Geometry 3

A.Y. 2021/2022
Overall hours
Learning objectives
The course aimt at providing the basic notions on topological structures, also useful in the study of Geometry and Analysis.
Expected learning outcomes
Improving of the logical-deductive skills, of the ability to abstract and of the flexibility in facing mathematical problems. Ability to solve specific exercises on the topics presented during the class.
Course syllabus and organization

Single session

Lesson period
First semester
More specific information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation.
Course syllabus
Topological spaces: definitions, examples and properties.
Continuous functions; omeomorphisms.
Induced topology and product topology. Quotient topology.
Separation axioms.
Connectedness; path connectedness.
Complements of general topology.
Introduction to homotopy theory.
Prerequisites for admission
Basic knowledge of Algebra, Linear Algebra and Analysis (suggested courses: Geometria 1, Geometria 2, Analysis 1)
Teaching methods
Classroom lessons (36 hours lessons, 24 hours exercises sessions; a tutoring is also provided).
Teaching Resources
Suggested textbooks:
M.Manetti, Topologia (seconda edizione), Springer,
E.Sernesi, Geometria 2, Bollati Boringhieri,
Assessment methods and Criteria
The final examination consists of two parts, a written exam and an oral exam.
During the written exam, the student must solve some exercises analogous to those presented during the exercises sessions, with the aim of assessing the student's ability to solve problems in topology.
During the semester there will be a partial written examination and a second one will take place on the day of the first complete written examination.
The oral exam can be taken only if the written component has been successfully passed. The oral exam will be an interview on the topics of the course.
MAT/03 - GEOMETRY - University credits: 6
Practicals: 24 hours
Lessons: 36 hours
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