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Course Description Course Name : Linear Algebra - II Course Code : MAT112 Course Type : Compulsory Level of Course : First Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 4 Name of Lecturer(s) : Asst.Prof.Dr. ELA AYDIN Learning Outcomes of the Course : Can find a base and dimension of vector space Understands linear transformation and their properties Can write a matrix form for a linear transformation Can alculate the length and angle using inner product and find the orthogonal complement of a space Can determine eigenvalue and related eigenvector Can write similar matrices and diagonal matrices Can do different applications of determinants Calculate the rank of a matrix Can calculate with complex numbers in linear algebra and solve the systems Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To find a base of vector space and determine its dimension,To calculate the length of vectors in inner products spaces and the angles between them,To understand the relation between matrices and linear transformation,To determine eigenvalue and eigenvector and find similar matrices Course Contents : Linear dependence and independence applications, Dimension of vector spaces, iner product spaces, orthogonal and orthonormal vectors, Gramm-Schmidt orthogonalization process, linear transformations of vector spaces, representation of linear transformations by matrices, permutations, determinant function and applications, eigenvalues and eigenvectors, diagonalization and triangularization of matrices, complex numbers and solving systems of complex equations. Language of Instruction : Turkish Work Place : Department classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Linear functions, one to one and onto functions Reading the relevants sections in the textbook and solve problems Lecture and discussion 2 Kernel and images of linear functions Reading the relevants sections in the textbook and solve problems Lecture and discussion 3 Matrices of linear transformations Reading the relevants sections in the textbook and solve problems Lecture and discussion 4 equvalences of matrices Reading the relevants sections in the textbook and solve problems Lecture and discussion 5 Sthandard inner product in space and plane Reading the relevants sections in the textbook and solve problems Lecture and discussion 6 Inner products and orthogonality Reading the relevants sections in the textbook and solve problems Lecture and discussion 7 Gramm-Schmidt orthogonalization Reading the relevants sections in the textbook and solve problems Lecture and discussion 8 Mid-term exam Review and problem solving Written exam 9 Eigenvalues and eigenvectors Reading the relevants sections in the textbook and solve problems Lecture and discussion 10 Diagonalization and triangularization of matrices Reading the relevants sections in the textbook and solve problems Lecture and discussion 11 Diagonalization of symetric matrices Reading the relevants sections in the textbook and solve problems Lecture and discussion 12 Determinant function applications Reading the relevants sections in the textbook and solve problems Lecture and discussion 13 Rank of matrices Reading the relevants sections in the textbook and solve problems Lecture and discussion 14 Complex numbers in Linear algebra Reading the relevants sections in the textbook and solve problems Lecture and discussion 15 Solving problems Solving problems Lecture and discussion 16/17 Final exam Review and problem solving Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Bernard Kolman, David R. Hill, " Lineer Cebir" (Çeviri ) Palme Yayıncılık Press,2000  Veli Şahmurov, Gökhan Uzgören, " Lineer Cebir Uygulamaları" Papatya Yayıncılık Press,1999.  Arif Sabuncuoğlu, "Lineer Cebir", Nobel yayın dağıtım,2000. 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 Utilize computer systems and softwares 4 2 Apply the statistical analyze methods 5 3 Make statistical inference(estimation, hypothesis tests etc.) 5 4 Generate solutions for the problems in other disciplines by using statistical techniques 0 5 Discover the visual, database and web programming techniques and posses the ability of writing programme 3 6 Construct a model and analyze it by using statistical packages 0 7 Distinguish the difference between the statistical methods 0 8 Be aware of the interaction between the disciplines related to statistics 1 9 Make oral and visual presentation for the results of statistical methods 0 10 Have capability on effective and productive work in a group and individually 0 11 Develop scientific and ethical values in the fields of statistics-and scientific data collection 0 12 Explain the essence fundamentals and concepts in the field of Probability, Statistics and Mathematics 3 13 Emphasize the importance of Statistics in life 0 14 Define basic principles and concepts in the field of Law and Economics 2 15 Produce numeric and statistical solutions in order to overcome the problems 5 16 Construct the model, solve and interpret the results by using mathematical and statistical tehniques for the problems that include random events 5 17 Use proper methods and techniques to gather and/or to arrange the data 3 18 Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs 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 10 10     Final Exam 1 15 15 Total Workload: 109 Total Workload / 25 (h): 4.36 ECTS Credit: 4