COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Linear Algebra II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 106
Spring
2
2
3
6
Prerequisites
 MATH 105To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives Linear Algebra II course is theoretic course, which deals with linear vector spaces and fundamental theories related with these spaces. The scope of this course is to derive different algebraic techniques and to utilize these techniques in a variety of mathematical areas.
Learning Outcomes The students who succeeded in this course;
  • will be able to identify bases and dimensions of vector spaces.
  • will be able to employ rank of a matrix.
  • will be able to analyze row, column, null spaces.
  • will be able to use linear transformations.
  • will be able to analyze ortogonallity, ortogonal and ortonormal sets and ortogonal complements.
  • will be able to define inner product spaces.
  • will be able to identify eigenvalues and related eigenvectors.
  • will be able to employ diagonalization.
Course Description In this course, the concepts of bases, dimensions, linear transformations, orthogonality, inner product spaces, eigenvalues, eigenvectors and diagonalization are discussed.

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Vector spaces and subspaces "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 4.1.
2 Null spaces, column spaces and linear transformations "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 4.2.
3 Linearly independent sets, bases "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 4.3.
4 Coordinate systems "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 4.4.
5 The dimension of a vector space, rank "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 4.5, 4.6.
6 Change of basis "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 4.7.
7 Eigenvectors and eigenvalues "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 5.1, 5.2.
8 Diagonalization "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 5.3.
9 Eigenvectors and linear transformations "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 5.4.
10 Inner product, length and orthogonality "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 6.1.
11 Orthogonal sets "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 6.2.
12 Orthogonal projections "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 6.3.
13 The Gram-Schmidt process "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 6.4.
14 Least squares problems "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition. Section 6.5.
15 Review of semester. "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition.
16 Review of semester. "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition.
Course Notes/Textbooks "Linear Algebra and Its Applications" by David C.Lay, Stephan R.Lay and Judi J. McDonald, Pearson, Global Edition.
Suggested Readings/Materials “Introductory Linear Algebra with applications” by Bernard Kolman, David R. Hill. Prentice Hall, 9th edition.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
2
60
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
4
64
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
16
4
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
9
Final Exams
1
19
    Total
165

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

X
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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