– analysis: real and complex numbers, functions, limits, derivatives, integrals
– algebra: vectors, matrices, linear systems
– numerical analysis: methods for linear systems, Newton method, interpolation.
The presentation modalities and the course structure itself allow attendance and learning also for those who possibly do not possess some of the above requisites.
– laboratory activities and exercises on learning and using mathematical software
– possible seminars on specific arguments.
– laboratory project of computational character, on a subject to be arranged with the lecturer, accompanied by a brief written essay including a brief theoretical description of the problem, of the targets of the project and of what done and obtained;
– oral discussion on the developed activities and on the course program, with questions on both theory and applications, and exercises on computational problems.
– teaching language: Italian (the course can be taught in English on proposal of the competent didactic structure)
– the arguments proposed for the project can be related to the final thesis for what concerns the possible computational aspects
– the course notes, written by the lecturer in English, are complete and self-contained relatively to the program, and include laboratory activities and relevant codes.
The student will have to:
Knowledge and comprehension:
– know the basic aspects of the mutual interaction between mathematics and computer
– understand the class of mathematical problems in which the model resides
– learn the guidelines to translate the mathematical problem into a computable one
Capacity of applying knowledge and comprehension:
– develop skills in self-learning general mathematical software
– know how to select the mathematical software best suited to the solution of the problem and to program the relevant codes for obtaining the solution itself
Autonomy of judgement:
– be able to analyze in a critical and autonomous manner computer results in relation with theoretical expectation
– know how to illustrate the computational processes in a clear and comprehensible fashion
– know how to represent effectively the computational results
– know how to tackle critically and autonomously mathematical problems with computational techniques
– nonlinear equations and Newton method (application proposal: Newton fractals);
– matrices and linear systems (application proposal: Google’s PageRank);
– differential equations and dynamical systems (application proposal: bifurcation analysis and chaos);
– approximation of data and functions (application proposal: FFT and JPEG compression).
The treated arguments will thus furnish an occasion to tackle some of the issues concerning the interaction with a computing system and its potentialities/limitations with respect to the study of mathematical problems: representation of mathematical objects and their manipulation, problem solving and simulation of models, data management.