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.

 

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

Readings/Bibliography

Lecture notes covering all the contents of the course are available on Virtuale.

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

For further reading:

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

 

Teaching methods

Traditional classes using the blackboard or a tablet

 

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

 

Assessment methods

The assessment is made through a written exam.


The full exam is made by a multiple choices quiz covering all the topics of the course program.

A mid-term written exam is scheduled between the two sub-cycles based on about 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. Students that obtain a score lower that 15 out of 33 must take the full exam, based on the entire program. The final exam is scheduled simultaneously to the first two full winter exams. Mid-term, final and full exams are made of a multiple choices quiz. In case of mid-term+final exams, 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 anymore.
- if a student sits the final exam 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 necessarily 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 the third winter call and on the summer call, it is possible to sit only the full exam.

 

With regard to assessment, the use of AI is prohibited. Any use of AI constitutes a violation of academic integrity.

Students may freely decide to repeat the written test, even if they have passed the exam.

Students with specific learning disabilities (SLDs) or temporary or permanent disabilities are advised to contact the relevant University office well in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). The office will propose appropriate accommodations to the students concerned. These accommodations must, in any case, be submitted to the course instructor for approval at least 15 days in advance. The instructor will assess their suitability, also in relation to the learning objectives of the course.

 

 

Teaching tools

Blackboard and tablet

Office hours

See the website of Sabrina Mulinacci