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 | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH 111 Basic Logic and Algebra |
| Course Language | English |
|---|---|
| Course Type | N/A |
| 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 | 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 | ||||
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 | ||