Course Name Code Semester T+U Hours Credit ECTS
Algebraic Number Theory II MAT 568 0 3 + 0 3 6
Precondition Courses
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

The topic given in Algebraic number theory I will be continued and the applications of algebraic numbers will be examined by considering Bachet-Mordell Diophantine equation.

Course Content

Algebraic integers, Number fields, Norms and discriminants, Modules, Ideals and ideals as Z-modules, Residue class, Cancellation laws, Divisibility of ideals, Decompositions of primes, Principal ideal test, Class group, Finitiness of class number, Computation of class groups, Bachet-Mordell equation.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/ she learns to decomposite the ideals to prime ideals in algebraic number ring. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework,
2 After learning decompositions of ideals to prime ideals, he/ she applies this in solving Pell equations. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework,
3 He/ she calculates the class number and uses this in solving Pell eqautions. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Algebraic integers
2 Number fields
3 Norms and discriminants
4 Modules
5 Ideals and ideals as Z-modules
6 Residue class
7 Residue class
8 Cancellation laws
9 Divisibility of ideals
10 Decompositions of primes
11 Principal ideal test
12 Class group, Finitiness of class number
13 Computation of class groups
14 Bachet-Mordell equation
Resources
Course Notes
Course Resources

1. Ian Stewart and David Tall, Algebraic Number Theory and Fermats Last Theorem, A K Peters, Ltd., 2002.
2. Şaban Alaca and Kenneth S. Williams, Introductory Algebraic Number Theory, Cambridge University Press, 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
2 Student follows the current journals in his/her field and puts forward problems. 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
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
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
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
6 Student determines the problems to be solved within his/her field and if necessary takes the lead.
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.
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
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
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
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
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
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
Final examination 1 30 30
Total Workload 126
Total Workload / 25 (Hours) 5.04
dersAKTSKredisi 6