Course Name Code Semester T+U Hours Credit ECTS
Elementary Number Theory IME 306 6 3 + 0 3 3
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Bachelor's Degree
Course Type Compulsory
Course Coordinator Dr.Öğr.Üyesi ERCAN MASAL
Course Lecturers Dr.Öğr.Üyesi ERCAN MASAL,
Course Assistants

Res.Assist.Emine Nur BİLGİÇ

Course Category Available Basic Education in the Field
Course Objective

To give detailed information to students of elementary education about divisibility on integers, products on integers. Intoduce relations among congruents and some applcation fields, primitive roots and indexes and groups. To give relations among continuous fraction and rational and irrational numbers.

Course Content

Divisibility on integers, prime numbers, important functions on number theories, congruents, linear congruents, seperating prime products on integers, primitive roots and indexes, quadric residues (second degree), cryptography subjects and usage areas in real life, continuous fractions.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 Explain divisibility rules on integers Lecture, Drilland Practice, Testing, Homework,
2 Explain the relation between prime numbers and products on integers and express division on integers, highest common factor (H.C.F.), lowest common multiple (L.C.M.) by the help of this relation Drilland Practice, Lecture, Testing, Homework,
3 Explain special functions on number theory Lecture, Drilland Practice, Homework, Testing,
4 Explain the concept of congruents and solve problems related congruents Lecture, Drilland Practice, Testing, Homework,
5 Explain the solution of linear and higher order congruents Drilland Practice, Lecture, Homework, Testing,
6 Express the properties of primitive roots and indexes and solve related problems Lecture, Drilland Practice, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Divisibility on integers
2 Prime numbers and products on integers
3 Euler’s function
4 Congruents
5 Linear congruents
6 Chinese remainder theorem
7 Higher order congruents
8 Primitive roots
9 Mid –Term Exam
10 Indexes
11 Quadric residues
12 Cryptography
13 Continuous fractions
14 Arithmetic functions
Resources
Course Notes
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
1 Have general information about basic concept, theory and applicaitons on mathematics X
2 Have ability of mathematical thinking and apply to real life X
3 Classify a problem systematically also create comprehensible, understandable and objective solutions X
4 Establish relationship among events looked different X
5 Get clear and exact ideas about relationships among time, place and numbers X
6 Use principles of scientific method on problem solving X
7 Have character on explorer, impartial, disinterested, give sound decisions, open mind and believe that spreading information is needed X
8 Think creative and critical X
9 Improve methods as fast, understandable and practical to faced problems X
10 Have information about national and international modern problems
11 Get life long learning behaviour
12 Know and apply approach, aim, goal, principle and techniques of teaching program on special field with basic value and principles of Turkish National Education System
13 Evaluate development and learning of students, provide to evaluate self-assessment and other students. Use the assessment results to better instruction; share the results with student, parent, administrators and teachers.
14 Endeavor for constant development by making self-evaluation. Open the new knowledge and ideas, have a role to develop himself/herself and his/her institution. Have enough knowledge and conscious to protection subjects on society values and environment.
15 Interrogator ( get habit to find source of knowledge by asking “Why?” question instead of direct acceptance to given knowledges ) X
Evaluation System
Semester Studies Contribution Rate
1. Ödev 10
1. Ara Sınav 50
1. Kısa Sınav 20
2. Kısa Sınav 20
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 1 16
Mid-terms 1 10 10
Quiz 2 1 2
Assignment 1 3 3
Final examination 1 8 8
Total Workload 87
Total Workload / 25 (Hours) 3.48
dersAKTSKredisi 3