Probability theory 
Probability theory 
Academic year 2019/2020 
Course ID MAT0034 
Teachers 
Year 1st year 
Teaching period First semester 
Type D.M. 270 TAF B  Distinctive 
Credits/Recognition 9 
Course disciplinary sector (SSD) MAT/06  probabilita' e statistica matematica 
Delivery Formal authority 
Language English 
Attendance Mandatory 
Type of examination Written and oral 
Prerequisites An undergrauate level class in Probability and good knowledge of real analysis. Good abilities in elementary probabilistic problem solving are also necessary for the success in this class. 
Propedeutic for Stochastic Processes, Statistics for Stochastic Processes and EDSStochastic Dfferential Equations use concepts and tools introduced in this course. 
Course objectivesTopics taught in this class are essential tools required to a statistician and a probabilist. They are fundamental for any modern mathematician. Students rethink to subjects of their undergraduate studies with a different level of abstraction.This new approach allows them to control some advanced methods of probability theory, useful for applications as wel as for research. 
Results of learning outcomesKnowledge and Understanding Students attain a detailed knowledge of the foundations of modern theory of probability and related topics in measure theory. Applying Knowledge and Understanding Students attain good ability in probabilistic problem solving becoming able to deal both with theoretical and applied problems related with conditional expectation, convergence features, characteristic functions and martingales. Making Judgements and Learning Skills Students become able to prove new results related with the studied theory and to deepen topics by looking at suitable scientific articles and alternative textbooks. Communication Skills Students become able to properly use English and probability to correctly present in written and oral forms their theoretical studies and the results of exercises and homeworks. 
Program

Course deliveryThere will be 72 hours of lessons, including 16 hours of in class exercises. Personal training on assigned exercises is important for the success in this class. 
Learning assessment methodsThe final exam includes both a written and an oral test. The two tests are scheduled on different dates. The written test is valid until the following oral exam. The written test requires the solution of two exercises and the proof of a theorem (selected from those discussed during classes). It is mandatory to pass this test to be admitted to the oral test. Only for the winter session, the written test is reduced to one exercise on martingales and the proof of a theorem if the student has passed the homeworks given during the lessons. The use of textbooks and personal notes during the written test is not allowed. The oral examination includes a discussion on the written test as well as two questions, taken at random by the student. The list of the possible questions for the oral examination will be provided in advance. For the A.Y. 2019/2020 the final grade is determined in the following way: let x = MAX(grade of written exam, grade of oral exam), y = MIN(grade of written exam, grade of oral exam); the final grade is given by z = 0.7*x + 0.3*y and then rounding it to the closest ineteger. 
Support activitiesThe course include exercises classes; extra exercises are suggested as homework. 
Suggested readings and bibliographyTextbooks:
Further suggested books:

NotesAttention: students must register on the exams webpage to be admitted to the written/oral exams (in time). Not registered students will not be admitted being impossible to register their final mark.

Enroll Open 
Enrollment opening date 01/09/2018 at 00:00 
Enrollment closing date 30/06/2019 at 00:00 