FACULTY OF ARTS AND SCIENCES
Department of Mathematics
SOCIAL MEDIA
MATH 472 | Course Introduction and Application Information
| Course Name |
Introduction to Computational Commutative Algebra
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|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 472
|
Fall/Spring
|
3
|
0
|
3
|
6
|
| Prerequisites |
None
|
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| Course Language |
English
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| Course Type |
Elective
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| Course Level |
First Cycle
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| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | ||||||
| Course Objectives | The main objective of this course is to provide an introduction to emerging area of computational commutative algebra. The course will cover basic computational techniques and algorithms in the area over multivariate polynomial rings. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | The main subjects of the course are monomial orders, Groebner basis, elimination theory, dimension theory, resultants, Zariski topology and geometry-algebra bridge, affine and projective varieties, and invariant theory. |
|
|
Core Courses | |
| Major Area Courses |
X
|
|
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Geometry, algebra and algortihms | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 1, pp1-47 |
| 2 | Monomial orders and Hilbert basis theorem | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 2, pp 49-81 |
| 3 | Groebner bases | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 2, pp 82-113 |
| 4 | Elimination, its geometry and implicitization | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 3, pp 115-136 |
| 5 | Resultants and related theorems | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 3, pp 137-167 |
| 6 | Hilbert's Nullstellensatz, ideal-variety correspondance | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 4, pp 169-192 |
| 7 | Decompositions of ideals and varities | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 4, pp 193-214 |
| 8 | Polynomial rings and quotients | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 5, pp 215-238 |
| 9 | Coordinate rings | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 5, pp 239-264 |
| 10 | Invariant theory | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 7, pp 317-335 |
| 11 | Syzygies | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 7, pp 336-355 |
| 12 | Projective geometry | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 8, pp 357-378 |
| 13 | Projective varieties | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 8, pp 379-407 |
| 14 | Bezout's theorem and dimension | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 Chapter 8, pp 408-438 |
| 15 | Semester Review | |
| 16 | Final Exam |
| Course Notes/Textbooks | "Ideals, Varietiesi and Algorithms" by D. Cox, J. Little, D. O'Shea, Springer UTM, 3rd Edition, 2007. ISBN: 978-0-387-35651-8 |
| Suggested Readings/Materials |
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 Exams | ||
| Midterm |
2
|
40
|
| Final Exam |
1
|
40
|
| Total |
| Weighting of Semester Activities on the Final Grade |
4
|
60
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
| Total |
ECTS / WORKLOAD TABLE
| 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 |
2
|
10
|
20
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
20
|
40
|
| Final Exam |
1
|
30
|
30
|
| Total |
180
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
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. |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
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| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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