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

Course Description Course Name : Advanced Linear Algebra Course Code : MT 414 Course Type : Optional Level of Course : First Cycle Year of Study : 4 Course Semester : Spring (16 Weeks) ECTS : 5 Name of Lecturer(s) : Asst.Prof.Dr. ELA AYDIN Learning Outcomes of the Course : Knows the basics of vector spaces. Understands the relationship between linear transformations and matrices. Is able to find the diagonal form of linear transformations and matrices. Finds dual and double dual of vector spaces. Finds the annihilator of subspaces and its bases. Is able to define an isometric embedding from a space to another if existing. Find the transpose of a linear function. Finds the Jordan form of a linear function. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : Give elementary knowledge about vector spaces,The algebra of Linear Transformations, Inner product spaces, Isometries between vector spaces. Finding Dual vector spaces and double dual, Determine Annihilators of vector spaces, Relationship between functionals and linear systems, Representation of Linear Transformations by matrices. Invariant subspaces, To compute triangular, diagonal and Jordan canonical forms. Course Contents : Vector Spaces. Inner product spaces and orthogonality, The algebra of Linear Transformations, Isometries, Dual and double dual of vector spaces, Invariant Subspaces, Diagonalization. Jordan Canonical Forms. Language of Instruction : Turkish Work Place : Mathematics Depertment Classroom   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Vector spaces and finding their bases Read the relevant parts of the textbook and solve the problems Lecture and discussion 2 Inner product and inner product spaces Read the relevant parts of the textbook and solve the problems Lecture and discussion 3 Orthonormal bases and orthogonal projection space Read the relevant parts of the textbook and solve the problems Lecture and discussion 4 Linear Transformations and isometries Read the relevant parts of the textbook and solve the problems Lecture and discussion 5 Linear functionals and dual of vector spaces Read the relevant parts of the textbook and solve the problems Lecture and discussion 6 Double dual, hyperspaces and annihilators Read the relevant parts of the textbook and solve the problems Lecture and discussion 7 Relationship between linear functionals and homogeneous systems Read the relevant parts of the textbook and solve the problems Lecture and discussion 8 Mid-term exam and solving problems Review written exam 9 The transpose of a Linear Transformation Read the relevant parts of the textbook and solve the problems Lecture and discussion 10 The algebra of Polynomials and basic theorems Read the relevant parts of the textbook and solve the problems Lecture and discussion 11 Eigenvalues and eigenvectors of Linear Transformations and Diagonalization Form Read the relevant parts of the textbook and solve the problems Lecture and discussion 12 Invariant Subspaces Read the relevant parts of the textbook and solve the problems Lecture and discussion 13 Direct sums Read the relevant parts of the textbook and solve the problems Lecture and discussion 14 The Jordan Form and applications Read the relevant parts of the textbook and solve the problems Lecture and discussion 15 Solving problems Read the relevant parts of the textbook and solve the problems Lecture and discussion 16/17 Final exam Review written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Prof. Dr. H. Hilmi HACISALİHOĞLU," Lineer Cebir", Gazi Üniversitesi Yayın No: 152, 1985. 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. 5 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 5 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 2 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. 4 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 3 42 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: 119 Total Workload / 25 (h): 4.76 ECTS Credit: 5