DICLE UNIVERSITY
SCIENCE INSTITUTE
Department of Mathematics
COURSE INFORMATION PACKAGE
Course Code
504037
Course Title
Year/Semester
Status
Programme’s Name
Language of Instruction
Prerequisites
Disable Students
Student Responsibilities
Lecturer
Course Assistant
Course Objectives
Special Quota for
Other Departments
Optic Code
10504037
Consultation Hours
T+A
3+0
Credit
3
ECTS
8
REAL ANALYSIS I
FALL
SELECTİVE
MATHEMATICS
TURKISH
NO
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
Prof. Dr. H. Özlem GÜNEY, e-mail: ozlem@dicle.edu.tr , Phone:
To Teach advanced concepts and topics in Theory of Real Functions
The most 10 (ten) student
At the end of this course the student;
-
-
-
Learning Outcomes
-
Student through this course realizes that there is a need for a new point of view
between this course and the previous analysis course from the aspect the meaning
and the functioning.
Through this new understanding and this interpretation the student is to be
equipped with enough knowledge of how the construction of the fundamentals of
mathematics is achieved.
The student’s ability of thinking mathematically is to be improved in the case that
he/she is being introduced with the processes, spaces and the models which he/she
has never known before and probably never heard of.
May improve his/her ability of analyzing.
Improves the ability of self-motivation
May become competent of debating mathematics.
Acquires the enthusiasm for investigation, exploration of building strategies and
reinforcing his/her intuitive approach.
504037
REAL ANALYSIS I
10504037
3+0
3
8
Contents, learning activities
Week
Topic
Learning Activities
1
Sets and Relations
The student’s approaches to the subject are questioned under
the light of the knowledge that is gained through the
education process. The students are to be wanted to be ready
after reminding them the subject of next week. A notice is
made that the volunteers are free to make presentation.
2
The Real Number System
To reinforce the concepts. The students are wanted to be
ready by reminding them the title of the next week.
3
The Extended Real Numbers Sequences of Real Numbers
To give examples about application area of the subject.
Question is asked and answer provided.
4
Continuous Functions
To reinforce the concepts. Discussion with questions and
answers.
5
Borel Sets
To be given Homeworks / Term Paper / Presentation
6
Metric Spaces
Expressing their ideas before explaining the subject as
controlling their information about subject. Examples are
given. Questions are directed and answered. To be given
research subject.
7
Open and Closed Sets
To work out the previous knowledge of students,
Discussing results of research subject.
8
Midterm
Discussions on solution after midterm examination
9
Convergence
Presentation and criticism of Homeworks / Term Paper /
Presentation
10
Completeness
Presentation and criticism of Homeworks / Term Paper /
Presentation
11
Uniform Continuity, Subspaces
Students will stimulate for next week's issue to be prepared.
Students who wish to make presentations.
12
Compact Metric Spaces
Lecturing, Discussing, Questions-Answer
13
Baire Category Theorem
14
Connectedness
15
Hilbert Space.
To work out the previous knowledge of students, The
students are wanted to be ready by reminding them the title
of the next week.
The presentation of this subject by three different students
is provided. Examples are given. Questions are directed and
answered.
Summary of the semester will be done.
If any, mark as x
Assessment criteria
Percent (%)
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 vb).
Final Exam
Others
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
Textbook / Material
H.L.Royden; Real Analysis , Third Edition Macmillan Publishing Company.
Recommended Reading
Norman B.Haaser and Joseph A. Sullivan ; Real Analysis.
Regulating
Analysis and Theory of Functions Department
1.
2.
3.
4.
5.
6.
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.
Course’s time is determined according to examination, quiz, homework, project, and contribution to class.
Average mark about course is determined by above activities and booked down student information system
of university.
Midterm exam will be planned between 7 and 10’th week of semester by related lecturer.
ECTS calculation form will contain checkout of course.
Checkout course paper will be given to students at beginning of each semester.