Course Information
TitleΚΛΑΣΙΚΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ ΙΙ / Classical Differential Geometry II
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
Course ID40000470

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 0
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specialization635.5

Class Information
Academic Year2019 – 2020
Class PeriodSpring
Faculty Instructors
Weekly Hours3
Class ID
Type of the Course
  • Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Instruction, Examination)
  • French (Instruction, Examination)
  • German (Instruction, Examination)
Required Courses
  • 0301 Analytic Geometry I
  • 0302 Analytic Geometry II
  • 0303 Classical Differential Geometry I
Learning Outcomes
Introduction, deeping and understanding of advanced topics in Differential Geometry
General Competences
  • Apply knowledge in practice
  • Make decisions
  • Work autonomously
  • Work in teams
  • Work in an international context
  • Work in an interdisciplinary team
  • Generate new research ideas
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Reminder of basic constructions of Differential Geometry (principal and mean curvature, Gauss curvature, Geodesics and geodesic curvature), local and global Gauss-Bonnet theorem, surfaces of constant curvature, topological structure of surfaces, Euler characteristic.
Curvature, Gauss-Bonnet Theorem, Euler characteristic.
Educational Material Types
  • Notes
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
Reading Assigment150.5
Student Assessment
Written examination
Student Assessment methods
  • Written Exam with Multiple Choice Questions (Summative)
  • Written Exam with Short Answer Questions (Summative)
  • Written Exam with Extended Answer Questions (Summative)
  • Written Assignment (Summative)
  • Written Exam with Problem Solving (Summative)
Course Bibliography (Eudoxus)
- A. Pressley: Στοιχειώδης Διαφορική Γεωμετρία.Ηράκλειο : Πανεπιστημιακές Εκδόσεις Κρήτης, 2011 - B. O'Neill: Στοιχειώδης Διαφορική Γεωμετρία, Ηράκλειο : Πανεπιστημιακές Εκδόσεις Κρήτης, 2002 - Α. Αρβανιτογεώργος: Στοιχειώδης Διαφορική Γεωμετρία, Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, 2015 - Σ. Σταματάκης: Εισαγωγή στην Κλασική Διαφορική Γεωμετρία, Θεσσαλονίκη, Εκδόσεις Αϊβάζη, 2008 - Δ. Κουτρουφιώτης: Στοιχειώδης διαφορική γεωμετρία, Αθήνα : Leader Books, 2006
Additional bibliography for study
- M. Abate, F. Tovena: Curves and Surfaces. Springer, 2012 - M. P. do Carmo: Differential Geometry of Curves and Surfaces. Prentice – Hall, 1976 - J. Oprea: Differential Geometry and its Applications. Prentice Hall, 1997
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