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Course Description Course Name : Abstract Mathematics I Course Code : MT 153 Course Type : Compulsory Level of Course : First Cycle Year of Study : 1 Course Semester : Fall (16 Weeks) ECTS : 4 Name of Lecturer(s) : Assoc.Prof.Dr. AHMET TEMİZYÜREK Learning Outcomes of the Course : Is able to express the concept of proposition. Explains the deductive techniques of proving theorems. Defines the concept of set and proves theorems about the sets. Defines the concept of relation and knows the properties of equivalence equation. Defines the order relation, explains the concepts of exact order and well ordering. Knows that a function is a specific relation. Identifies the specific type functions. Defines the concept of operation. Defines and describes the properties of binary and unary operations. Defines the algebraic structures such as group, ring, field, vector space and module. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : MT 153 Abstract Mathematics I Recommended Optional Programme Components : None Aim(s) of Course : This course aims to give student the ability to think abstractly, to prove mathematical facts and introduce the basic concepts of analysis and algebra. Course Contents : Symbolic logic, proof techniques, Set theory, relation, function and binary operations, algebraic structures. Language of Instruction : Turkish Work Place : Faculty of Science and Art Annex Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Propositions Review of the relevant pages from sources Narration and discussion 2 Basic proof techniques Review of the relevant pages from sources Narration and discussion 3 Set theory Review of the relevant pages from sources Narration and discussion 4 Operations on sets Review of the relevant pages from sources Narration and discussion 5 Relations and their properties Review of the relevant pages from sources Narration and discussion 6 Equivalance relation and partitions Review of the relevant pages from sources Narration and discussion 7 Order relations and its properties Review of the relevant pages from sources Narration and discussion 8 Mid-term exam Review of the topics discussed in the lecture notes and sources Written exam 9 Functions Review of the relevant pages from sources Narration and discussion 10 operations, unary, binary and n-ary operations Review of the relevant pages from sources Narration and discussion 11 External and internal operations Review of the relevant pages from sources Narration and discussion 12 Algebraic structures, Groups and its basic properties. Review of the relevant pages from sources Narration and discussion 13 Rings and fields Review of the relevant pages from sources Narration and discussion 14 The structure of module Review of the relevant pages from sources Narration and discussion 15 Vector spaces Review of the relevant pages from sources Narration and discussion 16/17 Final exam Review of the topics discussed in the lecture notes and sources Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  F. Çallıalp, Soyut Matematik, İstanbul Technical Üniv. İstanbul, 1995. Required Course Material(s)  S. Akkaş, H.H. Hacısalihoğlu, Soyut Matematik, Gazi Üniversitesi press No:43, Ankara, 1984.   A. Dönmez., Kümeler Kuramı ve Soyut Matematik, Atatürk University press No. 638, Erzurum, 1987.   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 Is able to prove Mathematical facts encountered in secondary school. 5 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 4 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 3 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. 1 6 Expresses clearly the relationship between objects while constructing a model 2 7 Draws mathematical models such as formulas, graphs and tables and explains them 3 8 Is able to mathematically reorganize, analyze and model problems encountered. 0 9 Knows at least one computer programming language 0 10 Uses effective scientific methods and appropriate technologies to solve problems 1 11 Knows programming techniques and is able to write a computer program 0 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 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