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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5063 INVARIANT THEORY ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR MURAT ALTUNBULAK

Offered to

Mathematics Mathematics

Course Objective

The purpose of this course is to provide the students with a firm grounding in the basics of classical invariant theory.

Learning Outcomes of the Course Unit

1   will be able to understand the concept of invariants. 2   will be able to describe the algebra of invariants. 3   will be able to identify the invariants of linear groups. 4   will be able to understand the concept of algebraic group and reductive group. 5   will be able to find the invariants of reflection groups.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Noetherian rings and modules 2 Krull dimension. 3 Linear representations and algebra of invariants. 4 Noether's bound for a number of generators. 5 Linearly reductive algebraic groups, finite generation of invariants. 6 Hilbert-Serre theorem. 7 Poincare series. Minimal resolution. 8 Midterm Exam 9 Hilbert syzygy theorem. 10 Molien's theorem. 11 Reflecting Hyperplanes. 12 Groups generated by pseudoreflections. 13 Polinomiality of invariant ring. 14 The Shephard-Todd theorem.

Recomended or Required Reading

Textbook(s): T.A. Springer, Invariant Theory, Springer-Verlag, 1977. Supplementary Book(s): 1-Peter J. Olver, Classical Invariant Theory (London Mathematical Society Student Texts), Cambridge University Press, Jan 13, 1999. 2-Jean A. Dieudonne, James B. Carrell, Invariant Theory, Old and New, Academic Press, New York and London, 1971. 3-Hanspeter Kraft, Claudio Procesi, Classical Invariant Theory, A primer, Lecture Notes.

Planned Learning Activities and Teaching Methods

Lecture Notes Problem Solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

Office: B-220 (Math. Dept.) Phone: (30)1 85 92

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 6 78 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparing assignments 2 10 20 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 193

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 4 4 3 3 4 3 3 3 4 3 LO.2 4 4 3 3 4 3 3 3 4 3 LO.3 4 4 3 3 4 3 3 3 4 3 LO.4 4 4 3 3 4 3 3 3 4 3 LO.5 4 4 3 3 4 3 3 3 4 3