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B005492 - GEOMETRY II
Main information
Course Content
Learning Objectives
Prerequisites
Teaching Methods
Further information
Course program
Academic Year 2014-15
Coorte 2013 - 3-years First Cycle Degree (DM 270/04) in MATHEMATICS
Course year
Second year - Annualità singola
Belonging Department
Mathematics and Computer Science "Ulisse Dini" (DIMAI)
Course Type
Single education field course
Scientific Area
MAT/03 - GEOMETRY
Credits
12
Teaching Hours
116
Teaching Term
22/09/2014 ⇒ 12/06/2015
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Course Content
Topological space. Continuous application. Subspaces, products and quotients of topological spaces. Homeomorphisms. Hausdorff spaces. Connected spaces. Compact spaces. Complete metric spaces. Differential geometry of curves and surfaces.
Learning Objectives
Knowledge acquired:
The course is focused on topology, metric space, Non-differentiable curve and surface. Exercises and applications will be illustrated.
Competence acquired: Basic notions of General Topology, Metric Spaces and classical Differential Geometry
Skills acquired (at the end of the course): Ability to use the foundamental notions of General Topology and Differential Geometry
The course is focused on topology, metric space, Non-differentiable curve and surface. Exercises and applications will be illustrated.
Competence acquired: Basic notions of General Topology, Metric Spaces and classical Differential Geometry
Skills acquired (at the end of the course): Ability to use the foundamental notions of General Topology and Differential Geometry
Prerequisites
Courses required: Geometry I, Mathematical Analysis I.
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 300
Hours reserved to private study and other indivual formative activities: 180
Contact hours for: Lectures (hours): 120
Hours reserved to private study and other indivual formative activities: 180
Contact hours for: Lectures (hours): 120
Further information
Frequency of lectures, practice and lab: Recommended
Teaching Tools
Teaching Tools
Course program
PART 1 - TOPOLOGY: Metric spaces. Topological spaces and continuos maps. Subspaces. Products. Quotiens. Separation axioms. Compact Spaces. Connected spaces. Complete metric spaces.
PART 2 - DIFFERENTIAL GEOMETRY: Submanifolds of R^n. Regular curves , curvature, torsion, fundamental theorem of local theory. Surfaces in R^3, first and second fundamental form, curvature and local theory of surfaces. Teorema Egregium. Geodetics. First notions of global theory of surfaces.
PART 2 - DIFFERENTIAL GEOMETRY: Submanifolds of R^n. Regular curves , curvature, torsion, fundamental theorem of local theory. Surfaces in R^3, first and second fundamental form, curvature and local theory of surfaces. Teorema Egregium. Geodetics. First notions of global theory of surfaces.