The aim of this lesson is to improve the abstract thinking ability of students and give a background for an advanced degree in mathematics and related areas.
-Sayılar Teorisi, Fethi Çallıalp, Birsen Yayınevi, İstanbul 2009.
-Sayılar Kuramına Giriş, Matematik Vakfı Yayınları, ISBN 975-8367-02-1, 2000.
Other Sources
-Elementary Number Theory, David M. Burton, 5th ed. Mc Graw- Hill, 2002, ISBN 0-07-232569-0.
-Topics in Number Theory,W.J. LeVeque, Dover ed.,2002, ISBN 0-486-42539-8.
-An introduction to the Theory of Numbers, G.H. Hardy &E.M. Wright, , 5th ed. Oxford Science Publications, 2005, , ISBN 0 19 8531710.
-Elementary Number Theory in Nine Chapter,James J.Tattersall, 2nd ed.,CambridgeUniversity Press 2005.
-Elementary number theory, WWL Chen, 2003,
http://rutherglen.science.mq.edu.au/wchen/lnentfolder/lnent.html
Course Schedules
Week
Contents
Learning Methods
1. Week
Divisibility Theory in Integers.
Oral and written presentation.
2. Week
The Division Algorithm, The Euclidean Algorithm.
Oral and written presentation.
3. Week
The Linear Diophant Equations.
Oral and written presentation.
4. Week
Primes, The Fundamental Theorem of Arithmetic.
Oral and written presentation.
5. Week
Basic Properties of Congruences, Special Divisibility Tests.
Oral and written presentation.
6. Week
Linear Congruences.
Oral and written presentation.
7. Week
Chinese Remainder Theorem.
Oral and written presentation.
8. Week
Fermat’s Theorem, Wilson’s Theorem.
Oral and written presentation.
9. Week
Midterm Exam
Written
10. Week
Arithmetic Functions.
Oral Presentation.
11. Week
Arithmetic Functions.
Oral and written presentation.
12. Week
The Möbius Inversion Formula.
Oral and written presentation.
13. Week
Euler’s Phi-Function.
Oral and written presentation.
14. Week
Euler’s Phi-Function, Primitive Roots
Oral and written presentation.
15. Week
Primitive Roots
Written
16. Week
Final Examinations
Written
17. Week
Final Examinations
Written
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Quizzes
4
20
Final Exam
1
40
Program Outcomes
PO-1
Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science.
PO-2
Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science.
PO-3
Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence.
PO-4
Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline.
PO-5
Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science.
PO-6
Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish.
PO-7
Using time effectively in inventing solutions by implementing analytical thinking.
PO-8
Understanding professional ethics and responsibilities.
PO-9
Having the ability to behave independently, to take initiative, and to be creative.
PO-10
Understanding the importance of lifelong learning and developing professional skills continuously.
PO-11
Using professional knowledge for the benefit of the society.
Learning Outcomes
LO-1
Have the basic knowledge on divisibility theory in integers, the linear diophant equation ax+by=c and primes, and solve problems related to these subjects.
LO-2
Have the basic knowledge on congruences and the Special Divisibility Tests, and apply them to other areas of mathematics.
LO-3
Solve the problems related the linear congruences and Chinese Remainder Theorem, and use them for the solution of various problems.
LO-4
Prove the Fermat’s theorem and Wilson's theorem, and apply these theorems to the solution of various problems.
LO-5
Have the basic knowledge about the Arithmetic Functions, the Möbius Inversion Formula and Euler’s Phi Function, and interpret these information.
