The goal of the Course is to provide students who have an interest in applications of mathematical ideas to Architecture with a compact overview of the tools and technique which are used or are of inspiration in some areas, such as computational design. Knowledge and understanding of mathematical concepts which go beyond what is traditionally taught in basic courses of Architectural Schools are now needed for some sophisticated applications, and this course aims to help students to be aware of and acquire such knowledge, according to their interests

Students are expected to become aware of some key mathematical ideas which are behind technicques used in contemporary architecture. Students are expected to be able to apply such ideas in an investigation of a topic of their interest.

Mathematical tools for descriptive and computational modelling of surfaces will be introduced: n-order Bezier curves and Bezier surfaces, NURBS, Coon patches. Problem of continuity at joinings of curves or surfaces.

Curvature and basic notions about geometry of curves and surfaces.

Application to the derivation of the Euler model for an elastic rod.

Properties of minimal surfaces and their use in some contemporary architectural projects will be investigated, together with some connections to the mechanical properties of membranes.

Tasseletions of the plane will be introduced, with some of their applications in arts and architecture, and their classification into 17 classes through the notion of "symmetry group".

Basic introduction to "fractality" and some connections with Architectural theory, together with "L-systems", for some contemporary applications. Self-similarity, compass and box-counting dimensions and their use in Architecture.

Deformations and Algorithmic manipulation of curves and surfaces. Examples and applications of the modelling software "Grasshopper".

Students will be invited to provide ideas and proposals of topics of their interest where some connections bewteen Architecture and Mathematics are relevant.

The approach of the course will not be strictly mathematical and, in view of this, some software tools typical of modern Architectural Design. In specific recitation sections students will be receive a basic introduction to Grasshopper.

A basic knowledge of Calculus and Linear Algebra is required. Some ideas about curves and surfaces will be useful.

A basic knowledge of Calculus and Linear Algebra is required. Some ideas about curves and surfaces will be useful.

Students will have a choice between:

(1) evaluation based on a project about mathematics applied to Computational Design and Architecture, chosen according to their interests, among the topics suggested by the teacher during the Course. Students will also have the possibility of suggesting fields or themes of their own choice, taken from their previous experience.

(2) a classical oral exam concerning the main topics discussed in the course.