Title  ΔΙΑΦΟΡΙΣΙΜΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ Ι / Differential Manifolds I 
Code  0304 
Faculty  Sciences 
School  Mathematics 
Cycle / Level  1st / Undergraduate 
Teaching Period  Winter 
Coordinator  Fani Petalidou 
Common  No 
Status  Active 
Course ID  40000468 
Programme of Study: UPS of School of Mathematics (2014today)
Registered students: 50
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Elective Courses belonging to the selected specialization  7  4  5.5 
Academic Year  2019 – 2020 
Class Period  Winter 
Faculty Instructors 

Weekly Hours  3 
Class ID  600147617

Type of the Course
 Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600147617
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
 Greek (Instruction, Examination)
 English (Examination)
 French (Examination)
Prerequisites
Required Courses
 0131 Group Theory
 0303 Classical Differential Geometry I
 0332 Classical Differential Geometry II
 0201 Calculus I
 0202 Calculus II
 0203 Calculus III
 0204 Topology of Metric Spaces
 0205 Calculus IV
 0108 Linear Algebra
General Competences
 Work autonomously
 Work in teams
 Work in an international context
 Work in an interdisciplinary team
 Generate new research ideas
Course Content (Syllabus)
Homeomorphic topological spaces. Topological manifolds. Differentiable manifolds. The tangent space. Differential of a map. Tensor algebra. Tensor fields. Gradient and covariant diffrentiation of functions. Lie brackets. Covariant differentiation of tensor fileds. Affine connections. Parallel transport of tangent vectors. Geodesics. Parallel vector fields. The curvature tensor.
Keywords
Manifolds
Educational Material Types
 Notes
 Book
Use of Information and Communication Technologies
Use of ICT
 Use of ICT in Communication with Students
Course Organization
Activities  Workload  ECTS  Individual  Teamwork  Erasmus 

Lectures  130  4.3  ✓  
Reading Assigment  32  1.1  ✓  
Exams  3  0.1  
Total  165  5.5 
Student Assessment
Description
Written examination
Student Assessment methods
 Written Exam with Multiple Choice Questions (Summative)
 Written Exam with Short Answer Questions (Formative, Summative)
 Written Exam with Extended Answer Questions (Formative, Summative)
 Written Assignment (Formative, Summative)
 Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Β. Παπαντωνίου: Διαφορίσιμες Πολλαπλότητες
Additional bibliography for study
1. Δημητρίου Κουτρουφιώτη, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων 1994.
2. Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011.
3. John M. Lee, Introduction to Smooth Manifolds, GTM 218, Springer 2003.
4. M. Spivak, A comprehensive Introduction to Differential Geometry, Publish or Perish, Inc., 1999.
Last Update
03092019