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Course Description Course Name : Vector Spaces Course Code : MT-517 Course Type : Optional Level of Course : Second Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Asst.Prof.Dr. ELA AYDIN Learning Outcomes of the Course : Learns some concepts vectors and matrices and relationship between them Writes a basis of a vector space and find the coordinates Finds dual and double dual of the vector spac eand determines the annihilator By constructing the polynomial algebra says fundamental theorems about it Learns the determinant functions and permutations Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To give insight and skill about the concrete aspects of linear algebra,To provide basic concepts of matrices and the systems of homogeny and linear equations,To solve the systems using matrices,To teach vector spaces and abstract mathematical concepts,To teach abstract thought Course Contents : Linear systems relationship between matrices and linear systems,Row-matrice operators and solvind linear systems,vector spaces and subspaces,bases, dimensions and coordinates,Linear transformations and The algebra of linear transformations,linear functionals,dual spaces,annihilating polynomials,Lagrange interpolation,commutative rings and determinant function,permutations. Language of Instruction : Turkish Work Place : Department of Mathematics Seminar hall   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Linear equation systems,solving systems by using matrices Review of the relevant pages from sources Lecture and discussion 2 Solving homogen and linear systems with Elementary row- operations Review of the relevant pages from sources Lecture and discussion 3 Matrix multiplication,inverse matrices, Cramer system Review of the relevant pages from sources Lecture and discussion 4 Vector spaces and subspaces Review of the relevant pages from sources Lecture and discussion 5 Bases, dimensions and coordinates Review of the relevant pages from sources Lecture and discussion 6 Linear Transformations and Tha algebra of Linear transformations Review of the relevant pages from sources Lecture and discussion 7 İsomorphisms and representations of matrices Review of the relevant pages from sources Lecture and discussion 8 Mid-term exam Review of the relevant pages from sources Lecture and discussion 9 Linear functionals,dual spaces,annihilating polynomials Review of the relevant pages from sources Lecture and discussion 10 Double dual and the transpose of a Linear Transformation Review of the relevant pages from sources Lecture and discussion 11 Lagrange interpolation Review of the relevant pages from sources Lecture and discussion 12 Polynomial ideals and unique factorization Review of the relevant pages from sources Lecture and discussion 13 Commutative rings and determinant function Review of the relevant pages from sources Lecture and discussion 14 Permutations Review of the relevant pages from sources Lecture and discussion 15 Solving problems None Lecture and discussion 16/17 Final exam Review of the relevant pages from sources Lecture and discussion   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 20 20 Total Workload: 143 Total Workload / 25 (h): 5.72 ECTS Credit: 6