COURSE SYLLABUS
COMPUTATIONAL ALGEBRAIC NUMBER THEORY I
| 1 |
Course Title: |
COMPUTATIONAL ALGEBRAIC NUMBER THEORY I |
| 2 |
Course Code: |
MAT6427 |
| 3 |
Type of Course: |
Optional |
| 4 |
Level of Course: |
Third Cycle |
| 5 |
Year of Study: |
2 |
| 6 |
Semester: |
3 |
| 7 |
ECTS Credits Allocated: |
6 |
| 8 |
Theoretical (hour/week): |
3 |
| 9 |
Practice (hour/week) : |
0 |
| 10 |
Laboratory (hour/week) : |
0 |
| 11 |
Prerequisites: |
None |
| 12 |
Recommended optional programme components: |
None |
| 13 |
Language: |
Turkish |
| 14 |
Mode of Delivery: |
Face to face |
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Course Coordinator: |
Prof. Dr. GÖKHAN SOYDAN |
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Course Lecturers: |
Doç. Dr. Musa DEMİRCİ |
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Contactinformation of the Course Coordinator: |
Prof. Dr. Gökhan SOYDAN
Fen Edebiyat Fakültesi, Matematik Bölümü,
02242942870; gsoydan@uludag.edu.tr |
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Website: |
|
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Objective of the Course: |
To learn computational concepts and applications in algebraic number theory |
| 20 |
Contribution of the Course to Professional Development |
To develop analytical thinking skills.
|
| 21 |
Learning Outcomes: |
| 1 |
To know unique factorization in natural numbers, the fundamental theorem of arithmetic;
|
| 2 |
To learn algebraic numbers, minimal polynomials, integrality;
|
| 3 |
To know the ring of algebraic integers;
|
| 4 |
To learn rings of integers of number fields;
|
| 5 |
To know fields, discriminants and integral bases;
|
| 6 |
To know rings of integers in some quadratic and cubic fields;
|
| 7 |
To learn non-unique factorization in quadratic number fields and know its examples;
|
| 8 |
To know ideals and generating sets for ideals;
|
| 9 |
To know ideals in quadratic fields;
|
| 10 |
Know how to find class group;
|
|
| Week |
Theoretical |
Practical |
| 1 |
Unique factorization in natural numbers, the fundamental theorem of arithmetic, Gaussian integers and their application |
|
| 2 |
Algebraic numbers, minimal polynomials, integrality |
|
| 3 |
The ring of algebraic integers |
|
| 4 |
Rings of integers of number fields |
|
| 5 |
fields, discriminants and integral bases |
|
| 6 |
Rings of integers in some cubic fields |
|
| 7 |
Uniqueness of factorization revisited |
|
| 8 |
Non-unique factorization in quadratic number fields |
|
| 9 |
Kummer's ideal numbers |
|
| 10 |
Ideals and generating sets for ideals |
|
| 11 |
Ideals in quadratic fields |
|
| 12 |
Unique factorisation domains and principal ideal domains |
|
| 13 |
Class group |
|
| 14 |
Splitting of primes, primes in quadratic fields |
|
| 23 |
Textbooks, References and/or Other Materials: |
1) Algebraic Number Theory, F. JARVIS, Springer 2014
2) Introductory Algebraic Number Theory, Ş.ALACA, K. WILLIAMS, Cambridge, 2003 |
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Assesment |
|
| TERM LEARNING ACTIVITIES |
NUMBER |
PERCENT |
| Midterm Exam |
0 |
0 |
| Quiz |
0 |
0 |
| Homeworks, Performances |
0 |
0 |
| Final Exam |
1 |
100 |
| Total |
1 |
100 |
| Contribution of Term (Year) Learning Activities to Success Grade |
0 |
| Contribution of Final Exam to Success Grade |
100 |
| Total |
100 |
| Measurement and Evaluation Techniques Used in the Course |
The system of relative evaluation is applied. |
| Information |
|
| 25 |
|
ECTS / WORK LOAD TABLE |
| Activites |
NUMBER |
TIME [Hour] |
Total WorkLoad [Hour] |
| Theoretical |
14 |
3 |
42 |
| Practicals/Labs |
0 |
0 |
0 |
| Self Study and Preparation |
14 |
9 |
126 |
| Homeworks, Performances |
0 |
0 |
0 |
| Projects |
0 |
0 |
0 |
| Field Studies |
0 |
0 |
0 |
| Midtermexams |
0 |
0 |
0 |
| Others |
0 |
0 |
0 |
| Final Exams |
1 |
12 |
12 |
| Total WorkLoad |
|
|
180 |
| Total workload/ 30 hr |
|
|
6 |
| ECTS Credit of the Course |
|
|
6 |
| 26 |
CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS |
|
PQ1
|
PQ2
|
PQ3
|
PQ4
|
PQ5
|
PQ6
|
PQ7
|
PQ8
|
PQ9
|
PQ10
|
|
LO1
|
4
|
5
|
1
|
2
|
5
|
1
|
2
|
2
|
2
|
1
|
|
LO2
|
3
|
5
|
1
|
2
|
5
|
1
|
3
|
2
|
2
|
1
|
|
LO3
|
4
|
5
|
1
|
3
|
5
|
1
|
3
|
3
|
2
|
1
|
|
LO4
|
5
|
5
|
1
|
2
|
5
|
1
|
2
|
2
|
2
|
1
|
|
LO5
|
5
|
5
|
1
|
2
|
5
|
1
|
3
|
2
|
2
|
1
|
|
LO6
|
5
|
5
|
1
|
3
|
5
|
1
|
3
|
3
|
2
|
1
|
|
LO7
|
5
|
5
|
1
|
3
|
5
|
1
|
3
|
2
|
2
|
1
|
|
LO8
|
5
|
5
|
1
|
3
|
5
|
1
|
3
|
2
|
2
|
1
|
|
LO9
|
5
|
5
|
1
|
3
|
5
|
1
|
3
|
2
|
2
|
1
|
|
LO10
|
5
|
5
|
1
|
3
|
5
|
1
|
3
|
2
|
2
|
1
|
|
| LO: Learning Objectives |
PQ: Program Qualifications |
| Contribution Level: |
1 Very Low |
2 Low |
3 Medium |
4 High |
5 Very High |
