COURSE UNIT TITLE

: LINEAR ALGEBRA I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 2037 LINEAR ALGEBRA I 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 aim of this course is to give the basic subjects of linear algebra such as solutions of linear systems of equations, the concepts of matrices, determinants, vectors in n dimension and vector spaces, linear transformations and operators.

Learning Outcomes of the Course Unit

1   be able to analyse linear systems of equations using vectors and matrices.
2   be able to use the matrix algebra, inverse of matrices, elementary matrices and transpose of a matrix.
3   be able to apply determinant and its properties.
4   be able to understand vectors, linear dependence and linear independence of vectors, orthogonality of vectors.
5   be able to analyse vector spaces and subspaces using bases for subspaces, the dimension of a subspace, nullspace, column space and row space of a matrix, orthogonal complements of subspaces, orthogonal and orthonormal bases for subspaces.
6   be able to use linear transformations, their matrices with respect to bases, the Change-of-Basis formula for the matrix of a linear transformation and the orthogonal projection map onto a subspace.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Vectors and Matrices; Dot Product; Hyperplanes in the n-dimensional space Rn.
2 Systems of Linear Equations and Gaussian Elimination.
3 Row-Reduced Echelon Form of a Matrix; The Theory of Linear Systems.
4 Matrix Algebra; Matrix Operations.
5 Linear Transformations.
6 Inverse Matrices; Elementary Matrices.
7 Transpose.
8 Vector Spaces; Subspaces of the n-dimensional space Rn.
9 The Four Fundamental Subspaces Corresponding to a Matrix: Nullspace, Row Space, Column Space and Left Nullspace.
10 Linear Independence and Basis; Coordinates; Dimension and Its Consequences.
11 Projections and Linear Transformations: Inconsistent Systems and Projection; Orthogonal Bases.
12 The Matrix of a Linear Transformation and the Change-of-Basis Formula; Representation of Linear Transformations by Matrices.
13 Determinants; Its Properties.
14 Cofactors and Cramer's Rule; Signed Area in the plane R2 and Signed Volume in the 3-dimensional space R3.

Recomended or Required Reading

Textbook(s): Linear Algebra: A Geometric Approach, 2nd Edition; T. Shifrin, M.R. Adams, W.H. Freeman and Company, New York, 2010.

Supplementary Book(s):
1- Introduction to Linear Algebra, 5th Edition; Gilbert Strang, Wellesley-Cambridge Press, 2016.
2-Linear Algebra, 2nd Edition; Serge Lang, ADDISON-WESLEY PUBLISHING COMPANY.
3-Linear algebra, 4th Edition; S.H.Friedberg, A.J.Insel, L.E.Spence, Pearson, 2014.

Materials: Instructor's lecture notes and presentations

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50


Further Notes About Assessment Methods

1 Midterm Exam
Final Exam

Assessment Criteria

%50 (Midterm examination) +%50 (Final examination)

Language of Instruction

English

Course Policies and Rules

You can be successful in this course by studying from your textbooks and lecture notes on the topics to be covered every week, coming to class by solving the given problems, establishing the concepts by discussing the parts you do not understand with your questions, learning the methods, and actively participating in the course.

Contact Details for the Lecturer(s)

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

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 4 56
Preparation for final exam 1 30 30
Preparation for midterm exam 1 20 20
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 166

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1554453
LO.2555453
LO.3554453
LO.445444
LO.544434
LO.644334

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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