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, together with elementary and introductory ideas associated with mechanical properties of membranes. Ideas and properties of minimal surfaces and their use in some contemporary projects will be investigated.

Moreover, tasseletions of the plane will be introduced, with their applications in arts and architecture, and their classification through the notion of "symmetry group". Students will be invited to search for appropriate examples among the monuments and builidings in the Milan region.

The idea of "fractality" is of some importance, together with the related notion of "L-systems", for some contemporary applications.

The approach of the course will not be strictly mathematical and, in view of this, some software tools typical of modern Architectural Design will be used.

Main Topics:

Curves. Curvature. Bezier Curves. Torsion and curvature. Mean and total curvature of a surface and their properties. Algorithms for the creation of parametric curves and surfaces. Freeform Surfaces. NURBS. Mechanics of membranes and minimal surfaces. Fractal sets and L-systems. Deformations and Algorithmic manipulation of curves and surfaces. Examples and applications of the modelling software "Grasshopper"

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

Evaluation and grading will be based on a project of mathematics applied to Computational Design and Architecture, chosen by the students 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.