MATH123 INTRODUCTION TO NUMBER THEORY
| Course Code: | 2360123 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 4.5 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Assoc.Prof.Dr. TOLGA KARAYAYLA |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
At the end of the course students are expected to:
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Know the basic properties of greatest common divisors, apply the Euclidean algorithm to compute it and solve linear Diophantine equations,
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Learn the Fundamental Theorem of Arithmetic and use prime factorization to compute greatest common divisor, least common multiple etc. Of several integers,
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Find all solutions of linear congruences and systems of linear congruences (by means of Chinese remainder theorem),
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Know Fermat’s little theorem and its generalization Euler’s theorem and their consequences,
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Be able to derive formulas of and identities involving number theoretic functions in terms of the prime factorization of the integer,
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Learn important properties of Euler’s Phi function and be aware of its application to public key cryptography.
Course Content
Well ordering of integers, mathematical and strong induction, Divisibility, Division algorithm, Greatest common divisor, Euclidean algorithm, Linear Diophantine equations, Prime numbers, Fundamental theorem of arithmetic, General information about Goldbach conjecture and gaps between primes and Drichlet`s theorem, Congruence modulo n, Modular arithmetic, Linear congruences, Chinese remainder theorem, Fermat`s little theorem, Wilson`s theorem, Number theoretic functions, Tau and sigma functions, Greatest integer function, Moebius inversion, Euler`s phi function, Euler`s theorem and its applications to cryptography.
Course Learning Outcomes
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