English

This course is designed to equip students with a comprehensive understanding of fundamental ecology principles, their practical applications, and how the concepts relate to the real world with examples from published scientific studies. Ecology is introduced at its different levels of organization, including organism-environment (biotic-abiotic) interactions, adaptations of plants and animals, the characteristics of populations as a basic biological unit in an ecosystem, intra and inter-specific interactions, community ecology, and ecosystem ecology. Students develop critical thinking and analytical skills by interpreting ecological data and applying theoretical knowledge to real-life scenarios. By the end of the course, students have a solid foundation in ecological principles, preparing them for further study or careers in conservation, environmental science, scientific research, and related fields.

This subject explores traditional and contemporary relationships between tangata whenua and the urban environment in Aotearoa New Zealand. It examines how Māori worldviews shape urban planning practice, with a focus on the impact of Treaty of Waitangi settlements. Key topics include Indigenous development, governance, and resource management, as well as the responsiveness of planning processes to Māori values and aspirations.

This course explores the concept of equality through the lens of analytic philosophy, applying normative theories to pressing global ethical issues. The first part of the course engages in conceptual analysis of equality, examining key debates in distributive justice, structural injustice, and recognition theory. The second part of the course applies these theoretical foundations to real-world ethical challenges, including climate justice, post-colonialism, minority rights, war and conflict, migration, and human rights. Students are evaluated on their ability to mobilize normative concepts in their discussion of the problems and solutions particular to the global sphere.

This course embraces documentary film to approach the history of Taiwan. Due to rapidly changing regimes of rule and a contentious geopolitical status, the people living on this island continue to grapple with multiple layers of coloniality, ways of healing from historical trauma, and expressions of identity. The development of documentary film-making in Taiwan is uniquely connected with the democratic movements against authoritarianism and the ethics of representing marginal voices and suppressed memories. Moreover, many directors have utilized cross-overs of film genre and the performing arts to illuminate certain “truths” unreachable through traditional documentary evidence.  

This course focuses on the ways that documentary (and fiction) filmmakers based in Taiwan use music, sound, and the performing arts as both subject and resource to shape narratives of Taiwan. In turn, the class focuses on Taiwanese documentary film to expand their understanding of the potentials and pitfalls of documentary film in the 21st century, especially through experiencing its creative uses of sounds and performances.

This course covers the fundamental concepts of databases—an essential component in implementing e-business information systems—including the entity-relationship model, relational databases, and the use of structured query language (SQL). Through individual projects, students also explore how to integrate databases with business information systems. Topics include Introduction to Database Industrial Information Management, Introduction to Structured Query Language (SQL), Relational model and normalization, Database design using normalization, Data modelling with the entity-relationship model, Transforming data models into a database design, SQL for database construction and application processing, Database redesign, Managing multi-user databases, Web Server Environment, and Data warehouses, business intelligent systems, and big data. 

This course examines venture capital and private equity investments. In particular, it focuses on issues surrounding the funding of entrepreneurial firms that are financed by venture capital or private equity funds. The course departs from conventional investment approaches that examine risk and return of publicly listed securities and analyzes issues associated with financing growing, innovation intensive private businesses.

This course introduces the basic principles and techniques in genetics (in the context of oncology), to develop basic competences in the planning and performance of experiments and the evaluation of results, as well as writing reports. The course consists of 6 sessions of approx. 4 hours and covers topics such as DNA isolation/purification, gel electrophoresis, staining procedures, protein detection, and basic bioinformatics (commonly used databases, finding the genetic location of a specific gene and its gene sequences, design amplification primers for a specific genetic region, etc) using online available tools. Furthermore, this course provides basic knowledge on Good Laboratory Practice (GLP) and Laboratory Safety Regulations. Besides the hands-on time in the lab, each session requires preparation beforehand and reporting afterwards. Students work in pairs. Lab experience is not required, although biological and chemical background knowledge at secondary school level is recommendable for full understanding of the provided techniques. If necessary, in the first lab session, pipetting skills will be trained or refreshed. This course is designed to be taken in combination with SCI2022 Genetics and Evolution. Students who wish to take this course should concurrently enroll in SCI2022 Genetics and Evolution or have taken SCI2022 Genetics and Evolution before. 

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrollment is by permission of the instructor. This course covers the theoretical understanding and working knowledge of the principal gravitational phenomena determining the structure, the dynamics and the evolution of stellar systems, from open and globular clusters, to galaxies, to galaxy clusters. At the end of the course, the student is able to use in autonomy some of the advanced mathematical techniques needed in potential theory and in epicyclic theory. The course content is divided into 2 parts:

1. GENERALS

Gravitational field of point particles, principle of superposition. Integral representation for any distributions. Most important properties of the divergence operator and its coordinate-free representation starting from Gauss's Theorem. Operational introduction to the one-dimensional and multidimensional Dirac Delta in Cartesian and curvilinear coordinates. Calculation of the divergence of the field of extended distributions, Poisson's equation for the field. Direct proof of the First and Second Newton's theorem (homogeneous spherical shells). Alternative demonstration using Gauss's theorem. Coordinate-free representation of the gradient, curl, and Laplacian operators. Notes on differential forms. Exact fields and their properties, potential and work. Closed fields. Stokes' theorem, closed fields in simply and non-simply connected domains. Existence of the potential and its connection with the total energy of a particle. Potential difference as a line integral. Formal calculation of the potential of a point mass. Potential of extended distributions, general expression and discussion of the meaning of the additive constant. Poisson and Laplace equations. First and second Green's identities, uniqueness of the solution of the Poisson equation in bounded volumes with prescribed boundary conditions. Field inside cavities with equipotential boundary. Helmholtz Decomposition Theorem. Definition of concentric and similar ellipsoids. Definition of homoeoid. Statement of the Third Newton's Theorem for finite homoeoids. Field inside a heterogeneous hollow homoeoid from the principle of superposition. Co-area theorem, relationship with the field of homoeoids. Definition of confocal ellipsoidal coordinates. Classification of the three families of associated quadrics. Ellipsoidal coordinates: orthogonality, gradient, Laplacian. Application to the problem of the ellipsoidal layer with zero internal field. Potential of the heterogeneous ellipsoid. Chandrasekhar's formula. Introduction to the multipole expansion of potential in the far field. Monopole, dipole and quadrupole terms.

Introduction to the concept of Green's function for linear differential operators and their use in solving nonhomogeneous problems. The potential of a material point as an explicit example of a Green's function for the Laplacian. Separation of variables for the Laplacian in Cartesian coordinates. Fourier transform and inverse transform in Rn, the case of the Dirac Delta. Green's function in Cartesian coordinates. Green's function in spherical coordinates. Separation of variables. Rotational invariance and the azimuthal quantum number m. Orthogonality of azimuthal functions. Associated Legendre equation for the latitude angle, transformation into an algebraic equation. Outline with examples of singularities of ODEs, both mobile and fixed. Fuchs' theorem, regular points, regular singularities, and essential singularities. Classification for the Legendre equation. Frobenius method and polar quantum number. Legendre functions and associated functions P and Q. Legendre polynomials. Rodrigues formulas, norm of associated polynomials. Orthogonality of solutions with Sturm-Liouville theory. Spherical harmonics as eigenfunctions of the angular part of the Laplacian. Systems with cylindrical symmetry. Generating function for Legendre polynomials, multipole moments. Gegenbauer polynomials. Addition theorem for spherical harmonics. Separation of variables for the vacuum solution of the Laplacian in cylindrical coordinates. Bessel equation and its properties: orthogonality of solutions, singular points. Asymptotic analysis of Bessel functions for large values of the argument. Closure relation and Hankel transform. Green's function in cylindrical coordinates for the Laplacian. Any density potential with Fourier-Bessel transforms. Case of axisymmetric systems. Infinitely thin axisymmetric disks, potential in the plane of the disk, homogeneous rings. Thin disk rotation curve. Mestel's disc and exponential, implications for the dark matter halos. Potential of axisymmetric systems using elliptical integrals.

2. COLLISIONLESS SYSTEMS

Introduction to the epicyclic approximation. Notes on curvilinear coordinates, velocity and acceleration in cylindrical coordinates. Newtonian equations of motion in general axisymmetric potentials, conservation of energy and Jz. Deduction of equations from the Euler-Lagrange equations. The meridional plane, its motion, and effective potential. Equations of motion in the meridional plane, orbital families, circular orbits and their (equivalent) equations. Interpretation of total energy as energy for motion in the meridional plane, extremum properties for the energy of circular orbits, centrifugal barrier, zero-velocity curves. Development of the effective potential to second order. Frequency of vertical and radial epicycles. Radial and vertical motion on the epicycle in the case of stable orbits, zero-velocity ellipses. Rayleigh criterion and examples of applications. First-order angular motion, coordinates on the equatorial plane referred to the deferent, equation of the epicycle on the equatorial plane, and determination of the axes for the epicyclic ellipse. Epicycles in Coulomb, harmonic, and flat rotation potentials: frequency and shape. Relation of Oort constants to the radial epicyclic frequency. Closed, rosette, and open orbits: closure conditions, pattern angular velocity, Lindblad kinetic waves, and the dynamical phenomenology of disks.

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrollment is by permission of the instructor. This advanced course focuses on the main theoretical approaches to promote well-being across the life-span, tools for assessing the quality of life and psychological well-being in children and adults with typical and atypical development, and interventions aimed at improving well-being in developmental and learning contexts. 

The course presents theories, methods, and assessment and intervention tools to promote wellbeing, quality of life and learning in a development and education perspective in the lifecycle. The course involves the following integrated and complementary modules:

The first module is designed to provide the principal theoretical approach of the course concerning the wellbeing promotion in children, students, youth, and adults. The module also explores the role of technologies in human development, by considering both their functional use to develop knowledge, skills and their dysfunctional effects on lifecycle development.

The second module provides an advanced theoretical and empirical approach to understand the developmental and educational consequences of social stigma on children’s health, quality of life and psycho-social well-being, and cognitive functioning. Evidence-based interventions to reduce stigma and its consequences in educational settings are illustrated.