Course Name Code Semester T+U Hours Credit ECTS
Continued Fractions With Aplications MAT 558 0 3 + 0 3 6
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Prof.Dr. REFİK KESKİN Course Lecturers Prof.Dr. REFİK KESKİN, Course Assistants Course Category Available Basic Education in the Field Course Objective To generalize subjects and methods of approximations theory and rational approximation of numbers Course Content The methods of approximation theory and rational approximation of numbers
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she knows basic knowledge related with continued fractions. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
2 He/she compares the continued fractions and the power series. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 He/she finds the convergence of continued fractions. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 He/she computes continued fractions of Fibonacci numbers. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 He/she computes the periodic continued fractions Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 He/she solves the numeric problems. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
7 He/she computes example of this fractions. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Definitions and basic concepts
2 Formal definitions and notations.
3 Some particular examples.
4 From pover series to continued fractions.
5 From continued fractions to pover series.
6 Classical convergence theorems.
7 Worpitzkys theorem.
8 Classical remark on convergence.
9 Exam
10 Another concept of convergence.
11 Modified approximants.
12 Computation of approximants
13 Tail sequences, some properties of linear fractional transformations.
14 Speed of convergence, general convergence.
Resources
Course Notes <p>Rational Approximations and Orthogonality, E.M. Nikishin and V.N. Sorakin</p>
Course Resources

Continued Fractions with Applications,L. Lorentzen and H. Waadeland, 1992.

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ödev 100
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
Total 100