MATH 490 | Course Introduction and Application Information - Department of Mathematics

Course Name

Introduction to Algebraic Geometry

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 490	Fall/Spring	3	0	3	6

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	First Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	-
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Dr. Öğr. Üyesi Sevin GÜMGÜM
Assistant(s)	Araş. Gör. Gökçe ÖZALTUN Araş. Gör. Ayşe BELER

Course Objectives

To introduce fundamental topics of algebraic geometry.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	will be able to define variety.
2	will be able to relate varieties and ideals.
3	will be able to explain geometric problems with algebraic methods.
4	will be able to apply algebraic methods to geometric problems.
5	will be able use fundamental theorems.

Course Description

This course covers some fundamental topics about algebraic varieties. Projective geometry is also introduced and as a final topic homogeneous invariants of finite groups are studied. Algebraic geometry is a central topic which has tight connections with number theory, singularity theory, Diophantine problems. Prerequisites for this course are abstract algebra and multivariate calculus.

Course Category	Core Courses
	Major Area Courses	X
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Preliminaries from algebra: Groups, rings	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
2	Ideals, varieties	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626Geometry” by Miles Reid, Cambridge.
3	Plane conics and their classifications	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
4	Cubics and group law	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
5	Curves and their genus	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
6	Affine varieties	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
7	Hilbert's Nullstellensatz	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
8	Functions on varieties	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
9	Projective geometry	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
10	Rational and birational maps	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
11	Tangent spaces	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
12	Blowup	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
13	Invariant theory of finite groups	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
14	Generators for the ring of invariants	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
15	Semester Review
16	Final Exam

Course Notes/Textbooks	“Undergraduate Algebraic Geometry” by Miles Reid, Cambridge University Press, 1st Edition, 2010, ISBN-13: 978-0521356626
Suggested Readings/Materials	“Ideals, Varieties, and Algorithms” by D. Cox, J. Little, and D. O'Shea, Springer, 3rd Edition, 2008. ISBN-13: 978-0387356501

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	10	20
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	2	40
Final Exam	1	40
Total

Weighting of Semester Activities on the Final Grade	12	60
Weighting of End-of-Semester Activities on the Final Grade	1	40
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	10	3	30
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	2	20	40
Final Exam	1	20	20
		Total	180

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.		-	-	-	X	-
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.		-	-	X	-	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.		-	-	-	-	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.		-	-	X	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.		-	-	-	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.		-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.		-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.		-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.		-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.		-	-	-	X	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.		-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.		-	-	-	-	-