Information Package / Course Catalogue - Adnan Menderes University

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Number Theory

Course Code	: MTK513
Course Type	: Area Elective
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 8

Objectives of the Course

This course gives the fundamental concepts of algebraic numbers.

Course Content

Principal ideal domain and unique factorization domains, commutative fields, residue classes, quadratic residues,algebraic ıntegers, ıntegral basis, discriminant, the decomposition of ıdeals, the norm and classes of ıdeals, units and estimations fort he discriminant, ramification, discriminant and different, the ramification of prime ıdeals in galois extension, the fundamental theorem of abelian extensions, miscellaneous numerical examples.

Name of Lecturer(s)

Learning Outcomes

1.	To be able to give fundamental properties of number theory
2.	To be able to relate number theory with other fields of algebra
3.	To be able to develop some theoretical approach on number theory
4.	To be able to develop individual work on number theory
5.	To be able to relate number theory with some other fields except algebra

Recommended or Required Reading

1.	Algebraic Numbers, P. Ribenboim, Wiley-Interscience,1972
2.	Number Theory, Z. I. Borevich and I.R. Shafarevich, Academic Press, 1967

Weekly Detailed Course Contents

Week 1 - Theoretical

Principal ideal domain and unique factorization domains

Week 2 - Theoretical

Fields

Week 3 - Theoretical

Residue classes

Week 4 - Theoretical

Quadratic residues

Week 5 - Theoretical

Algebraic integers, integral basis

Week 6 - Theoretical

Discriminant

Week 7 - Theoretical

The decomposition of ideals

Week 8 - Theoretical

The norm and classes of ideals

Week 9 - Theoretical

Units and estimations for the discriminant

Week 10 - Theoretical

Ramification, discriminant and different

Week 11 - Theoretical

Ramification, discriminant and different

Week 12 - Theoretical

The ramification of prime ideals in Galois Extension

Week 13 - Theoretical

The fundamental theorem of abelian extensions

Week 14 - Theoretical

Miscellaneous numerical examples

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Assignment	2	%30
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	3	3	84
Assignment	2	16	2	36
Individual Work	14	0	2	28
Final Examination	1	50	2	52
TOTAL WORKLOAD (hours)				200

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13	PÇ-14	PÇ-15
OÇ-1	5	5	4	5	4	3	2								2
OÇ-2	3	5	4	4	5	3	3								4
OÇ-3	4	4	5	5	5	3	4								4
OÇ-4	5	4	5	5	5	3	5								5
OÇ-5	5	5	4	5	4	3	3				4				5

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