Linear Algebra I (MATH231) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Linear Algebra I MATH231 3. Semester 4 0 0 4 7
Pre-requisite Course(s)
None
Course Language English Compulsory Departmental Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Drill and Practice. The aim of the course is to provide the basic linear algebra background needed by mathematicians. Many concepts in the course will be presented in the familiar setting of the plane and n-dimensional space, and will be developed with an awareness of how linear algebra is applied. The students who succeeded in this course; understand basics of matrix theory, solve linear systems of equations using matrices, understand fundamentals of vector spaces, understand the theory of linear transformations. Matrices and linear equations, determinants, vector spaces, linear transformations.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Matrices, Matrix Operations, Algebraic Properties of Matrix Operations, Partitioned Matrices, Special Types of Matrices pp. 16-31, 36-40
2 Elementary Row Operations, Row Equivalence, Equivalent Matrices, Invertible Matrices pp. 44-59
3 Systems of Linear Equations pp. 65-79
4 Determinants, Cramer’s Rule pp. 90-106
5 Vector Spaces pp. 129-140
6 Subspaces, Span pp. 144-147, 154-157
7 Linear Independence, Basis and Dimension pp. 163-180
8 Coordinates, Isomorphisms pp. 182-187
9 Subspaces associated with a matrix (Row space, Column space, Homogeneous Systems), Rank of a Matrix pp. 192-201
10 Intersections, Sums, Direct Sums, Quotient Spaces pp. 202-214
11 Linear Transformations pp. 228-239
12 Kernel, Image, Injectivity, Surjectivity pp. 242-262
13 Dual Space (Theorem and Definition 3.3.7), The Algebra of Linear Operators pp. 265-266, 269-273
14 Matrix of a Linear Transformation, Transition Matrix, Similarity pp. 279-288
15 General Review
16 Final Exam

Sources

Course Book 1. Cemal Koç, Linear Algebra I, METU Ankara, 1998. 2. B. Kolman and D.R. Hill, Elementary Linear Algebra, 8th Edition, Prentice-Hall, New Jersey, 2004. 3. T. S. Blyth and E. F. Robertson, Basic Linear Algebra, Springer Undergraduate Mathematics Series, Springer-Verlag. 4. K. Hoffman and R. Kunze, Linear Algebra, 2nd Edition, Prentice-Hall, New Jersey, 1971.

Evaluation System

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 35 100

Course Category

Core Courses X

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 4 64
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 4 20
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 15 15