|
Week
|
Topics
|
Study Metarials
|
|
1
|
Division algorithm, representation of Integers
|
R1: Section 1.5, 2.1
|
|
2
|
Greatest common divisor, the Euclidean algorithm
|
R1: Section 3.3,3.4
|
|
3
|
The fundamental theorem of arithmetic
|
R1: Section 3.5
|
|
4
|
Factorizarion Methods and Fermat Numbers
|
R1: Section 3.6
|
|
5
|
Linear Diaphontine Equations
|
R1: Section 3.7
|
|
6
|
Introduction to Congruences
|
R1: Section 4.1
|
|
7
|
Linear Congruences, Chinese Remainder Theorem, and solution of polynomial congruences
|
R1: Section 4.2,4.3, 4.4
|
|
8
|
Systems of Linear Congruences
|
R1: Section 4.5
|
|
9
|
Divisible Test
|
R1: Section 5.1
|
|
10
|
Wilson`s Theorem and Fermat`s Littel Theorem
|
R1: Section 6.1
|
|
11
|
Euler`s Theorem
|
R1: Section 6.3
|
|
12
|
Euler Phi Function
|
R1: Section 7.1
|
|
13
|
Primitive Roots
|
R1: Section 9.1, 9.2
|
|
14
|
The existence of Primitive roots
|
R1: Section 9.3
|
|
Prerequisites
|
-
|
|
Language of Instruction
|
English
|
|
Responsible
|
Assoc. Prof. Dr. Faruk KARAASLAN
|
|
Instructors
|
-
|
|
Assistants
|
-
|
|
Resources
|
R1. Rosen, K. H. (2011). Elementary number theory. London: Pearson Education.
|
|
Supplementary Book
|
SR1. Hardy, G. H., & Wright, E. M. (1979). An introduction to the theory of numbers. Oxford university press.
SR2. Silverman, J. H. (2014). A friendly introduction to number theory. Pearson.
SR3. Kumanduri, R., & Romero, C. (1998). Number theory with computer applications. Pearson.
|
|
Goals
|
Teaching fundamental properties of integers to explain some problems that are easy to ask and still unsolved. To provide some idea about why generalizations have to be made.
|
|
Content
|
Division algorithm, Euler`s Phi function, Properties of congruence equations, Linear congruences and Chinese remainder theorem, Number of roots of Linear congruence equations, Lagrange and Wilson theorems
|
|
Program Learning Outcomes |
Level of Contribution |
|
1
|
Having advanced theoretical and applied knowledge in the basic areas of mathematics
|
3
|
|
2
|
Ability of abstract thinking
|
3
|
|
3
|
To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
|
3
|
|
4
|
Associating mathematical achievements with different disciplines and applying them in real life
|
-
|
|
5
|
Ability to work independently in a problem or project that requires knowledge of mathematics
|
2
|
|
6
|
Ability to work harmoniously and effectively in national or international teams and take responsibility
|
-
|
|
7
|
Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
|
2
|
|
8
|
To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
|
-
|
|
9
|
To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
|
-
|
|
10
|
Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
|
-
|
|
11
|
Being able to produce projects and organize events with social responsibility awareness
|
-
|
|
12
|
Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
|
-
|
|
13
|
Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
|
-
|
|
14
|
Being conscious of acting in accordance with social, scientific, cultural and ethical values
|
-
|