Course 2024-2025 a.y.

30672 - QUANTITATIVE METHODS FOR SOCIAL SCIENCES (MODULE I - MATHEMATICS FOR SOCIAL SCIENCES)

Department of Decision Sciences

Course taught in English
Go to class group/s: 45
BIG (6 credits - I sem. - OB  |  SECS-S/01)
Course Director:
FRANCESCA BECCACECE

Classes: 45 (I sem.)
Instructors:
Class 45: FRANCESCA BECCACECE


Mission & Content Summary

MISSION

Political and Social Science traditionally lies at the intersection of some disciplines which all require mathematical skills, both the knowledge of mathematical concepts and the development of rigorous thinking. Advanced quantitative models are used to analyze socio-political scenarios, and interpret the evolution of social, economic and political systems. Theoretical models are adopted to describe dynamics in political choices. Merging Social Science with Data Science expand the toolkit in mathematical skills needed to lay solid foundations for deep knowledge. The course has a twofold purpose. It provides the mathematical tools to build up and analyze the quantitative models used in Social Sciences from one hand, and it pays a particular attention to basic mathematics for Data Science, from the other.

CONTENT SUMMARY

  • One-variable functions. Bounded functions. Monotonicity and convexity. Maxima and minima. Continuity.
  • Differential calculus of one-variable functions. First and second order derivatives. Differentiability. Optimization. Plotting the graph of a one-variable function.
  • Indefinite integral. Definitive integral. Properties and applications. Integration by substitution and by parts.
  • Probability. Definitions and properties. Elements of combinatorics. Conditional, marginal and joint probability. Bayes' rule.
  • Discrete and continuous random variables. Probability distribution function and cumulative distribution function.
  • Linear Algebra. Vectors and matrices. Algebra of vectors and matrices. Square matrices: determinant, inverse matrix. Linear systems. Eigenvalues and eigenvectors.
  • Differential calculus of two-variable functions. Quadratic forms. Optimization.

Intended Learning Outcomes (ILO)

KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Describe mathematical formulae rigorously.
  • Explain in detail some mathematical topics through definitions and theorems.
  • Develop rigorous thinking: specification of hypothesis, their testing and discussion of results 
  • Acquire a deep knowledge of mathematical structures usually used in Data Science

APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course student will be able to...
  • Use selected basic computational techniques (derivatives, integrals, determinant).
  • Justify the use of the acquired mathematical tools for solving specific problems.
  • Construct models requiring the knowledge of probability theory

Teaching methods

  • Lectures
  • Practical Exercises

DETAILS

Teaching methods include lecture-based classes focusing on the solution of exercises requiring the concepts illustrated during the course. In-class exercises encourage the students' active participation.


Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
   x x

ATTENDING AND NOT ATTENDING STUDENTS

The exam can be taken in two alternative modalities:

  • Two partial written exams, both composed by open-answers questions. The final mark will be the average of the points gained with the two partial exams.
  • A general written exam, composed by open-answers questions.

The partial exams and the general exam are composed by the same kind of questions.

All types of questions contribute to the assessment of the students’ acquired knowledge.

The variety of questions composing the exams aims at verifying:

  • the students’ knowledge of specific properties of mathematical objects.
  • The students’ ability to identify and implement the learnt calculation techniques in several topics.
  • The students’ skills to face and solve complex problems by means of the acquired mathematical tools.

Teaching materials


ATTENDING AND NOT ATTENDING STUDENTS

Adopted textbooks

 

  • SYDSAETER K., HAMMOND P., STROM A., CARVAJAL A., Essential Mathematics  for Economic Anaysis, 2021, Pearson.
  • IMAI K., Quantitative Social Science: An introduction, 2018, Princeton University Press.

 

 

Suggested Textbook

  • MOORE W.H., SIEGEL D.A., A Mathematics Course for Political and Social Research, 2013, Princeton Univerisity Press.

 

Last change 18/05/2024 18:07