# Differenrial Manifolds

 Title ΘΕΩΡΙΑ ΔΙΑΦΟΡΙΣΙΜΩΝ ΠΟΛΛΑΠΛΟΤΗΤΩΝ / Differenrial Manifolds Code 0658 Faculty Sciences School Mathematics Cycle / Level 2nd / Postgraduate Teaching Period Winter Coordinator Panagiotis Batakidis Common No Status Active Course ID 40000046

### Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)

Registered students: 7
OrientationAttendance TypeSemesterYearECTS
THEŌRĪTIKA MATHĪMATIKACore Courses A31110

 Academic Year 2020 – 2021 Class Period Winter Faculty Instructors Fani Petalidou 39hrs Weekly Hours 3 Class ID 600177926
Course Type 2016-2020
• Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
• Face to face
Digital Course Content
Language of Instruction
• Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus. Linear Algebra. Group Theory. Differential Geometry Differentiable Manifolds I and II
General Competences
• Apply knowledge in practice
• Work autonomously
• Work in teams
• Work in an interdisciplinary team
Course Content (Syllabus)
Differentiable Manifolds (basic concepts). Fibre bundles. Covectors and 1-forms. Flow of a vector field and integral curves. Distributions. Frobenius theorem. Integral submanifolds. Basic concepts of foliations. Lie groups and Lie algebras (geometric consideration). Invariant vector fields. Integrations of Lie algebras and the exponential map. Examples.
Educational Material Types
• Notes
• Book
Use of Information and Communication Technologies
Use of ICT
• Use of ICT in Course Teaching
• Use of ICT in Communication with Students
Course Organization
Lectures1605.3
Seminars200.7
Exams50.2
Total30010
Student Assessment
Description
Seminars. Written Examination.
Student Assessment methods
• Written Exam with Extended Answer Questions (Formative, Summative)
• Written Assignment (Formative, Summative)
• Oral Exams (Formative)
• Performance / Staging (Formative)
• Written Exam with Problem Solving (Formative, Summative)
Bibliography