Introduction to Number Theory(MAT364)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT364 | Introduction to Number Theory | 6 | 5 | 0 | 0 | 3 | 5 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | English |
| Course Type | Elective |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Ezgi KANTARCI OĞUZ ezgikantarcioguz@gmail.com (Email) |
| Assistant | |
| Objective | In this course, we will go over some introductory topics in number theory. |
| Content | Divisibility, Prime Numbers, Modular Arithmetics, Multiplicative Functions, Diaphontine Equations, Rational Approximations, Continued Fractions |
| Course Learning Outcomes | Understanding basic number theoretic structures and proof methods. |
| Teaching and Learning Methods | Lectures and problem solving in class, homework, exams |
| References | An Introduction to the Theory of Numbers-Ivan Niven, Herbert S. Zuckerman, Hugh L. Montgomery |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Divisibility, Euclidean Algorithm, Greatest Common Divisor Function |
| 2 | Primes, Fundamental Theory of Arithmetics |
| 3 | Binomial Theorem, Pascal Triangle |
| 4 | Modular Arithmetics |
| 5 | Solutions of modular equations, Chinese Remainder Theorem |
| 6 | Primitive Roots |
| 7 | Midterm |
| 8 | Greatest Integer Function |
| 9 | Multiplicative Functions |
| 10 | Möbius Inversion |
| 11 | Diophantine Equations |
| 12 | Markov Equation, Vieta Jumps |
| 13 | Farey Tree, Rational Approximations |
| 14 | Continued Fractions |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 15 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 16 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 13 | 30 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 25 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 1 | 5 |
| Make-up | 0 | 0 |
| Toplam | 15 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 13 | 3 | 39 |
| Working Hours out of Class | 13 | 1 | 13 |
| Assignments | 13 | 3 | 39 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 20 | 20 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Total Workload | 121 | ||
| Total Workload / 25 | 4.84 | ||
| Credits ECTS | 5 | ||