CODE 42916 ACADEMIC YEAR 2016/2017 CREDITS 7 cfu anno 1 MATEMATICA 9011 (LM-40) - 7 cfu anno 2 MATEMATICA 9011 (LM-40) - SCIENTIFIC DISCIPLINARY SECTOR MAT/08 LANGUAGE Italiano (Inglese a richiesta) TEACHING LOCATION SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW The credits for the course Application of Mathematics to Medicine (AMM, code 42916) are 7. The course is held during the first semester of the 1°, 2° LM years. On request of one student, the lectures and teaching activities will be delivered in English, otherwise in Italian. AIMS AND CONTENT LEARNING OUTCOMES (FURTHER INFO) This course aims to describe the mathematical modeling of three medical imaging problems: the X-ray tomography, the Positron Emission Tomography and the Magnetic Resonance Imaging. The scope of the course is two-fold: on one hand, we want to highlight how sophisticated mathematics is needed for the comprehension of problems with high practical significance; on the other hand, we want to equip the students with the numerical analysis tools required for the processing of the data acquired with these three modalities. TEACHING METHODS Traditional lectures. Six lab lessons are planned SYLLABUS/CONTENT Part I: X-ray tomography (overview); Radon transform, formulas for the inversion of the Radon transform (as back projection and filtered back projection), issues of uniqueness. Part II: positron emission tomography (overview); on the two inverse problems related to positron emission tomography: an imaging problem (inversion of the Radon transform) and a compartment alone (Gauss-Newton optimization scheme) Part III: magnetic resonance imaging (overview); models for data acquisition and magnetic field distortion, Fourier transform, inversion of the Fourier transform from undersampled data. RECOMMENDED READING/BIBLIOGRAPHY Professor’s lecture notes TEACHERS AND EXAM BOARD MICHELE PIANA Ricevimento: Office hours by appointment via email CRISTINA CAMPI Ricevimento: Office hours by appointment via email Exam Board MICHELE PIANA (President) CRISTINA CAMPI Anna Maria MASSONE LESSONS LESSONS START September 26, 2016 Class schedule APPLICATIONS OF MATHEMATICS TO MEDICINE EXAMS EXAM DESCRIPTION Oral Exam Exam schedule Data appello Orario Luogo Degree type Note 05/06/2017 09:00 GENOVA Orale 05/06/2017 09:00 GENOVA Scritto 23/06/2017 09:00 GENOVA Orale 23/06/2017 09:00 GENOVA Scritto 30/06/2017 12:40 GENOVA Orale 12/07/2017 09:00 GENOVA Orale 12/07/2017 09:00 GENOVA Scritto 01/08/2017 09:30 GENOVA Orale 04/09/2017 09:00 GENOVA Orale 04/09/2017 09:00 GENOVA Scritto FURTHER INFORMATION The prerequisites are: Hilbert spaces, continuous linear operators between Hilbert spaces, Fourier analysis