MATH365 ELEMENTARY NUMBER THEORY I

Course Code:2360365
METU Credit (Theoretical-Laboratory hours/week):3 (3.00 - 0.00)
ECTS Credit:6.0
Department:Mathematics
Language of Instruction:English
Level of Study:Undergraduate
Course Coordinator:Assist.Prof.Dr EROL SERBEST
Offered Semester:Fall Semesters.

Course Objectives

At the end of the course students are expected to:

  • Know the basic properties of primitive roots and quadratic residues of an integer
  • Use indices to solve some congruences
  • Compute the Legendre symbol using Quadratic reciprocity law, and solve quadratic congruences using quadratic residues
  • Learn special properties of perfect numbers, Mersenne primes, Fermat numbers and Fibronacci numbers
  • Solve linear and quadratic Diophantine equations parametrically
  • Understand Fermat’s infinite descent argument while proving that a Diophantine equation has no solution
  • Learn how integers can be represented as sums of two or more squares
  • Find all solutions of Pell’s equation either using the primitive solution or by means of continued fractions
  • Use basic properties of infinite continued fractions

Course Content

Divisibility, congruences, Euler, Chinese Remainder and Wilson`s Theorems. Arithmetical functions. Primitive roots. Quadratic residues and quadratic reciprocity. Diophantine equations.


Course Learning Outcomes

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Program Outcomes Matrix

Level of Contribution
#Program Outcomes0123
1Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields.
2Can produce innovative thoughts and products.
3Can design mathematics related problems, devise solution methods and apply them when appropriate.
4Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly.
5Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak).
6Contributes to solving global, environmental and social problems either individually or as being part of a social group.
7Respects ethical values and rules; applies them in professional and social issues.
8Can work cooperatively in a team and also individually.
9Is responsive to life-long learning, improving his/her skills and abilities
10Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others

0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution