GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
THEORY OF NUMBERS/MAT- 301
Course Title: THEORY OF NUMBERS
Credits 4 ECTS 5
Semester 5 Compulsory/Elective Compulsory
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
   Assoc.Prof. Aynur Arıkan, Assoc.Prof. Ercan Altınışık
 -- WEB SITE(S) OF LECTURER(S)
   http://websitem.gazi.edu.tr/site/yalincak, http://websitem.gazi.edu.tr/site/ealtinisik, -- ÖĞRETİM ELEMANI E-POSTASI/E-POSTALARI yalincak@gazi.edu.tr -- ÖĞRENME ÇIKTILARI Matematik D&am
 -- EMAIL(S) OF LECTURER(S)
   yalincak@gazi.edu.tr,ealtinisik@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
Define integers, understand and apply the proof techniques of induction and the well ordering principle
Understand divisibility, understand and apply division algorithm and Euclid algorithm, and solve linear Diophantine equations
Prove and apply the fundamental theorem of arithmetic and write an integer, greater than 1, in the standart form.
Define Euler's fi-function, prove and apply Euler's theorem and Wilson's theorem
Solve linear congruences and find recurrence relations for solutions of congruences of higher degree
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 -- PREREQUISITES AND CO-REQUISITES
  There is no prerequisite or co-requisite for this course.
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  There is no recommended optional programme component for this course
 --COURSE CONTENT
1. Week  Axioms of integers
2. Week  Basic properties of divisibility
3. Week  Prime numbers
4. Week  Basic properties of congruences
5. Week  Euler's fi-function
6. Week   Euler's theorem and Wilson's theorem
7. Week  Solutions of linear congruences
8. Week  Mid-Term Exam
9. Week  Solutions of congruences of higher degree
10. Week   Primitive roots and indices
11. Week   Solutions of x^n ≡ a (mod m)
12. Week  Quadratic residues and quadratic reciprocity
13. Week  Jacobi's symbol
14. Week  Arithmetical functions
15. Week  Mobius inversion formula
16. Week  Final Exam
 -- RECOMMENDED OR REQUIRED READING
   Asar, Arıkan, "Sayılar Teorisi", ISBN 978 6054562442. Niven, Zuckerman, Montgomery, An introduction to the theory of numbers, ISBN 978-0471625469 Boston, 2003. 2. Abstract Algebra: an introduction, Thomas W. Hung
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
   None
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
40
 Assignment
0
0
 Exercises
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
40
 Contribution of Final Examination to Overall Grade  
60
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
14
3
42
 Practising Hours of Course Per Week
14
1
14
 Reading
8
2
16
 Searching in Internet and Library
9
2
18
 Designing and Applying Materials
0
0
0
 Preparing Reports
0
0
0
 Preparing Presentation
0
0
0
 Presentation
0
0
0
 Mid-Term and Studying for Mid-Term
1
12
12
 Final and Studying for Final
1
20
20
 Other
7
1
7
 TOTAL WORKLOAD: 
129
 TOTAL WORKLOAD / 25: 
5.16
 ECTS: 
5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To train individuals who are contemporary, entrepreneur and have unique and aesthetic values, self-confidence and capable of independent decision-making.X
2To give good education in the program fields as algebra, geometry, applied mathematics, topology and analysis in order to be equipped with enough mathematics.X
3To teach mathematical thinking methods in order to improve the ability to express mathematics both orally and in writing.X
4To train individuals who are knowledgeable about the history of mathematics and the production of scientific knowledge and can follow developments in these disciplines.X
5To provide necessary equipments to take positions such areas as banking, finance, econometrics, and actuarial.X
6To acquire ability to solve problems encountered in real life by means of mathematical modeling using mathematical methods.X
7To provide ability to do necessary resource researches in the areas of mathematics and to use accessed information.X
8To give appropriate training in such areas as in computer programming and creating algorithms in order to take parts in developing IT sector.X
9To gain substructure to be able to study at graduate level.X
10To enable the student to gain the ability of relating mathematics with the other sciences.X