DEGREE PROGRAMS  Associate's Degree (Short Cycle)  Bachelor’s Degree (First Cycle)  Master’s Degree (Second Cycle)

Course Description Course Name : Introduction To Matrix Theory Course Code : MT 401 Course Type : Optional Level of Course : First Cycle Year of Study : 4 Course Semester : Fall (16 Weeks) ECTS : 5 Name of Lecturer(s) : Asst.Prof.Dr. DİLEK KAHYALAR Learning Outcomes of the Course : knows the basic terms about matrices and their special types Calculate the Laplace Expansion by using algebraic component and minors. relate matrix equivalent to similarity. calculate the determinants by using elementary row(column) operations. know the methods of finding the inverse of matrix Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To teach the matrix theory which is used in various areas of mathematics and to demostrate the ways in which it is used. Course Contents : Matrix operations. Determinants and properties of determinants. Rank of a matrix, Equivalent matrices. Similar matrices. Elementary row (column) operations. Elementary matrices. Adjoint of a matrix. Inverse of a matrix. Solution of the system of linear equations. Canonical forms. Quadratic form. Bilinear form. Language of Instruction : Turkish Work Place : Classrooms Faculty of Science Annex   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Basic matrix operations Reading the relevant parts of the textbook and problem solving Lecture and discussion 2 Determinants of matrices Reading the relevant parts of the textbook and problem solving Lecture and discussion 3 Minors and cofactors Reading the relevant parts of the textbook and problem solving Lecture and discussion 4 Equivalence of matrices Reading the relevant parts of the textbook and problem solving Lecture and discussion 5 Adjoint and its properties Reading the relevant parts of the textbook and problem solving Lecture and discussion 6 Equivalent Matrices Reading the relevant parts of the textbook and problem solving Lecture and discussion 7 Inverse of a Matrix Reading the relevant parts of the textbook and problem solving Lecture and discussion 8 Mid -term exam Review and problem solving Written Exam 9 Solution of Linear Equations Systems using matrices Reading the relevant parts of the textbook and problem solving Lecture and discussion 10 LU Decomposition Reading the relevant parts of the textbook and problem solving Lecture and discussion 11 Biliner forms Reading the relevant parts of the textbook and problem solving Lecture and discussion 12 Canonical forms Reading the relevant parts of the textbook and problem solving Lecture and discussion 13 Matrix functions Reading the relevant parts of the textbook and problem solving Lecture and discussion 14 Generalized inverses Reading the relevant parts of the textbook and problem solving Lecture and discussion 15 Solving problems Review and problem solving Lecture and discussion 16/17 Final exam Review and problem solving Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Matrix Operations, Schaum´s Outlines, Richard Bronson  Matrix Theory, Fuzhen Zhang, Springer Verlag Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 0 0 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Is able to prove Mathematical facts encountered in secondary school. 4 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 4 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 5 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 1 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 1 6 Expresses clearly the relationship between objects while constructing a model 3 7 Draws mathematical models such as formulas, graphs and tables and explains them 5 8 Is able to mathematically reorganize, analyze and model problems encountered. 5 9 Knows at least one computer programming language 4 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 0 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 133 Total Workload / 25 (h): 5.32 ECTS Credit: 5