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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 2038 LINEAR ALGEBRA II COMPULSORY 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ENGIN MERMUT

Offered to

Mathematics (Evening) Mathematics

Course Objective

The focus of this course will be on abstract vector spaces, linear operators, canonical forms, inner product spaces and bilinear forms. Students will be expected to learn the important theorems of linear algebra and understand their proofs.

Learning Outcomes of the Course Unit

1   be able to identify eigenvalues and related eigenvectors. 2   be able to operate diagonalization. 3   be able to use linear operators. 4   be able to find the Jordan form of a matrix. 5   be able to define inner product spaces. 6   be able to apply inner product operation to Gram Schmidt orthogonalization process.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Polynomials. Invariant Subspaces. 2 Eigenvectors and Eigenvalues. 3 Triangular Form. Nilpotent Operators. 4 Jordan Canonical Form. 5 Polynomials of Matrices and Linear Operators. Minimal Polynomials. 6 Inner Product Spaces. Orthogonality. 7 Gram-Schmidt's Orthogonalization Process. 8 Midterm Exam 9 Linear Operators and Functionals on Inner Product Spaces. 10 Unitary Operators. Commutative Linear Operators. 11 Normal Operators. Orthogonal Projections. 12 Spectral Theory. Positive Operators. 13 Polar Decomposition. 14 Bilinear Forms. Symmetric and Skew-symmetric Bilinear Forms.

Recomended or Required Reading

Textbook(s): Linear Algebra, 2nd Edition; K. Hoffman, R. Kunze, Prentice-Hall, INC., Englewood Cliffs, New Jersey. Supplementary Book(s): Linear Algebra, 2nd Edition; Serge Lang, ADDISON-WESLEY PUBLISHING COMPANY. Materials: Lecture Notes.

Planned Learning Activities and Teaching Methods

Lecture notes. Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 FIN FINAL EXAM 4 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + ASG * 0.20 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + ASG * 0.20 + RST * 0.40

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail: engin.mermut@deu.edu.tr Phone: (232) 301 85 82

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 4 52 Preparations before/after weekly lectures 12 2 24 Preparing assignments 4 5 20 Preparation for quiz etc. 4 2,5 10 Preparation for final exam 1 30 30 Preparation for midterm exam 1 20 20 Final 1 2 2 Midterm 1 2 2 Quiz etc. 4 1 4 TOTAL WORKLOAD (hours) 164

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 PO.12 PO.13 LO.1 5 4 4 3 4 3 LO.2 5 4 4 3 5 3 LO.3 5 3 4 3 4 3 LO.4 4 3 4 3 4 LO.5 5 4 4 3 4 LO.6 5 4 4 3 4