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| MATL7400 | Elementary Geometry of Algebraic Curves | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Hüsnü Anıl ÇOBAN | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | With this course, it is aimed to introduce algebraic curves, to examine some properties of these curves, to examine the solution of the equivalence problem and to introduce affine algebraic curves. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Define algebraic curves | | 1,3, | | PO - 2 : | Know the differences between algebraic curves and transcendental curves | | 1,3, | | PO - 3 : | Recognize affine equivalent curves | | 1,3, | | PO - 4 : | Know the properties of affine curves | | 1,3, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Parametrized and implicit algebraic curves, Algebraic Curves in Planar Kinematics, General Affine Planes and Algebraic Curves, Zero Sets of Algebraic Curves, Factorization in Domains, Univariate Polynomials, Multivariate Polynomials, Homogeneous Polynomials, Formal Differentiation, Affine Maps, Affine Equivalent Curves, Affine Invariants: Degree, Centers, Classification for Affine Conics, Delta Invariants, Intersection Numbers, Multiplicity of a Point on a Curve, Singular Points, Generalities about Tangents, Tangents at Simple Points, Tangents at Double Points, Tangents at Points of Higher Multiplicity, Rational Affine Algebraic Curves, Diophantine Equations, Conics and Integrals |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Parametrized and Implicit Algebraic Curves, Algebraic Curves in Planar Kinematics | | | Week 2 | General Affine Planes and Algebraic Curves, Zero Sets of Algebraic Curves | | | Week 3 | Factorization in Domains, Univariate Polynomials | | | Week 4 | Multivariate Polynomials, Homogeneous Polynomials | | | Week 5 | Formal Differentiation, Affine Maps | | | Week 6 | Affine Equivalent Curves, Affine Invariants: Degree, Centers | | | Week 7 | Classification for Affine Conics | | | Week 8 | Delta Invariants | | | Week 9 | Midterm | | | Week 10 | Intersection Numbers, Multiplicity of a Point on a Curve | | | Week 11 | Singular Points, Generalities about Tangents | | | Week 12 | Tangents at Simple Points, Tangents at Double Points | | | Week 13 | Tangents at Points of Higher Multiplicity, Rational Affine Algebraic Curves | | | Week 14 | Diophantine Equations | | | Week 15 | Conics and Integrals | | | Week 16 | Final Exam | | | |
| 1 | Gibson, C.G., Elementary Geometry of Algebraic Curves, 1999, Chambridge University Press. | | | |
| 1 | Kuntz, E., Introduction to Plane Algebraic Curves, 2004, Birkhauser. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 22.11.2021 | 2 saat | 50 | | End-of-term exam | 16 | 10.01.2022 | 2 saat | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Arasınav için hazırlık | 6 | 2 | 12 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 8 | 2 | 16 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 130 |
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