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.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
Attendance
Instructor(s)
Course Assistant(s)
None
Schedule
Course is not opened
Office Hour(s)
Course is not opened
Teaching Methods and Techniques
-Lecture
Principle Sources
--Elementary Number Theory, David M. Burton, 5th ed. Mc Graw- Hill, 2002, ISBN 0-07-232569-0.
Other Sources
-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.
-Elementary Number Theory in Nine Chapter,James J.Tattersall, 2nd ed.,CambridgeUniversity Press 2005.
Course Schedules
Week
Contents
Learning Methods
1. Week
Linear Congruences in More Than One Unknown.
Oral and written presetation
2. Week
Congruences of Higer Degree.
Oral and written presetation
3. Week
Congruences with Prime Moduli, Primitive Roots.
Oral and written presetation
4. Week
Primitive Roots for Primes.
Oral and written presetation
5. Week
Composite Numbers having Primitive Roots.
Oral and written presetation
6. Week
The Theory of Indices.
Oral and written presetation
7. Week
Euler’s Criterion.
Oral and written presetation
8. Week
Midterm Examination.
Written
9. Week
Legendre Symb
Oral and written presetation
10. Week
Gauss’ Lemma
Oral and written presetation
11. Week
Quadratic Reciprocity, Jacobi Symbol.
Oral and written presetation
12. Week
Quadratic Congruences with Composite Moduli
Oral and written presetation
13. Week
Numbers of Special Form, Perfect Numbers.
Oral and written presetation
14. Week
Mersenne and Fermat Numbers
Oral and written presetation
15. Week
Final Examinations.
Written
16. Week
Final Examinations.
Written
17. Week
Final Examinations.
Written
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
45
Quizzes
2
0
Homework / Term Projects / Presentations
5
0
Attendance
21
5
Final Exam
1
50
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 about linear congruences in more than one unknown and congruences of higher degree, and solve problems related to these subjects.
LO-2
Prove the theorems on the Theory of Primitive Roots and determine all composite numbers having primitive roots and investigate all the primitive roots of them.
LO-3
Prove the theorems about the theory of indices and apply this theory to the solutions of various problems.
LO-4
Know the theory of concept of quadratic residue, and determine whether a given integer is a quadratic residue of a number and, research the solvability of quadratic congruences.
LO-5
Have some knowledge about numbers of special form such as Mersenne and Fermat numbers.
