Linear Algebra II (MATH232) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Linear Algebra II	MATH232	Area Elective	4	0	0	4	7

Pre-requisite Course(s)
MATH231

Course Language	English
Course Type	Elective Courses
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery
Learning and Teaching Strategies	Lecture, Question and Answer, Drill and Practice.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	Being a continuation of Math 231, the aim is to introduce the students to the very heart of the subject including topics such as inner product spaces and linear mappings on them, canonical (diagonal, triangular, Jordan, and rational) matrix forms of linear mappings, bilinear and quadratic forms.
Course Learning Outcomes	The students who succeeded in this course; understand the basics of inner product spaces, decompose a vector space as a direct sum of its subspaces, obtain special types of matrices representing a given linear map, understand and find eigenvalues and eigenvectors, determine if a matrix is diagonalizable, and if it is, diagonalize it, find bases for eigenspaces, find bases for dual space of a vector space, understand fundamentals of bilinear and quadratic forms.
Course Content	Eigenvalues and eigenvectors, elementary canonical forms, the rational and Jordan forms, inner product spaces, operators on Inner product spaces, bilinear forms.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Division in a Polynomial Ring, Prime Factorization, Factorization of Polynomials over C and R	pp. 1-17
2	Ideals, Matrices over Polynomials, Characteristic Polynomial and Minimal Polynomial	pp. 18-40
3	Eigenvalues and Eigenvectors, Diagonalization.	pp. 41-52
4	Normal Form of Polynomial Matrices, Equivalence of Characteristic Matrices and Similarity	pp. 66-81
5	Rational and Jordan Canonical forms	pp. 82-102
6	Normal Matrices, Real Symmetric Matrices	pp. 104-118
7	Hermitian Matrices, Positive Matrices, Standard Inner Products	pp. 119-132, 137-141
8	Unitary and Orthogonal Matrices, Reduction of Quadratic Forms, Orthogonal Similarity	pp. 142-160
9	Inner products, Norm and Orthogonality	pp. 162-178
10	Matrix Forms of Inner Products, Orthogonal and Orthonormal Basis, Orthogonal Projections	pp. 179-192
11	The Gram-Schmidt Orthogonalization process	pp. 193-194
12	Linear Operators and Their Adjoints on Inner Product Spaces, Normal Operators, Unitary Operators, Orthogonal Operators.	pp. 203-211
13	Linear Functionals on Inner Product Spaces	pp. 212-220
14	Bilinear Forms
15	General Review
16	Final Exam

Sources

Course Book	1. Topics in Linear Algebra, Cemal Koç, Doğuş University, Ankara, 2010
Other Sources	2. T. S. Blyth and E. F. Robertson, Further Linear Algebra, Springer-Verlag, London, 2002.
	3. K. Hoffman and R. Kunze, Linear Algebra, 2nd Edition, Prentice-Hall, New Jersey, 1971.
	4. T.S. Blyth and E.F. Robertson, Basic Linear Algebra, 2nd Edition, Springer-Verlag, London, 2002.
	5. B. Kolman and D. R. Hill, Elementary Linear Algebra, 9th Edition, Prentice-Hall, New Jersey, 2008.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	5	10
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	55
Final Exam/Final Jury	1	35
Toplam	8	100

Percentage of Semester Work	65
Percentage of Final Work	35
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Acquiring the skills of understanding, explaining, and using the fundamental concepts and methods of economics
2	Acquiring the skills of macro level economic analysis
3	Acquiring the skills of micro level economic analysis
4	Understanding the formulation and implementation of economic policies at the local, national, regional, and/or global level
5	Learning different approaches on economic and related issues
6	Acquiring the quantitative and/or qualitative techniques in economic analysis					X
7	Improving the ability to use the modern software, hardware and/or technological devices
8	Developing intra-disciplinary and inter-disciplinary team work skills					X
9	Acquiring an open-minded behavior through encouraging critical analysis, discussions, and/or life-long learning
10	Adopting work ethic and social responsibility
11	Developing the skills of communication.
12	Improving the ability to effectively implement the knowledge and skills in at least one of the following areas: economic policy, public policy, international economic relations, industrial relations, monetary and financial affairs.			X

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	14	28
Prepration of Final Exams/Final Jury
Total Workload			28