Course Outline - Faculty of Arts and Sciences

COURSE CODE MATH106
COURSE TITLE LINEAR ALGEBRA
COURSE TYPE Undergraduate course
EASTERN MEDITERRANEAN UNIVERSITY
FACULTY OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS
2012-2013 SPRING SEMESTER
LECTURER(S) Gr 01 : Müge SAADETOĞLU (office AS 243, Ext. 1030)
Gr 02 : Ersin KUSET BODUR (office AS 247, Ext. 1424)
ASSISTANT Hülya DEMEZ (office AS 249, Ext. 2197)
Sedef EMİN (office AS 371, Ext. 1420)
EMU CREDITS (3, 1) 3
ECTS CREDITS
PREREQUISITES None
COREQUISITES None
WEB LINK http://brahms.emu.edu.tr/msaadetoglu
http://brahms.emu.edu.tr/ersin
TEXTBOOK Howard Anton, Chris Rorres, Elementary Linear Algebra, 7th Ed, by, John Wiley
& Sons, Inc.
OTHER REFERENCES Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence, Linear Algebra, 2 nd
Ed. Prentice-Hall International, Inc.
TIME TABLE Gr 01 : Tuesday 14:30 – 16:20 in CL 103, Thursday 08:30 - 10:20, in CL A23
Gr 02 : Tuesday 08:30 – 10:20 in CL 109, Wednesday 14:30-16:20 in CL203
OFFICE HOUR will be announced later
AIMS & OBJECTIVES The main aim of this course is to provide students with an introductory yet
comprehensive overview of matrices, operations with matrices and their
applications in solving linear systems.
It also provides an opportunity to see basic concepts of linear algebra like linear
spaces, linear transformations and some other related concepts as well as
applications of earlier methods for solving linear systems to basis and
dimension problems and kernel and image of linear transformations problems.
CATALOGUE DESCRIPTION Systems of linear equations: elementary row operations, echelon forms,
Gaussian elimination method; Matrices: elementary matrices, invertible
matrices, symmetric matrices; Determinants: adjoint and inverse matrices,
Cramer’s rule. Vector spaces: linear independence, basis and dimension,
Euclidean spaces. Linear mappings: matrix representations, changes of bases;
Inner product spaces: Cauchy-Schwarz inequality, Gramm-Schmidt
orthogonalization; Eigenvalues and eigenvectors: characteristic polynomials,
Diagonalization.

GRADING CRITERIA Midterm 1 : 27% PERIOD April 03-13, TBA by the University Exam Committee
Midterm 2 : 27% PERIOD May 6, 2013 Monday 16:30- 18:00
Final : 40% PERIOD May 27- June 11, TBA by the University Exam Committee
Attendance: 6%
METHOD OF ASSESSMENT 85–100 (A); 80–84 (A-); 75–79 (B+); 70–74 (B); 66–69 (B-);
63–65 (C+); 60–62 (C); 57–59 (C-); 54–56 (D+); 50–53 (D);
45–49 (D- /FAIL); 0-44 (F/FAIL).
TEACHING METHOD Lectures and assignments.
RELATION TO OTHER COURSES This course is related with courses such as Abstract Algebra, Functional
Analysis, and Differential Equations.
GENERAL LEARNING OUTCOMES
On successful completion of this course, all students will have developed knowledge and understanding of:
- Matrices, matrix operations and related concepts and problems;
- Linear systems and various methods for solving the linear systems;
- Basic concepts of Linear Algebra such as vector spaces, subspaces, linear mappings, linear
independence and basis and dimension.
- Angle and orthogonality in inner product spaces, orthogonal basis and Gram-Schmidt
Process.
On successful completion of this course, all students will have developed their skills in:
- Manipulating matrices and matrix operations, solving linear systems
- Understanding algorithms as a tool to answer mathematical problems.
- Improving their critical thinking in making definitions and showing their logic connections.
Understanding Linear Algebra as a tool of modelling.
On successful completion of this course, all students will have developed their appreciation of and respect for
values and attitudes regarding the issues of:
- Mathematical thinking
- Critical thinking.
- Communication with other peoples.
Week Week 1
1
Feb 14-16
Week Week 2
2
Feb 18-22
Week Week 3
3
Feb 25- Mar 01
Week Week 4
4
March 04-08
Week Week 5
5
March 11-15
COURSE COURSE OUTLINE
OUTLINE
Chapter Chapter 1
1
1.3 Matrices and Matrix Operations
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination
1.4 Inverses; Rules of Matrix Arithmetic
1.5 Elementary Matrices and a Method for Finding A 1 −
1.6 Further Results on Systems of Equations and Invertibility
1.7 Diagonal, Triangular and Symmetric Matrices
Chapter Chapter 2
2
2.1 The Determinant Function
2.2 Evaluating Determinants by Row Reduction

Week Week 6
6
March 18-22
Week Week 7
7
March 25-29
Week Week 8
8
April 01-02
April 03-05
Week Week 9
9
April 08-13
Week Week 10
10
April 15-19
Week Week 11
11
April 22-26
Week Week 12 12
12
April 29- May 03
Week Week 13
13
May 06-10
Week Week 14
14
May 13-17
Week Week 15
15
May 20-23
Weeks Weeks 16 16-18 16 18
May 27- June 11
ACADEMIC HONESTY
2.3 Properties of the Determinant Function
2.4 Cofactor Expansion; Cramer’s Rule
Chapter Chapter 4
4
4.1 Euclidean n-Space
4.2 Linear Transformations from RRRR n
to RRRR m
MIDTERM MIDTERM MIDTERM MIDTERM Examinations
Examinations
Examinations
Examinations
MIDTERM MIDTERM MIDTERM MIDTERM Examinations
Examinations
Examinations
Examinations
4.3 Properties of Linear Transformations from RRRR n
to RRRR m
Chapter Chapter 5
5
5.1 Real Vector Spaces
5.2 Subspaces
5.3 Linear Independence
5.4 Basis and Dimension,
5.5 Row Space, Column Space and Nullspace
5.6 Rank and Nullity
Chapter Chapter 6
6
6.1 Inner Products
6.2 Angle and Orthogonality in Inner Product Spaces
6.3 Orthonormal Bases; Gram-Schmidt Process
Chapter Chapter 7
7
7.1 Eigenvalues, Eigenvectors
7.2 Diagonalization
Final Final Final Final Examinations
Examinations
Examinations
Examinations
Copying from others or providing answers or information (written or oral) to others is cheating. Copying from
another student’s paper or from another text without written acknowledgement is plagiarism. According to
University’s bylaws cheating and plagiarism are serious offences resulting in a failure from exam or project
and disciplinary action (which includes an official warning or/and suspension from the university for up to one
semester).
IMPORTANT NOTES
• Attendance is compulsory. Any student who has poor attendance and/or misses and examination
without providing valid excuse will be given NG grade.
• Students missing an examination should provide a valid excuse within three days following the
examination they missed. Make-up exams will be given after the final exams.
• The MAKE-UP for the Final and the RESIT exam for the course will be given on June 19-21, 2013. (The
date and the time will be announced by the University Exam Committee).
• The Make-up exams and the Resit exam will cover all topics from Weeks 1- 15.