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

Course Description Course Name : Linear Algebra Course Code : EM 205 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Fall (16 Weeks) ECTS : 5 Name of Lecturer(s) : Asst.Prof.Dr. ERSİN KIRAL Learning Outcomes of the Course : Recognizes the matrix algebra and the basic properties. Applies the properties of determinants Recognizes the systems of linear equations. Recognizes the real vector spaces, subspaces, basis, dimension and linear independence. Defines Matrix the linear transformations and representations of linear transformations. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : This module aims to provide an accessible review of the linear algebra from the text book to long after the class. Linear algebra is an essential part of the mathematical background required of mathematicians, engineers, physicists and other scientists. It presents a source for undergraduate students. In general it covers an introduction to linear algebra which will be found helpful to all readers. Course Contents : Students will be able to define matrices, matrix algebra, special types of matrices, elementary row and colon operations, echelon form, rank of a matrix, elementary matrices, inverses, equivalent matrices, determinants, properties of determinants, cofactor and adjoint of a matrix, derivation of inverse matrix, systems of linear equations, solutions of systems of linear equations, Cramer´s method, Gauss’s elimination method, vector spaces, subspaces, linear independence, bases and dimension, coordinates, change of basis, inner product spaces, standard inner product, orthogonal subspaces, orthogonal complement of a subspace, inner product, inner product spaces, orthogonal basis, orthogonal matrices, Gram-Schmidt orthogonalization methods, linear transformations, matrix representations of linear transformations, eigen values, eigen vectors, diagonalization, Cayley-Hamilton’s Theorem, quadratic forms, Hermitian forms, numerical applications. Language of Instruction : Turkish Work Place : İİBF clasrooms.   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Systems of Linear Equations and Matrices (I) Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 2 Systems of Linear Equations and Matrices (II) Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 3 Elementary Matrices permutations Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 4 Determinant Function Determinant Cramer Method Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 5 Vector Spaces Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 6 Vector Spaces Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 7 Vector Spaces Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 8 Midterm Exam 9 Linear Transformations and Matrices Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 10 Linear Transformations and Matrices Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 11 Linear Transformations and Matrices Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 12 Inner Product Space Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 13 Inner Product Space Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 14 Eigenvalues and Eigenvectors Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 15 Eigenvalues and Eigenvectors Students will be prepared by studying relevant subjects from source books according to the weekly program Direct expression, problem solving 16/17 Final Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Uygulamalı Lineer Cebir, Bernard KOLMAN, David R. Hill, Çeviri Editörü: Prof. Dr. Ömer Akın, Palme Yayıncılık, Ankara, 2002.  S. Lipschutz, Theory and Problems of Linear Algebra , Schaum’s Outline of McGraw-Hill Book Co.,1987,Singapore.   Lineer Cebir, Arif Sabuncuoğlu, Nobel Yayıncılık, İstanbul, 2008.  S. J. Leon, "Linear Algebra with Applications", Prentice Hall, 2002, Sixth Edition. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 60     Homeworks/Projects/Others 1 40 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 Models problems with Mathematics, Statistics, and Econometrics 4 2 Explains Econometric concepts 4 3 Estimates the model consistently and analyzes & interprets its results 4 4 Acquires basic Mathematics, Statistics and Operation Research concepts 4 5 Equipped with the foundations of Economics, and develops Economic models 4 6 Describes the necessary concepts of Business 1 7 Acquires the ability to analyze, benchmark, evaluate and interpret at conceptual levels to develop solutions to problems 4 8 Collects, edits, and analyzes data 4 9 Uses a package program of Econometrics, Statistics, and Operation Research 2 10 Effectively works, take responsibility, and the leadership individually or as a member of a team 2 11 Awareness towards life-long learning and follow-up of the new information and knowledge in the field of study 4 12 Develops the ability of using different resources in the form of academic rules, synthesis the information gathered, and effective presentation in an area which has not been studied 2 13 Uses Turkish and at least one other foreign language, academically and in the business context 3 14 Good understanding, interpretation, efficient written and oral expression of the people involved 2 15 Questions traditional approaches and their implementation while developing alternative study programs when required 4 16 Recognizes and implements social, scientific, and professional ethic values 4 17 Follows actuality, and interprets the data about economic and social events 2 18 Improves himself/herself constantly by defining educational requirements considering interests and talents in scientific, cultural, art and social fields besides career development 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 1 5 5     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 25 25 Total Workload: 129 Total Workload / 25 (h): 5.16 ECTS Credit: 5