GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
ANALYTICAL NUMBERS THEORY II/6241305
Course Title: ANALYTICAL NUMBERS THEORY II
Credits 3 ECTS 7.5
Course Semester 1 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
Learn arithmetical functions, Dirichlet convolution and multiplicative functions.
Learn characters, Dirichlet characters, Hecke characters.
Learn the Dirichlet polynomials, mean value estimates, the discrete mean- value estimates.
Learn sums over finite fields, finite and exponential sums, geometry of elliptic curves.
 -- MODE OF DELIVERY
  The mode of delivery of this course is face to face
 --WEEKLY SCHEDULE
1. Week  Arithmetical functions
2. Week  Distribution of additive functions
3. Week  Characters, Dirichlet characters
4. Week  Summation formulas, the Euler-Maclaurin formula, functional equations of Dirichlet functions.
5. Week  Classical analytic theory of L-functions
6. Week  Elementary Sieve methods
7. Week  Bilinear forms
8. Week  Exponential sums
9. Week  The Dirichlet polynomials, mean value estimates
10. Week  Dirichlet polynomials with characters
11. Week  Zero density estimates
12. Week  Sums over finite fields
13. Week  Character sums
14. Week  Holomorphic modular forms, Eisenstein and Poincare series, Hecke L-functions
15. Week  
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
30
 Assignment
2
10
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
1
10
 Percent of In-term Studies  
50
 Percentage of Final Exam to Total Score  
50
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
3
42
 Weekly Tutorial Hours
14
0
0
 Reading Tasks
8
7
56
 Searching in Internet and Library
8
7
56
 Material Design and Implementation
0
0
0
 Report Preparing
0
0
0
 Preparing a Presentation
0
0
0
 Presentation
0
0
0
 Midterm Exam and Preperation for Midterm Exam
1
8
8
 Final Exam and Preperation for Final Exam
1
18
18
 Other (should be emphasized)
0
0
0
 TOTAL WORKLOAD: 
180
 TOTAL WORKLOAD / 25: 
7.2
 Course Credit (ECTS): 
7.5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To be able to develop their knowledge of theory and applications at master degree depending on the competencies acquired in undergraduate level.X
2To be able to recognize different problems encountered in mathematics and to be able to make studies for their solutions.X
3To be able to formulate new solutions with scientific methods mostly based on analysis and synthesis.X
4To be able to carry out his/her works either independently or in groups within a project considering his/her knowledge on the field he/she works in a critical approach.X
5To be able to continue his/her works considering social, scientific and ethical values.X
6To be able to follow scientific and social developments related to his/her field.X
7To be able to carry out his/her works within the framework of quality management, workplace safety and environmental awareness and to be able to present systematically his/her works using various methods like written, oral or visual.X
8To be able to use methods of accessing knowledge effectively in accordance with ethical values.X
9To be able to use knowledge in other disciplines by combining it with mathematical information.X
10To be able to make activities in the awareness of need for lifelong learning.X
11To be able to make connections between mathematical and social concepts and produce solutions with scientific methods.X
12To be able to use his/her mathematical knowledge in technology.X
 -- NAME OF LECTURER(S)
   (Prof. Dr. Dursun TAŞCI)
 -- WEB SITE(S) OF LECTURER(S)
   (websitem.gazi.edu.tr/site/dtasci/)
 -- EMAIL(S) OF LECTURER(S)
   (dtasci@gazi.edu.tr)