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 Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends 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