MATHEMATICS FOR MODELLING IN MANAGEMENT

Modern societies and organizations have become more complex: physical, personal and informational linkages strongly affect managerial activities in several applicative contexts. This new framework deserves adequate quantitative tools to be properly analyzed. This course will provide PhD students in Management with the basic concepts behind the idea of network, the main measurement tools and techniques needed to analyze information flows in network structures.

This program addresses some classical and more recent advances in the context of network theory. We will analyze the main social network structures, their properties and the basic tools of mathematics of networks. Finally, we will study how information, innovation and opinions spread through networks due to social interactions.

This course is also intended to teach students the tools of the Python programming language for the execution of studies and analysis of Network Studies.

At the end of the course, the student will have acquired knowledges about the basic mathematical tools to deal with networks and social networks, the main measures and metrics related to networks, the concept of centrality and “importance” and their consequence for management studies (for example, the role of hubs and influencers). He/she will learn how to model diffusion of information on networks with applications to opinion dynamics, consensus formation and advice networks.

Thanks to the laboratory activity in Python, students will be able to independently develop basic software, design data collection processes, and infer information from data to discuss relevant case studies.

Students will be able to critically read, analyze, present and discuss academic papers related to the applications of network theory in the field of management.

We expect that students enrolled in the PhD in Management at Ca’ Foscari University already possess basic knowledge of mathematics and statistics. The following is a list of notions that students enrolling in the PhD in Management at Ca’ Foscari University should be familiar with before starting the PhD courses. Knowledge of these concepts could be assessed during the interview.


Mathematics

• Number sets - Powers and their properties - Logarithms and their properties - Equations – Inequalities
• The notion of real function - Graphs of functions – Linear and quadratic functions – Logarithmic and exponential functions
• Derivatives - Rates of change - Increasing/decreasing functions – Convexity and concavity
• Rules for differentiation - Maxima/Minima
• Indefinite integrals - Definite integrals - Improper integrals
• Basics of matrix algebra


Suggested reference:
K. Sydsaeter, P. Hammond and A. Strom (2016). Essential Mathematics for Economic Analysis (V edition), Pearson. Chapters 1-9.

Statistics

• Basic notions of probability theory
• Mean, median, variance , standard deviation
• Hypothesis testing
• Correlation (e.g., how to interpret a correlation coefficient)
• Linear Regression (e.g., how to interpret a regression coefficient)
• Types of variables (e.g., continuous, ordinal, categorical, dummy)
• Basic familiarity with computers and productivity software, like excel

Suggested reference:
OpenStax (2013). Introductory Statistics. Rice University. Free download of the pdf at: https://d3bxy9euw4e147.cloudfront.net/oscms-prodcms/media/documents/IntroductoryStatistics-OP_LXn0jei.pdf

0. Refresher in linear algebra, calculus and probability theory.
1. Networks and social networks. Examples and applications
2. The mathematics of networks 1 (adjacency matrices, degree, connectivity)
3. The mathematics of networks 2 (components, paths and degree distribution)
4. Metrics and measures (centrality, similarity): hubs and influencers
5. The mean field approximation (from the Bass ’69 model to the new media)
6. Diffusions on networks and social interactions – SIR and SIS models
7. Random walks on graphs. The De Groot model for consensus
8. Opinion leaders and social influence: an application to advice networks

Python Laboratory:
i. Getting used to Python’s main objects (managing variables, loops and ifelse decision trees)
ii. Creation and management of vectors and matrices on Python
iii. Creation and management of DataFrames and Dictionaries
iv. Creation and management of Network Objects through vectors and ad hoc modules (NetworkX)
v. Visualisation of Network objects, reasoning and methods
vi. Calculation of Network metrics
vii. Statistical Analysis with Python and data visualization
viii. Thorough knowledge with common modules (networkX; MatPlotLib; NumPy; Sci-Kit Learn; Pandas)

Jackson, M. O. Social and economic networks. Princeton University Press, 2010. [Ch. 1-3, 7-9]
Newman, M. Networks: an introduction. Oxford University Press, Second Edition, 2018. [Ch. 1-3, 6-8, 17]
Supplementary material and discussion papers will be provided by the instructor.

The evaluation is based on a written exam, a Python project, and an oral discussion. The written exam consists of a series of problems (exercises) related to the topics covered in class and some theoretical questions. Mockups will be provided to students during the course. The Python project will be based on the topics covered during the laboratory hours and will be discussed with the instructors during an oral exam.

Regarding the grading scale (criteria for assigning grades):

A. Scores in the range of 18-22 will be awarded for:
- Sufficient knowledge and applied comprehension of the course material;
- Sufficient ability to solve the given problems;
- Sufficient proficiency in using Python;
- Limited ability to explain the mathematical processes underlying the solutions of the proposed problems.

B. Scores in the range of 23-26 will be awarded for:
- Fair knowledge and applied comprehension of the course material;
- Fair ability to solve the given problems;
- Fair proficiency in using Python;
- Fair ability to explain the mathematical processes underlying the solutions of the proposed problems.

C. Scores in the range of 27-30 will be awarded for:
- Good or excellent knowledge and applied comprehension of the course material;
- Good or excellent ability to solve the given problems;
- Good or excellent proficiency in using Python;
- Good or excellent ability to explain the mathematical processes underlying the solutions of the proposed problems.

D. Honors will be awarded for:
- Outstanding knowledge and applied comprehension of the course material;
- Excellent ability to solve the given problems;
- Exceptional proficiency in using Python;
- Excellent ability to present and explain the solutions to the proposed problems.

Theoretical concepts and applications will be presented through standard (or in distance) classes. When needed, the analysis of theory and applications will be supported by the use of dedicated software. The Python classes are hands-on laboratory sessions. Students will be encouraged to read, analyze and, finally, discuss in class some academic papers.

Accessibility, Disability and Inclusion.

Accommodation and support services for students with disabilities and students with specific learning impairments Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding support services and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). If you have a disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

written and oral