COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Introduction to Invariant Theory
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 488
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
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives To introduce the invariant theory which has a very high impact on other branches of mathematics.
Learning Outcomes The students who succeeded in this course;
  • will be able to describe a linear representation of a group.
  • will be able to compute the invariants of given degree.
  • will be able to relate permutation invariants with linear invariants.
  • will be able to construct the ring invariants.
  • will be able to compute Hilbert ideal.
Course Description This course provides an introduction to invariance theory. Topics include: linear representations, algebra, invariance rings, permutation invariants, generators, boundaries on generators, construction of invariants, system parameters and rational invariants.
Related Sustainable Development Goals

 



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 Preliminaries: Groups, rings and algebras “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
2 Linear representations of groups “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
3 Rings of invariants “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
4 Permutation representantions “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
5 Fundamental theorems “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
6 Construction of invariants “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
7 Noether's bound “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
8 Reflection groups and invariants “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
9 Vector invariants “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
10 Modules and operations “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
11 Maschke's theorem and Schur's lemma “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
12 Finite generatedness “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
13 HilbertPoincare series, Molien's theorem “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
14 System of parameters “Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327
15 Semester Review
16 Final Exam
Course Notes/Textbooks

“Invariant Theory” by Mara Neusel, American Mathematical Society, 2006. ISBN-13: 978-0821841327

Suggested Readings/Materials

 

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
12
60
Weighting of End-of-Semester Activities on the Final Grade
1
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
14
3
42
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
10
3
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
20
Final Exams
1
20
    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.

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.

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