Algebraic Curves (MAE627)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE627
Semester	6
Course Title	Algebraic Curves
Independent Teaching Activities	Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes
Course Website (URL)	https://sites.google.com/site/apostolosthomamath/teaching/

Learning Outcomes

Learning outcomes	The students will acquire with the successful completion of the course the basic theory of Algebraic curves and the ability to solve problems on Algebraic curves.
General Competences	The course aim is for the student to acquire the ability in analysis and synthesis of knowledge in algebraic curves and produces free, creative and inductive thinking.

Syllabus

Affine plane, polynomial rings, unique Factorization Domains, resultants, Rational curves and Applications, Projective space, tangents, singular points, asymptotes. Intersection multiplicity, Bezout's Theorem, Linear Systems. Pascal's Theorem. Nine points Theorem. Inflection points. Elliptic Curves.

Teaching and Learning Methods - Evaluation

Delivery	Classroom (face-to-face)
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures (13X3) 39 Working independently 78 Exercises-Homeworks 33 Course total 150
Student Performance Evaluation	Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

Attached Bibliography

• Δ. Πουλάκης, Εισαγωγή στη γεωμετρία των αλγεβρικών καμπυλών, Εκδόσεις Ζήτη,ISBN 960-456-013-1, ISBN-13 978-960-456-013-4