Computer Engineering (English)
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

General course introduction information

Course Code: MATH215
Course Name: Mathematics III
Course Semester: Spring
Course Credits:
Theoretical Practical Credit ECTS
2 2 3 6
Language of instruction: EN
Course Requisites: MATH113 - Mathematics I
Does the Course Require Work Experience?: No
Type of course:
Course Level:
Bachelor TR-NQF-HE:6. Master`s Degree QF-EHEA:First Cycle EQF-LLL:6. Master`s Degree
Mode of Delivery: Face to face
Course Coordinator : Dr.Öğr.Üyesi MESERET TUBA GÜLPINAR
Course Lecturer(s): Prof. Dr. VASFİ ELDEM
Prof. Dr. SEZGİN SEZER
Prof. Dr. HASAN ÖZEKES
Course Assistants:

Course Objective and Content

Course Objectives: The aim of this course to understand basic concepts of linear algebra ( systems of linear equations and their solutions, the operations of the matrix and vector algebra, evaluations of the determinants and inverse matrix, properties of determinants, Cramer’s Rule, vector spaces, subspaces, linear independence, basis, row space, column space, null space, rank, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces, orthogonality, Gram-Schmidt process, least squares, orthogonal diagonalization and singular value decomposition) and solve problems about it.

Course Content: This course will investigate systems of linear equations and their solutions, the operations of the matrix and vector algebra, evaluations of the determinants and inverse matrix, properties of determinants, Cramer’s Rule, vector spaces, subspaces, linear independence, basis, row space, column space, null space, rank, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces, orthogonality, Gram-Schmidt process, least squares, orthogonal diagonalization and singular value decomposition.

Learning Outcomes

The students who have succeeded in this course;
Learning Outcomes
1 - Knowledge
Theoretical - Conceptual
1) Able to calculate the set of all solutions for systems of linear equations if it exists, by using row echelon or reduced row echelon forms. Calculate the inverse of a square matrix, if it exists, using reduced row echelon form or elementary matrices and characterize invertible matrices.
2) Calculate the determinant of a square matrix. Use Cramers Rule to solve linear systems of equations. Determine the linear dependence or independence of a set of nonzero vectors.
3) Identify vectors spaces and subspaces and linear transformations between vector spaces. Calculate basis for null spaces and images of linear transformations. Calculate the representation of linear transformation under various bases.
4) Able to calculate the eigenvalues and the corresponding eigenvectors in order to diagonalize a square matrix by similarity transformation. Characterize diagonalizable matrices
5) Able to use Gram-Schmidt Process to obtain a set of orthogonal vectors and diagonalize a symmetric matrix using orthogonal matrices. Calculate orthogonal projections onto a given subspace and solve the least squares problems. Calculate Singular Value Decomposition of a given matrix.
2 - Skills
Cognitive - Practical
3 - Competences
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Lesson Plan

Week Subject Related Preparation
1) Syllabus. Systems of linear equations. Elementary row operations. Gauss-Jordan Elimination Lecture Notes
2) Matrix Algebra Lecture Notes
3) Matrix Algebra Lecture Notes
4) Determinants Lecture Notes
5) Determinants Lecture Notes

Sources

Course Notes / Textbooks: Linear Algebra and Its Applications, 5th Edition
David C. Lay, Stephan R. Lay, Judi J. McDonald
Pearson Education Limited
References: Lecture notes - Ders notları

Course-Program Learning Outcome Relationship

Learning Outcomes

1

2

3

4

5
Program Outcomes
1) Adequate knowledge in mathematics, natural sciences, and computer engineering; ability to apply theoretical and applied knowledge in these areas to model and solve engineering problems.
2) Ability to identify, define, formulate, and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.
3) Ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic, environmental, sustainability, manufacturability, ethical, health, safety, social, and political issues, depending on the nature of the design.)
4) Ability to develop, select, and use modern techniques and tools necessary for computer engineering applications; ability to effectively use information technologies.
5) Ability to design experiments, conduct experiments, collect data, analyze and interpret results for the investigation of computer engineering problems.
6) Ability to work effectively both individually and in intra-disciplinary and multi-disciplinary teams.
7) Ability to communicate effectively in oral and written form; proficiency in at least one foreign language.
8) Recognition of the need for lifelong learning; ability to access information, follow developments in science and technology, and continuously improve oneself.
9) Awareness of professional and ethical responsibility.
10) Knowledge of business practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
11) Knowledge of the universal and societal impacts of computer engineering practices on health, environment, and safety, as well as contemporary issues; awareness of the legal consequences of engineering solutions.

Course - Learning Outcome Relationship

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Adequate knowledge in mathematics, natural sciences, and computer engineering; ability to apply theoretical and applied knowledge in these areas to model and solve engineering problems.
2) Ability to identify, define, formulate, and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. 1
3) Ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic, environmental, sustainability, manufacturability, ethical, health, safety, social, and political issues, depending on the nature of the design.) 4
4) Ability to develop, select, and use modern techniques and tools necessary for computer engineering applications; ability to effectively use information technologies. 2
5) Ability to design experiments, conduct experiments, collect data, analyze and interpret results for the investigation of computer engineering problems.
6) Ability to work effectively both individually and in intra-disciplinary and multi-disciplinary teams. 5
7) Ability to communicate effectively in oral and written form; proficiency in at least one foreign language.
8) Recognition of the need for lifelong learning; ability to access information, follow developments in science and technology, and continuously improve oneself.
9) Awareness of professional and ethical responsibility.
10) Knowledge of business practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development. 3
11) Knowledge of the universal and societal impacts of computer engineering practices on health, environment, and safety, as well as contemporary issues; awareness of the legal consequences of engineering solutions.

Learning Activity and Teaching Methods

Lesson
Reading
Homework
Problem Solving
Q&A / Discussion

Assessment & Grading Methods and Criteria

Written Exam (Open-ended questions, multiple choice, true-false, matching, fill in the blanks, sequencing)
Homework

Assessment & Grading

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 5 % 20
Midterms 2 % 40
Final 1 % 40
total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
total % 100

Workload and ECTS Credit Grading

Activities Number of Activities Duration (Hours) Workload
Course Hours 15 4 60
Study Hours Out of Class 15 3 45
Homework Assignments 5 5 25
Midterms 2 10 20
Final 1 15 15
Total Workload 165