Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
6MATH366NUMBER THEORY3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course To give the students the essentials of number theory. To give the students some methods to solve some type of equations by using the concepts of number theory
Course Content Pythagorean Triples. Sums of Higher Powers and Fermat’s Last Theorem. Divisibility and Greatest Common Divisor. Factorization and Fundamental Theorem of Arithmetic. Congruences, Powers, Fermat’s Little Theorem and Euler’s Formula. Chinese Remainder Theorem. Prime Numbers, Counting Primes. Mersenne Primes and Perfect Numbers. Powers, Roots and Codes. Primality Tests. Euler’s Phi Function and Sums of Divisors. Primitive Roots and Indices. Which Numbers are Sums of Two Squares. Continued Fractions, Square Roots and Pell’s Equation. Generating Functions. Sums of Powers. Cubic curves and Elliptic Curves.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. ENGİN BÜYÜKAŞIK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers", Sixth edition. Revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. Oxford University Press, Oxford, 2008.
Underwood Dudley,"Elementary number theory", Second edition. A Series of Books in the Mathematical Sciences. W. H. Freeman and Co., San Francisco, Calif., 1978.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 60
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 3 14 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 5 10 50
Exams and Exam Preparations 5 17 85
Total Work Load   Number of ECTS Credits 6 177

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To identify divisibility, congruences and fundamental theorem of arithmetic.
2 To state the definitions of prime numbers, perfect numbers and mersenne primes.
3 To identify Fermat theorems, Euler phi function and their applications.
4 To apply some type of Pell Equations, cubic equations and elliptic equations.


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Pythagorean Triples. Sums of Higher Powers and Fermat’s Last Theorem. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
2 Divisibility and Greatest Common Divisor. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
3 Factorization and Fundamental Theorem of Arithmetic. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
4 Congruences, Powers, Fermat’s Little Theorem and Euler’s Formula. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
5 Chinese Remainder Theorem. Prime Numbers, Counting Primes. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
6 Infinitude of primes G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
7 Mersenne Primes and Perfect Numbers. Powers, Roots and Codes G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
8 Primality Tests. Euler’s Phi Function and Sums of Divisors. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
9 Primitive Roots and Indices. Which Numbers are Sums of Two Squares. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
10 Continued Fractions, Square Roots and Pell’s Equation. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
11 Legendre symbol and Gauss' theorem G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
12 Generating Functions. Sums of Powers. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
13 Cubic curves G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
14 Elliptic Curves. G. H.Hardy, E. M. Wright, "An introduction to the theory of numbers"
15 Final 1st week
16 Final 2nd week


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 3
C2 4 3
C3 4 2
C4 4 2

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


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