Course Detail
Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| ABSTRACT MATHEMATICS | İM1114927 | Fall Semester | 2+0 | 2 | 6 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | Turkish |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Damla SÖNMEZ |
| Name of Lecturer(s) | Assist.Prof. Damla SÖNMEZ |
| Assistant(s) | |
| Aim | This course aims for students to: explain symbolic logic and proof techniques; explain sets, set algebra, set families, partitions of set families, and Cartesian products of sets; explain relations, inverse of a relation, composition of relations, equivalence relations and equivalence classes, and ordering relations; explain functions, one-to-one and onto functions, composition of functions, and inverse functions, modular arithmetic and operations. |
| Course Content | This course contains; Symbolic Logic,Statements, Compound Statements,Universal and Existential Quantifiers,Proof Methods,Sets, Subsets and Some Properties of Subsets,Difference, Intersection and Union in Sets, Complement of a Set,Some Properties of Intersection, Union and Complement of a Set,Symmetric Difference,Family of Sets, Some Properties of Intersection and Union in the Family of Sets,Cartesian Product of Sets,Relations and Relation Types,Functions and Function Types,Countable Infinite Sets, Modular arithmetic and operations. |
| Course Learning Outcomes | Teaching Methods | Assessment Methods |
| Explains symbolic logic and its applications. | 12, 9 | A |
| Explain the types of sets. | 12, 9 | A |
| Operates on set algebra. | 12, 9 | A |
| Knows the concepts of relation, function and makes applications. | 12, 9 | A |
| Explain modular arithmetic and operations. | 12, 9 | A |
| Teaching Methods: | 12: Problem Solving Method, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Symbolic Logic | [1], [2], [3] |
| 2 | Statements, Compound Statements | [1], [2], [3] |
| 3 | Universal and Existential Quantifiers | [1], [2], [3] |
| 4 | Proof Methods | [1], [2], [3] |
| 5 | Sets, Subsets and Some Properties of Subsets | [1], [2], [3] |
| 6 | Difference, Intersection and Union in Sets, Complement of a Set | [1], [2], [3] |
| 7 | Some Properties of Intersection, Union and Complement of a Set | [1], [2], [3] |
| 8 | Symmetric Difference | [1], [2], [3] |
| 9 | Family of Sets, Some Properties of Intersection and Union in the Family of Sets | [1], [2], [3] |
| 10 | Cartesian Product of Sets | [1], [2], [3] |
| 11 | Relations and Relation Types | [1], [2], [3] |
| 12 | Functions and Function Types | [1], [2], [3] |
| 13 | Countable Infinite Sets | [1], [2], [3] |
| 14 | Modular arithmetic and operations | [1], [2], [3] |
| Resources |
| [1] Pişkin, E. Soyut Matematik. Pegem Yayıncılık. (Last Edition) [2] Çallıalp, F. Örneklerle Soyut Matematik. Birsen Yayınevi. (Last Edition) [3] Arıkan, A., & Halıcıoğlu, S. Soyut Matematik. (Last Edition) |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | It compares the fundamental theoretical frameworks in the field of elementary mathematics education (constructivism, cognitive development theories, models of mathematical thinking) along with their strengths and weaknesses. | X | |||||
| 2 | It compares the national mathematics curriculum (MEB) with international frameworks (NCTM, PISA, TIMSS) in terms of learning objectives and content areas. | X | |||||
| 3 | Explains the principles of assessment and evaluation, research methods, and ethical guidelines relevant to their profession, as well as their practical applications. | X | |||||
| 4 | Applies appropriate pedagogical interventions in connection with the training received regarding the instructional situations and challenges encountered in the field of elementary mathematics education. | X | |||||
| 5 | By analyzing students' misconceptions and learning difficulties in mathematics, they design appropriate teaching strategies and materials to address them. | X | |||||
| 6 | Solves professional problems related to mathematics education independently using scientific methods. | X | |||||
| 7 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 8 | By formulating a research question on a professional topic, they plan the appropriate research method. | X | |||||
| 9 | Distinguishes between situations that fall within the scope of their professional duties and responsibilities and those that do not. | X | |||||
| 10 | Monitors the instructional activities and implementation process aimed at the development of the students under their supervision. | X | |||||
| 11 | Guides the professional development process by integrating this information in line with national and international developments and research findings in mathematics education. | X | |||||
| 12 | By interpreting the results of their own teaching practices, they develop recommendations for professional development. | X | |||||
| 13 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 14 | Ensures compliance with research ethics, professional ethics for teachers, and national education regulations in their professional practice. | X | |||||
| 15 | In the math classroom, we plan for an equitable and inclusive learning environment, activities that support each student’s mathematical potential, and the necessary safety measures regarding workplace safety. | X | |||||
| 16 | In mathematics instruction, they use dynamic software (GeoGebra, Desmos, etc.), learning management systems, and other information and communication technologies at a level equivalent to at least the ECDL Advanced Level. | X | |||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 40 | |
| Rate of Final Exam to Success | 60 | |
| Total | 100 | |
| ECTS / Workload Table | ||||||
| Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||
| Course Hours | 0 | 0 | 0 | |||
| Guided Problem Solving | 0 | 0 | 0 | |||
| Resolution of Homework Problems and Submission as a Report | 0 | 0 | 0 | |||
| Term Project | 0 | 0 | 0 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 0 | 0 | 0 | |||
| Midterm Exam | 0 | 0 | 0 | |||
| General Exam | 0 | 0 | 0 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 0 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(0/30) | 0 | |||||
| ECTS of the course: 30 hours of work is counted as 1 ECTS credit. | ||||||
Detail Informations of the Course
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| ABSTRACT MATHEMATICS | İM1114927 | Fall Semester | 2+0 | 2 | 6 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | Turkish |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Damla SÖNMEZ |
| Name of Lecturer(s) | Assist.Prof. Damla SÖNMEZ |
| Assistant(s) | |
| Aim | This course aims for students to: explain symbolic logic and proof techniques; explain sets, set algebra, set families, partitions of set families, and Cartesian products of sets; explain relations, inverse of a relation, composition of relations, equivalence relations and equivalence classes, and ordering relations; explain functions, one-to-one and onto functions, composition of functions, and inverse functions, modular arithmetic and operations. |
| Course Content | This course contains; Symbolic Logic,Statements, Compound Statements,Universal and Existential Quantifiers,Proof Methods,Sets, Subsets and Some Properties of Subsets,Difference, Intersection and Union in Sets, Complement of a Set,Some Properties of Intersection, Union and Complement of a Set,Symmetric Difference,Family of Sets, Some Properties of Intersection and Union in the Family of Sets,Cartesian Product of Sets,Relations and Relation Types,Functions and Function Types,Countable Infinite Sets, Modular arithmetic and operations. |
| Course Learning Outcomes | Teaching Methods | Assessment Methods |
| Explains symbolic logic and its applications. | 12, 9 | A |
| Explain the types of sets. | 12, 9 | A |
| Operates on set algebra. | 12, 9 | A |
| Knows the concepts of relation, function and makes applications. | 12, 9 | A |
| Explain modular arithmetic and operations. | 12, 9 | A |
| Teaching Methods: | 12: Problem Solving Method, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Symbolic Logic | [1], [2], [3] |
| 2 | Statements, Compound Statements | [1], [2], [3] |
| 3 | Universal and Existential Quantifiers | [1], [2], [3] |
| 4 | Proof Methods | [1], [2], [3] |
| 5 | Sets, Subsets and Some Properties of Subsets | [1], [2], [3] |
| 6 | Difference, Intersection and Union in Sets, Complement of a Set | [1], [2], [3] |
| 7 | Some Properties of Intersection, Union and Complement of a Set | [1], [2], [3] |
| 8 | Symmetric Difference | [1], [2], [3] |
| 9 | Family of Sets, Some Properties of Intersection and Union in the Family of Sets | [1], [2], [3] |
| 10 | Cartesian Product of Sets | [1], [2], [3] |
| 11 | Relations and Relation Types | [1], [2], [3] |
| 12 | Functions and Function Types | [1], [2], [3] |
| 13 | Countable Infinite Sets | [1], [2], [3] |
| 14 | Modular arithmetic and operations | [1], [2], [3] |
| Resources |
| [1] Pişkin, E. Soyut Matematik. Pegem Yayıncılık. (Last Edition) [2] Çallıalp, F. Örneklerle Soyut Matematik. Birsen Yayınevi. (Last Edition) [3] Arıkan, A., & Halıcıoğlu, S. Soyut Matematik. (Last Edition) |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | It compares the fundamental theoretical frameworks in the field of elementary mathematics education (constructivism, cognitive development theories, models of mathematical thinking) along with their strengths and weaknesses. | X | |||||
| 2 | It compares the national mathematics curriculum (MEB) with international frameworks (NCTM, PISA, TIMSS) in terms of learning objectives and content areas. | X | |||||
| 3 | Explains the principles of assessment and evaluation, research methods, and ethical guidelines relevant to their profession, as well as their practical applications. | X | |||||
| 4 | Applies appropriate pedagogical interventions in connection with the training received regarding the instructional situations and challenges encountered in the field of elementary mathematics education. | X | |||||
| 5 | By analyzing students' misconceptions and learning difficulties in mathematics, they design appropriate teaching strategies and materials to address them. | X | |||||
| 6 | Solves professional problems related to mathematics education independently using scientific methods. | X | |||||
| 7 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 8 | By formulating a research question on a professional topic, they plan the appropriate research method. | X | |||||
| 9 | Distinguishes between situations that fall within the scope of their professional duties and responsibilities and those that do not. | X | |||||
| 10 | Monitors the instructional activities and implementation process aimed at the development of the students under their supervision. | X | |||||
| 11 | Guides the professional development process by integrating this information in line with national and international developments and research findings in mathematics education. | X | |||||
| 12 | By interpreting the results of their own teaching practices, they develop recommendations for professional development. | X | |||||
| 13 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 14 | Ensures compliance with research ethics, professional ethics for teachers, and national education regulations in their professional practice. | X | |||||
| 15 | In the math classroom, we plan for an equitable and inclusive learning environment, activities that support each student’s mathematical potential, and the necessary safety measures regarding workplace safety. | X | |||||
| 16 | In mathematics instruction, they use dynamic software (GeoGebra, Desmos, etc.), learning management systems, and other information and communication technologies at a level equivalent to at least the ECDL Advanced Level. | X | |||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 40 | |
| Rate of Final Exam to Success | 60 | |
| Total | 100 | |