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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;
|
| Course Description |
|
| 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 | Preliminaries: Groups, rings and algebras. | “Invariant Theory” by Mara Neusel, AMS. |
| 2 | Linear representations of groups. | “Invariant Theory” by Mara Neusel, AMS. |
| 3 | Rings of invariants. | “Invariant Theory” by Mara Neusel, AMS. |
| 4 | Permutation representantions. | “Invariant Theory” by Mara Neusel, AMS. |
| 5 | Fundamental theorems. | “Invariant Theory” by Mara Neusel, AMS. |
| 6 | Construction of invariants. | “Invariant Theory” by Mara Neusel, AMS. |
| 7 | Noether's bound. | “Invariant Theory” by Mara Neusel, AMS. |
| 8 | Reflection groups and invariants. | “Invariant Theory” by Mara Neusel, AMS. |
| 9 | Vector invariants. | “Invariant Theory” by Mara Neusel, AMS. |
| 10 | Modules and operations. | “Invariant Theory” by Mara Neusel, AMS. |
| 11 | Maschke's theorem and Schur's lemma. | “Invariant Theory” by Mara Neusel, AMS. |
| 12 | Finite generatedness. | “Invariant Theory” by Mara Neusel, AMS. |
| 13 | HilbertPoincare series, Molien's theorem. | “Invariant Theory” by Mara Neusel, AMS. |
| 14 | System of parameters. | “Invariant Theory” by Mara Neusel, AMS. |
| 15 | Review. | |
| 16 | Review of the Semester |
| Course Notes/Textbooks | “Invariant Theory” by Mara Neusel, AMS. |
| Suggested Readings/Materials | “Polynomial Invariants of Finite Groups” by Larry Smith, AMS.“Classical Invariant Theory” by Peter J. Olver, Cambridge. |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | 10 | 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 | 15 | 1 | |
| Field Work | |||
| Quizzes / Studio Critiques | |||
| Portfolio | |||
| Homework / Assignments | 10 | 3 | |
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 2 | 15 | |
| Final Exams | 1 | 20 | |
| Total | 143 |
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, | X | ||||
| 4 | To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, | X | ||||
| 5 | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, | X | ||||
| 6 | To be able to criticize and renew her/his own models and solutions, | X | ||||
| 7 | To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, | X | ||||
| 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, | |||||
| 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, | X | ||||
| 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