Mathematics

Topology(MAT301)

Content
Course Code Course Name Semester Theory Practice Lab Credit ECTS
MAT301 Topology 5 4 0 0 4 8
Prerequisites MAT101, MAT102
Admission Requirements MAT101, MAT102
Language of Instruction French
Course Type Compulsory
Course Level Bachelor Degree
Course Instructor(s) Serap GÜRER serapgurer@gmail.com (Email)
Assistant
Objective Master elementary topology via the study of the topology of metric spaces.
Content Metric spaces (main inequalities, distances, equivalent distances, examples of metric sapces, normed vector spaces and convexity, distance between two sets and diametre, open and closed balls, neighborhood, open and closed sets, closure and interior, dense subsets). Topology (topological spaces, induced topology). Sequences in metric spaces (convergence, convergence in a product of metric spaces, limit point, caractersation of closed sets with sequences, Cauchy sequences, complete spaces). Continuous maps between metric spaces (sequential and topological caracterisation of continuity, uniform continuity, lipshizt maps). Compacity. Connectedness
Course Learning Outcomes
Teaching and Learning Methods
References Léa Blanc-Centi - Cours de Topologie

http://math.univ-lille1.fr/~blanccen/Enseignement/td/1314/L3/Topologie_Cours.pdf

James Munkres, Topology.

Georges Skandalis - Topologie et analyse -Dunod (2004)
Print the course contents
Weekly Contents
Theory Topics
Week Weekly Contents
1 Metric Spaces
2 Metric Spaces
3 Metric spaces
4 Metric spaces
5 Topological spaces
6 Topological spaces
7 Topological spaces
8 Topological spaces
9 Continuity
10 Continuity
11 Continuity
12 Compacity
13 Compacity
14 Connexity
Practice Topics
Week Weekly Contents
Assessment System
Contribution to Overall Grade
  Number Contribution
Contribution of in-term studies to overall grade 0 60
Contribution of final exam to overall grade 0 40
Toplam 0 100
In-Term Studies
  Number Contribution
Assignments 0 0
Presentation 0 0
Midterm Examinations (including preparation) 2 50
Project 0 0
Laboratory 0 0
Other Applications 0 0
Quiz 2 50
Term Paper/ Project 0 0
Portfolio Study 0 0
Reports 0 0
Learning Diary 0 0
Thesis/ Project 0 0
Seminar 0 0
Other 0 0
Toplam 4 100
Relation of Proficiency
No Program Learning Outcomes Contribution
1 2 3 4 5
1 understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; X
2 can properly state and use concepts and results of major mathematical interest; X
3 masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; X
4 is able to express one’s mathematical ideas in an organised way both in written and oral forms; X
5 understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); X
6 has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems;
7 has a theoretical and practical knowledge in computer science well adapted for learning a programming language;
8 has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions;
9 has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; X
10 masters French language as well as other foreign languages, to a level sufficient to study or work abroad. X
ECTS
Activities Number Period Total Workload
Total Workload 0
Total Workload / 25 0.00
Credits ECTS 0
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