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: | Assist.Prof.Dr BURAK KAYA |
| 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.