exams.

The written 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.

Oral is optional and students with at least 16 out of 33 are admitted.

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 integrate the exam with a second written exam focused on the topics of the second part of the course in occasion of the first exam session after the end of the course and the final grade is the arithmetic average of the two single scores.

Teaching tools

Blackboard and tablet

Office hours

See the website of Sabrina Mulinacci