Mathematics

General objectives Addressing the study of varied mathematical content, favoring an "extensive" approach that highlights the links between content and other parts of mathematics and science, with particular attention to the historical evolution of concepts and their placement in a cultural frame that may help the future mathematics teacher to integrate the educational role of teaching mathematics more closely with that of other subjects. Specific objectives Knowledge and understanding: At the end of the course, students who have passed the exam will have the basic knowledge and methodological tools to place mathematics teaching in a wider cultural context that enriches its educational value. Apply knowledge and understanding: At the end of the course, students who have passed the exam will be able to face the reading and understanding of the general parts of mathematical articles of historical and cultural relevance, in particular of the nineteenth century (in one of the foreign languages ​​known to the student or in the translation into Italian) and to compare the methods used by their authors with those of contemporary mathematics which they learned about during their three-year degree studies. They will be able to appreciate the didactic value of a historical approach to mathematics and to apply it to the planning of didactic teaching paths in the school. They will have developed a critical and informed attitude towards the applications of mathematics to social sciences and the modeling of complex systems. Critical and judgmental skills: The student will receive the necessary bases to appreciate the historical development of the main concepts relating to the foundations of non-Euclidean geometry, differential and projective geometry, the idea of ​​function and the calculation of probabilities and the relationships between the topics covered in this course and those covered in other courses (of the three-year degree, in particular the History of Mathematics course, and of the master's degree, such as the course of Elementary Mathematics from a higher point of view and that of Fundamentals of Mathematics, Real Analysis and Differential Geometry). Communication skills: Ability to expose the contents in the oral part of the verification and to summarize the knowledge acquired in the development of the topic proposed in the written test. Particular attention will be devoted to developing the ability to communicate correctly, even if incomplete, a non-elementary mathematical content by relying on digital tools, heuristic analogies, examples and significant and illuminating exercises and to critically address the siege of available information. online or in libraries. Learning ability: the knowledge acquired will allow the student to develop a critical attitude, attentive to the historical and conceptual development, of mathematical ideas and their cultural value, also in relation to the other sciences and society.