TR
11111

COURSE INTRODUCTION AND APPLICATION INFORMATION

dm.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Fall/Spring
Prerequisites
None
Course Language
Course Type
Elective
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s) -
Assistant(s) -
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • will be able to describe structure of a ring and quotient ring
  • will be able to compute generators of an ideal
  • will be able to translate problems between algebra and geometry
  • will be able to apply techniques of computational algebra in various applications
  • will be able to perform operations of ideal arithmetic
Course Description

 



Course Category

 Core Courses
Major Area Courses
X
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Geometry, Algebra and Algortihms Chapter 1, pp1-47
2 Monomial Orders and Hilbert Basis Theorem Chapter 2, pp 49-81
3 Groebner Bases Chapter 2, pp 82-113
4 Elimination, Its Geometry and Implicitization Chapter 3, pp 115-136
5 Resultants and related theorems Chapter 3, pp 137-167
6 Hilbert's Nullstellensatz, Ideal-Variety Correspondance Chapter 4, pp 169-192
7 Decompositions of Ideals and Varities Chapter 4, pp 193-214
8 Polynomial Rings and Quotients Chapter 5, pp 215-238
9 Coordinate Rings Chapter 5, pp 239-264
10 Invariant Theory Chapter 7, pp 317-335
11 Syzygies Chapter 7, pp 336-355
12 Projective Geometry Chapter 8, pp 357-378
13 Projective Varieties Chapter 8, pp 379-407
14 Bezout's Theorem and dimension Chapter 8, pp 408-438
15 Review
16 Review
Course Notes/Textbooks Ideals, Varietiesi and Algorithms (Third Edition), D. Cox, J. Little, D. O'Shea, Springer UTM, 2007 ISBN 978-0-387-35651-8
Suggested Readings/Materials Using Algebraic Geometry, D. Cox, J. Little, D. O'Shea, Springer GTM, 2005 Combinatorial Commutative Algebra, E. Miller, B. Sturmfels, Springer GTM, 2005 A Singular Introduction to Commutative Algebra, G. M. Greuel, G. Pfister, Springer, 2008

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
2
20
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
2
40
Final Exam
1
40
Total

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

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
16
3
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
2
10
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
10
Final Exams
1
20
    Total
156

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods,
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials,
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,
6 To be able to criticize and renew her/his own models and solutions,
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way,
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

 X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

 X
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

 X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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