Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea in Matematica applicata - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2014/2015
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3° Year activated in the A.Y. 2015/2016
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Uno o due insegnamenti tra i seguenti per un totale di 12 cfu
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Uno o due insegnamenti tra i seguenti per un totale di 12 cfu
Modules | Credits | TAF | SSD |
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Geometry (2014/2015)
Teaching code
4S00247
Teacher
Coordinator
Credits
6
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/03 - GEOMETRY
Period
II sem. dal Mar 2, 2015 al Jun 12, 2015.
Learning outcomes
Introduction to general topology. Classical theory of curves and surfaces.
Program
Introduction to topology. Topological spaces, basic topological notions : isolated and accumulation points, closure, product and quotient topology, compactness, connectedness, separability and Hausdorff spaces. Continuous functions, homeomorphisms, Weierstrass' Theorem, Tychonoff Theorem, continuity vs compactness, connectedness and separability.
Classical theory of parametric curves, regular parametrization, arc length, tangent vector, curvature and normal . Osculating and normal plane, Binormal and torsion, Frénet-Serret equations.
Classical theory of parametrized surfaces in 3d euclidean. Space. Regular parametrizations, local coordinates, coordinate charts, atlas, tangent plane, normal vector, surface area, first fundamental form, local and global isometries, conformal maps, developable surfaces.
Gauss map, Weingarten map (shape operator), second fundamental form, principal curvatures, Meusnier's theorem, mean curvature, gauss curvature.
Covariant derivative, Christoffel symbols, Levi-Civita connection, Gauss' Theorema Egregium.
Examination Methods
written and oral exam
Teaching materials e documents
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Appunti -- Superfici (pdf, it, 332 KB, 6/8/15)
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Curve (pdf, it, 306 KB, 4/23/15)
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Practice test (pdf, it, 108 KB, 4/23/15)
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Soluzioni agli esercizi sulle superfici (pdf, it, 204 KB, 6/8/15)
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Topologia generale (pdf, it, 314 KB, 3/24/15)