21010265-3 - MATHEMATICAL AND STATISTICAL METHODS

The objectives of the individual module help to define the set of objectives of the entire course.
The workshop proposes design experimentation starting from the confrontation with some of the issues that characterise urban design today: the question of space, destruction, density, the identification of the resources indispensable to change and the agents that can produce it. The workshop will transmit technical knowledge from the perspective of looking at places as a reinvention of what surrounds us, innovating the operational and cultural schemes that contribute to defining the posture of the town planning architect. Students will configure the design proposal by reasoning, during the different transitions that characterise our time, on the possible transformative actions and confronting the complex governance of the factors that build the city.
teacher profile | teaching materials

Programme

● Sampling Data
○ Data Collection
○ Means and Standard Deviation
○ Percentiles
○ Curve Fitting
○ Variability and Inequality of Distributions
○ Lorenz Curve
○ Gini Coefficient
● Probability and Combinatorics
○ Random Variables and Discrete Distributions
○ Conditional Probability
○ Bayes' Theorem
○ Gaussian Distribution
○ Power and Exponential Distributions
○ Central Limit Theorem
● Statistical Inference
○ Null Models, z-scores, p-values
○ Chi-Square Test
○ Introduction to Machine Learning
● Graph Theory
○ Graph Representations, Adjacency Matrices
○ Paths on Graphs
○ Clustering, Measures of Centrality
○ Planar Graphs
○ Space Syntax (Introduction)
● Workshops and Seminars
○ Open, Georeferenced, Mobility Data. Analysis and Visualization Software
○ Urban Networks
○ Measuring Space and Time
○ Technology and the City: Why the Ideal City Changes Over Time
○ Population Density: The Healthy vs. Sustainable City Dilemma
○ What-if Scenarios and Twin-Cities
○ The Complex System of Cities

Core Documentation

Statistics:
Statistics for the Social Sciences. R . Mark Sirkin

Graph Theory:
Network Science. Albert-Laszlo Barabasi
Scale-free networks: complex webs in nature and technology. Guido Caldarelli

Urban data science:
Introduction to Space Syntax in Urban Studies. Akkelies van Nes, Claudia Yamu
The Statistical Physics of Cities. Marc Barthelemy (Review)

Attendance

Classes will be held in person, combining theoretical lessons and practical laboratory sessions. Active participation of students is required.

Type of evaluation

Written exam or project, to be assessed