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Course Description Course Name : Abstract Mathematics II Course Code : MT 156 Course Type : Compulsory Level of Course : First Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 6 Name of Lecturer(s) : Assoc.Prof.Dr. AHMET TEMİZYÜREK Learning Outcomes of the Course : Builds the natural numbers set using the Peano axioms Knows the principles of first and second inductionare equivalent and uses these principles to prove propositions. Constructs integers using the natural numbers. Understands the properties of integers and expresses the fundamental theorem of arithmetic Builds the set of rational numbers from integers and describes the properties of the set of rational numbers. Explains the concept of the Cauchy sequence and Builds the real numbers using Cauchy sequence of rational numbers. Defines and exemplifies countable and uncountable sets. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To construct number sets. To introduce the basic concepts of algebra, to understant the properties of finite and infinite sets. To develop the ability to prove propositions. Course Contents : Equivalent sets, construction of natural numbers, construction of integers and its properties, the construction of rational numbers and its properties, the construction of real numbers, finite and infinite sets Language of Instruction : Turkish Work Place : Faculty of Science Annex Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Equivalent sets and construction of natural numbers Required readings Lecture and discussion 2 Mathematical induction and solving problems Required readings Lecture and discussion 3 Construction of integers Required readings Lecture and discussion 4 Properties of integers Required readings Lecture and discussion 5 Arithmetic in the set of integers Required readings Lecture and discussion 6 Fundamental theorem of aritmetic and solving problems Required readings Lecture and discussion 7 Euler´s function Required readings Lecture and discussion 8 Mid-term exam Review of the topics discussed in the lecture notes and sources Written exam 9 Construction of rational numbers Required readings Lecture and discussion 10 Field structures of rational numbers Required readings Lecture and discussion 11 Properties of rational numbers Required readings Lecture and discussion 12 Cauchy sequence and construction of real numbers Required readings Lecture and discussion 13 Properties of the set of real numbers Review of the relevant pages from sources Lecture and discussion 14 Countability and cardinalities of sets Review of the relevant pages from sources Lecture and discussion 15 Cardinalities of sets Review of the relevant pages from sources Lecture 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 Univ. İstanbul, 1995.   A. Dönmez, Kümeler Kuramı ve Soyut Matematik. Atatürk Üniversitey Press No. 638, Erzrum, 1987. Required Course Material(s)  S. Akkaş,H.H. Hacısalihoğlu., Soyut Matematik, Gazi Üniversity press No:43, Ankara, 1984.   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 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. 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 4 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 0 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 4 56 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 20 20     Final Exam 1 30 30 Total Workload: 148 Total Workload / 25 (h): 5.92 ECTS Credit: 6