MATH476 ALGEBRAIC CURVES
| Course Code: | 2360476 |
| 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: | Assoc.Prof.Dr. ALİ ULAŞ ÖZGÜR KİŞİSEL |
| Offered Semester: | Fall Semesters. |
Course Objectives
This course is a first introduction to algebraic geometry, through the classical and important topic of algebraic curves. The topic of algebraic curves is central in the development of modern day mathematics and also has many applications. It is expected that students will be able to see the harmonious appearance of several concepts that they learned about in previous courses and appreciate the unity of the subject.
Course Content
Affine and projective plane curves, local properties of plane curves, multiple points, intersection numbers, Bezout`s theorem, Noether`s fundamental theorem. Applications to some enumerative geometry problems. Prerequisite: 2360 367 and 2360 353.
Course Learning Outcomes
By the end of this course, a student will:
- make use of the correspondence between algebraic varieties over an algebraically closed field k and finitely generated commutative k-algebras without nilpotents,
- determine basic properties of a given algebraic curve, compute its projective closure, degree, genus, singular and regular points,
- use Bezout’s theorem in order to prove various results including those about linear systems,
- understand and use the group law on an elliptic curve,
- resolve singularities using blow-ups,
- make computations and carry out proofs using the Riemann-Roch theorem.
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