MATHEMATICS FOR MODELLING IN MANAGEMENT
- Academic year
- 2024/2025 Syllabus of previous years
- Official course title
- MATHEMATICS FOR MODELLING IN MANAGEMENT
- Course code
- PHD168 (AF:530386 AR:298709)
- Modality
- On campus classes
- ECTS credits
- 6
- Degree level
- Corso di Dottorato (D.M.45)
- Educational sector code
- SECS-S/06
- Period
- 1st Term
- Course year
- 1
- Where
- VENEZIA
Contribution of the course to the overall degree programme goals
This course 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.
The course will be accompanied by a Python lab/exercise session through which the theoretical knowledge acquired in the lessons will be put into practice.
Expected learning outcomes
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.
Students will be able to analyze the characteristics of simple agent networks using Python and calculate appropriate metrics.
Pre-requirements
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
Contents
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
Referral texts
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.
Assessment methods
The written exam consists in a set of problems (exercises) related to the program seen in class and in some theoretical questions. Mock-ups will be provided to students during the course. The structure of the ongoing activities will be discussed at the beginning of the course.
Regarding the grading scale (how grades will be assigned):
A. Scores in the range of 18-22 will be awarded for:
- sufficient knowledge and applied understanding of the program;
- sufficient ability to solve the proposed problems;
- limited ability to explain the mathematical procedures underlying the solution of the proposed exercises;
- limited ability to use the software Python to analyze networks.
B. Scores in the range of 23-26 will be awarded for:
- fair knowledge and applied understanding of the program;
- fair ability to solve the proposed problems;
- fair ability to explain the mathematical procedures underlying the solution of the proposed exercises;
- fair ability to use the software Python to analyze networks.
C. Scores in the range of 27-30 will be awarded for:
- good or excellent knowledge and applied understanding of the program;
- good or excellent ability to solve the proposed problems;
- good or excellent ability to explain the mathematical procedures underlying the solution of the proposed exercises;
- good or excellent ability to use the software Python to analyze networks.
D. Honors will be awarded for:
- excellent knowledge and applied understanding of the program, and an outstanding ability to present and explain the solution of the exercises and in the use of Python.
Teaching methods
Further information
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.