Course Name Code Semester T+U Hours Credit ECTS
Algebraic Number Theory I MAT 567 0 3 + 0 3 6
Precondition Courses <p>Algebra I and Algebra II</p>
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Prof.Dr. REFİK KESKİN
Course Lecturers
Course Assistants
Course Category Other
Course Objective

To find the integer solutions of the Diophantine equations is an area of interest of many mathematicians. Here, our aim is to investigate solutions of some Diophantine equations by using the theorems of algebraic number theory. Therefore studying algebraic number theory becomes important.

Course Content

Rings and ideals, Quotient Rings, Prime and maximal ideals, Unique factorization domains and principal ideal domain, Algebraic numbers and albgebraic integers, Number fields, Rings of algebraic integers, Determinants and discriminants, Euclid domains, Norms and traces, Integral bases, Pell equations, Solvability of the Pell equations, The Ramanujan- Nagell equation

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she uses undergraduate algebra knowledge in order to conceive the algebraic number theory. Lecture, Drilland Practice, Group Study, Self Study, Problem Solving, Testing, Homework,
2 He/ she learns solutions of the Diophantine equations by using algebraic number theory. Lecture, Drilland Practice, Group Study, Self Study, Problem Solving, Testing, Homework,
3 He/ she understands how to use theory and application. Lecture, Drilland Practice, Group Study, Self Study, Problem Solving, Testing, Homework,
4 He/ she constitutes necessary background in order to understand Algebraic Number Theory II. Lecture, Drilland Practice, Group Study, Self Study, Problem Solving, Testing, Homework,
5 He/she learns investigating concerning with algebraic number theory from different sources. Lecture, Drilland Practice, Group Study, Self Study, Problem Solving, Testing, Homework,
6 He/she learns literature search and reading and understanding the articles concerning with the subject. Lecture, Drilland Practice, Group Study, Self Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Rings and ideals
2 Quotient Rings
3 Prime and maximal ideals
4 Unique factorization domains and principal ideal domain
5 Algebraic numbers and albgebraic integers
6 Number fields
7 Rings of algebraic integers
8 Determinants and discriminants
9 Euclid domains
10 Norms and traces
11 Integral bases
12 Pell equations
13 Solvability of the Pell equations
14 The Ramanujan- Nagell equation
Resources
Course Notes
Course Resources

1) Ian Stewart and David Tall, Algebraic Number Theory and Fermat´s Last Theorem, A K Peters, Ltd., 2002.
2) Şaban Alaca and Kennet S. Williams, Inductory Algebraic Number Theory, Cambridge University ress, 2004.
3) Algebraic Number Theory, Franz Lemmermeyer, http://www.fen.bilkent.edu.tr/~franz/ant-st.pdf
4) Algebraic Number Theory, Samir Siksek, http://www.warwick.ac.uk/~maseap/teaching/ant/antnotes.pdf

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 100
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 25 25
Quiz 1 10 10
Performance Task (Laboratory) 1 30 30
Total Workload 161
Total Workload / 25 (Hours) 6.44
dersAKTSKredisi 6