DICLE UNIVERSITY
SCIENCE INSTITUTE
Department of Mathematics
COURSE INFORMATION PACKAGE
Course Code
Optic Code
Consultation Hours
T+A
Credit
ECTS
504005
10504005
To be announced
3+0
3
8
Course Title
INTRODUCTION TO ALGEBRAIC TOPOLOGY
Year / Semester
- / FALL
Status
SELECTIVE
Programme’s Name
DOKTORATE
Language of Instruction
TURKISH
Prerequisites
NO
Disable Students
Student Responsibilities
In case of need, Handicapped students, can request some facilities by giving information about
herself.
In order to content of course, to get ready, to participate, and responsibilities, which are
homework, project, disputation, and reading the interested parts, about course have to be
performed
Lecturer
Prof. Dr. H. İlhan TUTALAR, e-mail:tutalarhi@dicle.edu.tr, Tel:3147
Course Assistant
NO
Course Objectives
To teach Categories, Abel(ian) groups and homotopy, Homology
Special Quota for
Other Departments
The most 10 (ten) student
At the end of the course, he students, in summary, post themselves up on a matter presence of
categories, Abel(ian) groups and homotopy, homology of complexes, singular homology,
cellular decompositions, and furthermore he should be able to
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Learning Outcomes
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know Integer and its properties, reinforce operation idea
go on duration of mathematical logic and conception
reorganize their ability an analyst has
improve ability about reading, comprehending and writing mathematical expressions
enhance capability about formulating mathematics and gain ability realizing for expressing
mathematics with respect to his previous case
understand how one of the important crisis in mathematics to overcome caused fractions
and rational numbers
learn some topics as set with together operations on it, relation and function
becoming conscious mathematics base on these notions
know Cartesian Product that is foundation for shaping and animating
learn about equivalence relations and congruence being one of the important way to make
available in point of its properties
Robust mathematics how to proceed and to make
detect the operation as general than previous is
learn to comment
are aware of countable and uncountable set idea
are informed mathematics how to make and construct for the first time
begin understanding the relation between concrete and abstract conception
learn to comment
reconstitute and repeat theoretical learning and teaching conscious
learn proving and solution strategies, and to come into beings necessity and proficiency
concept
robust point of view about existences and sufficiency
gather abilities about association
research relations between mathematical and actual life
live conflicts about this subject and gain conscious to carrying out it
gain experience about mathematical education
obtain some knowledge about foundation of their geometrical notions by force of real
numbers
are engaged in some new imaginer element not a number named complex number
meet distinctly some topological topics for the first time from their geometrical intelligence
504005
10504005
INTRODUCTION TO ALGEBRAIC TOPOLOGY
3+0
3
8
Contents, learning activities
Week
Topic
Learning Activities
1
Categories
Discussion with questions and answers
2
Abel(ian) groups
3
Exactness, direct sum
4
Free abel(ian) grouos
Applications on some and student presentations
5
Homotopy
Discussion with questions and answers
6
Connecting homomorphism, exact sequences
7
Free complexes
8
Written midterm
9
Homology of complexes
10
Invariance under homotopy
11
Singular homology
12
Applications to Euclidean space
13
Cellular decompositions and homology
14
Functors of complexes
Discussion with questions and answers
15
Applications to Written final exam
Discussion and attendance with previous
knowledge in class and mean of contradiction
Knowing some rule and realities, making evidence
applications
Expressing their ideas before explaining the
subject as controlling their information about
subject
Discussion with questions and answers
Discussions on solution after midterm
examination
Knowing some rule and realities, making evidence
applications
Discussion with questions and answers
Type of Criteria
Assessment criteria
Expressing their ideas before explaining the
subject as controlling their information about
subject
Discussion and attendance with previous
knowledge in class and mean of contradiction
Activities as discussing the subject in class with
students.
Knowing some rule and realities, making evidence
applications
If any, mark as x
Percent (%)
Note
Will be given
points to
determine his
marks of this
course in
certain
percentages
with respect to
activities
during the
process have
been realized
by student in
the class
Midterm Exams
X
30
Quizzes
X
10
Homeworks / Term Paper / Presentation
X
5
Projects
X
10
Attendance & cover a subject
X
5
X
40
Others (in training, field survey, thesis
preparation etc).
Final Exam
Textbook / Material
-Lecture on Algebraic Topology, A. Dold; Springer-Ferlag, Berlin, Heidelberg, New York, 1972.
-Algebraic Topology, Allen Hatcher; Copyright © 2002 by Cambridge University Press. Chapters 0
and 2
Recommended Reading
Regulating
Discipline of Abstract Algebra and Number Theory in Mathematics
1. Efficiency examples: Contribution to course, homework activities, seminars, study in laboratory, scanning on paper and
books, observation, contribution to activities, sample study on case, etc.
2. Course’s time is determined according to examination, quiz, homework, project, and contribution to class.
3. Average mark about course is determined by above activities and booked down student information system of
university.
4. Midterm exam will be planned between 7 and 10’th week of semester by related lecturer.
5. ECTS calculation form will contain checkout of course.
6. Checkout course paper will be given to students at beginning of each semester.