ECTS - Elementary Number Theory
Elementary Number Theory (MATH325) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Elementary Number Theory | MATH325 | Elective Courses | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Team/Group. |
| Course Lecturer(s) |
|
| Course Objectives | This course is designed to introduce the basic concepts of the theory of numbers. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | 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 |
| 14 | Quadratic Reciprocity, Quadratic Congruences | pp. 195-207 |
| 15 | Review | |
| 16 | Final Exam |
Sources
| Course Book | 1. David Burton, Elementary Number Theory, McGraw-Hill, Fifth Edition, 2002 |
|---|---|
| Other Sources | 2. Elementary Number Theory, G.A. Jones and J.M. Jones, Springer, 1998 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| 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 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | X |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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 | ||||
ECTS/Workload Table
| 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 |
| Total Workload | 130 | ||