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Course Description Course Name : Vector Spaces II Course Code : MT-516 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 6 Name of Lecturer(s) : Asst.Prof.Dr. ELA AYDIN Learning Outcomes of the Course : Knows the properties of the determinant function gives some special examples of linear transformations and proves some important theorems about linear transformations knows about very simple triangular and diagonal forms of linear transformations Finds out minimal polynomial.By determininig the class of the annihilating polynomials of linear transformation . Calculates the Jordan form of the linear transformation Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To calculate the length of vectors in inner products spaces and the angles between them,To understand the application of determinant.To determine eigenvalue and eigenvector and find similar matrices. Course Contents : Application of determinant functions,Uniqueness of determinant and properties,eigenvalue and eigenvectors,annihilating polynomials and invarient subspaces,diagonalization,direct-sum decompositions,invariant direct sums and The primary Decomposition Theorem,cyclic subalgebras and annihilators,The Jordan Form,inner product and inner product spaces Language of Instruction : Turkish Work Place : Departments Seminar Hall   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Applications of determinant function Review of the relevant pages from sources Lecture and discussion 2 Uniqueness of determinant and some properties of determinant Review of the relevant pages from sources Lecture and discussion 3 Eigenvalues and eigenvectors Review of the relevant pages from sources Lecture and discussion 4 Annihilating polynomials and invariant subalgebras Review of the relevant pages from sources Lecture and discussion 5 Diagonalizations and triangulation Review of the relevant pages from sources Lecture and discussion 6 Direct-sum decompositions Review of the relevant pages from sources Lecture and discussion 7 Invariant direct sums and The Primary Decomposition Theorem Review of the relevant pages from sources Lecture and discussion 8 Mid-term exam Review of the relevant pages from sources written exam 9 Cyclic subspaces and annihilators Review of the relevant pages from sources Lecture and discussion 10 Cyclic Decompositions Review of the relevant pages from sources Lecture and discussion 11 The Jordan Form Review of the relevant pages from sources Lecture and discussion 12 Inner products Review of the relevant pages from sources Lecture and discussion 13 Inner product spaces Review of the relevant pages from sources Lecture and discussion 14 Orthogonality and orthogonal complement Review of the relevant pages from sources Lecture and discussion 15 Final exam Review of the relevant pages from sources written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Kenneth Hoffman and Ray Kunze, “ Linear Algebra”, 1971. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 70     Homeworks/Projects/Others 1 30 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 Aquires sufficient knowledge to enable one to do research over and above the undergraduate level 5 2 Learns theoretical foundations of his/her field thoroughly 5 3 Uses the knowledge in his/her field to solve mathematical problems 5 4 Proves basic theorems in different areas of Mathematics 4 5 Creates a model for the problems in his/her field and expresses the relationship between objects in a simple and comprehensive way. 0 6 Uses technical tools in his/her field 5 7 Works independently in his/her field requiring expertise 4 8 Works with other colleagues collaboratelly, takes responsibilities if necessary during the research process 3 9 Argues and analyzes knowledge in his/her field and applies them in other fields if necessary 4 10 Has sufficient knowledge to follow literature in his/her field and communicate with stakeholders 4 11 Uses the language and technology to develop knowledge in his/her field and shares these with stakeholders systematically when necessary 4 12 Knows and abides by the ethical rules in analyzing, solving problems and publishing results 4 * 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 1 10 10     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 25 25 Total Workload: 148 Total Workload / 25 (h): 5.92 ECTS Credit: 6