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Course Description Course Name : Algebra I Course Code : MT 211 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Fall (16 Weeks) ECTS : 7 Name of Lecturer(s) : Prof.Dr. NAİME EKİCİ Learning Outcomes of the Course : Reads, interprets and uses the vocabulary and basic definitions used in linear algebra. Learns the importance of the concept of vector spaces, sub spaces, basis and dimension. Determines basis, computes dimensions. Evaluate linear transformations Computes matrix representations of a linear transformation. Solves systems of linear equations. Computes determinants. Evaluates eigen values and the corresponding eigen vectors of a linear tansformation. Develops specific skills and thought processes sufficient to support further studies in this or related fields. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : The objectives of this course are to introduce the students with the basic ideas of linear algebra including vector spaces, subspaces, basis, dimension, linear transformations, matrices, systems of linear equations, eigenvalues and eigenvectors and to teach the understanding of abstract mathematical concepts and abstract thought arising from the concepts covered in this course. Course Contents : Vectors in the plane and space; vector spaces, subspaces, linear dependence, bases and finite dimensional vector spaces, linear transformations, matrices, representation of linear transformations by matrices, direct sum, systems of linear equations, determinants, characteristic vectors and diagonalization. Language of Instruction : Turkish Work Place : Classrooms of Science and Letters Faculty   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Vector space, subspace Required readings Lecture and discussion 2 Linear dependence, independence and a basis of a vector space Required readings Lecture and discussion 3 Basic properties of a basis and dimension of a vector space Required readings Lecture and discussion 4 Sum of subspaces, direct sum Required readings Lecture and discussion 5 Linear transformations, their kernels and images Required readings Lecture and discussion 6 The rank of a linear transformation, isomorphism Required readings Lecture and discussion 7 Matrices Required readings Lecture and discussion 8 Mid-term exam Review of the topics discussed in the lecture notes and sources Written exam 9 Representation of linear transformations by matrices Required readings Lecture and discussion 10 The rank of a matrix, echelon matrix Required readings Lecture and discussion 11 Row equivalent matrices and systems of linear equations Required readings Lecture and discussion 12 Determinant function, properties of determinant, evaluation of determinant Required readings Lecture and discussion 13 Cramer Rule, eigen values and eigen vectors Required readings Lecture and discussion 14 Characteristic spaces and characteristic polynomial Required readings Lecture and discussion 15 Solving problems Required readings Lecture and discussion 16/17 Final exam Review of the topics discussed in the lecture notes and sources Witten exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Linear Algebra, Author:Arif Sabuncuoğlu Required Course Material(s)  Linear Algebra, Author:Larry Smith   Linear Algebra, Author:Jim Hefferon   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 90     Homeworks/Projects/Others 5 10 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 2 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 2 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 1 11 Knows programming techniques and is able to write a computer program 1 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 4 56     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 5 5 25     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 172 Total Workload / 25 (h): 6.88 ECTS Credit: 7