APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5003 | Linear Algebra and Its Applications | Fall Spring |
3 | 0 | 3 | 12 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | Turkish |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Prof. Dr. ERTUĞRUL ÖZDAMAR |
Recommended Optional Program Components: | None |
Course Objectives: | The purpose of this course is to give the basic concepts of linear algebra with applications to students who intend to study applied mathematics. |
The students who have succeeded in this course; The students who succeeded in this course; o will be able to describe solution methods for systems of linear equations. o will be able to apply the fundamental properties of determinants to solve the systems of equations, inverting matrices and also to decide whether a subset is linearly independent or not, spans the space or does not. o will be able to apply concepts of vector spaces to all relating areas including matrices. o will be able to formulate the change of basis , to obtain an orthonormal basis and to diagonalize a square matrix, to develop matrix representation of linear mappings. o will be able to distinguish the subsets that span the space or not , are linear independent or not, and the matrices are orthogonal diagonalizable or not, mappings are linear or not. o will be able to use determinants to solve the systems of equations, inverting matrices and also to evaluate the eigen vectors , effectively. o will be able to write equations of Curves and Surfaces passing through given points and apply linear algebra to Leontief economic model applications, Geometric Programming, Cryptography. |
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Week | Subject | Related Preparation |
1) | Systems of linear equations, network analysis, Balancing Chemical Equations, Design of Traffic Patterns | |
2) | Matrices, LU decomposition, | |
3) | Vector spaces,subspaces, bases and the dimension | |
4) | Determinants, multilinear functions , Cramer systems | |
5) | Inner product spaces, orthonormal sets, QR decomposition, least squares method | |
6) | Linear mappings, space of linear mappings | |
7) | Matrices and linear mappings | |
8) | Matrix polynomials, characteristic values, characteristic vectors, diagonalization of matrices | |
9) | Applications; genetics, population problems | |
10) | Qudratic forms, geometric applications | |
11) | Special mappings of iner product spaces | |
12) | Equation of curves and surfaces passing through given points, geometric programming | |
13) | Cryptography | |
14) | Leontief economical models |
Course Notes / Textbooks: | . |
References: | . |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | 14 | % 5 |
Homework Assignments | 2 | % 10 |
Midterms | 1 | % 35 |
Final | 1 | % 50 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 50 | |
PERCENTAGE OF FINAL WORK | % 50 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Homework Assignments | 2 | 40 | 80 |
Midterms | 1 | 30 | 30 |
Final | 1 | 40 | 40 |
Total Workload | 192 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | 3 |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | 4 |
3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | 2 |
4) | Ability to make individual and team work on issues related to working and social life. | 4 |
5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | 3 |
6) | Ability to use mathematical knowledge in technology. | 5 |
7) | To apply mathematical principles to real world problems. | 4 |
8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | 5 |
9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | 4 |
10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | 4 |
11) | 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. | 3 |
12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, | 5 |