# Elementary Number Theory (MATH325) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Elementary Number Theory MATH325 Area Elective 3 0 0 3 6
Pre-requisite Course(s)
MATH 111 Basic Logic and Algebra
Course Language English Elective Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Team/Group. This course is designed to introduce the basic concepts of the theory of numbers. The students who succeeded in this course; understand and use the properties of divisibility. solve linear Diophantine equations. solve congruences of various types, apply Chinese Remainder Theorem. understand and use Fermat's little theorem, Wilson's theorem. prove and apply properties of Euler’s phi-function. know the properties of Legendre symbol, use the laws of quadratic reciprocity. Divisibility, congruences , Euler, Chinese Remainder and Wilson?s Theorems, arithmetical functions, primitive roots, quadratic residues and quadratic reciprocity, diophantine equations.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Preliminaries pp. 1-12
2 Division Algorithm, Greatest Common Divisor pp. 12-26
3 Euclidean Algorithm, Linear Diophantine Equations pp. 26-40
4 The Fundamental Theorem of Arithmetic, Prime Numbers and Their Distribution pp. 40-62
5 Basic Properties of Congruences, Special Divisibility Tests pp. 62-72
6 Chinese Remainder Theorem, Solving Linear Congruences pp. 75-85
7 Fermat’s Factorization Method, Fermat’s Little Theorem pp. 84-98
8 Wilson’s Theorem, Some Number Theoretic Functions pp. 98-111
9 Number Theoretic Functions and Möbius Inversion Formula pp. 111-127
10 Euler’s Phi-Function, Euler’s Theorem, Some Properties of the Phi-Function pp. 129-156
11 Primitive Roots for Primes pp. 157-168
12 Composite Numbers Having Primitive Roots, The Theory of Indices pp. 168-178
13 Euler’s Criterion, The Legendre Symbol and Its Properties pp. 179-195
15 Review
16 Final Exam

### Sources

Course Book 1. David Burton, Elementary Number Theory, McGraw-Hill, Fifth Edition, 2002 2. Elementary Number Theory, G.A. Jones and J.M. Jones, Springer, 1998

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 8 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 8 40
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 15 30
Prepration of Final Exams/Final Jury 1 18 18