Course Detail
Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| ANALYSIS I | İM1114938 | Fall Semester | 3+0 | 3 | 7 |
| 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. Hüseyin KOCAMAN |
| Name of Lecturer(s) | Assist.Prof. Hüseyin KOCAMAN |
| Assistant(s) | |
| Aim | Clusters and number systems; correlation, types of functions, exponential functions and logarithmic functions; limit, continuity concepts and applications; derivative, derivative applications and graphic drawings |
| Course Content | This course contains; Sets, Number Sets,Cartesian Product,Cartesian coordinate system,Basıc Graphs Drawing,Function concept, Polynomials, Polynomial functions,Rational functions, Trigonometric functions, Exponential and logarithmic functions,Limits,First order indeterminate equation,Special Lİmits,Continuity-Discontinuity, Types of Discontinuity,Derivatives, Geometric Interpretation of Derivatives, Applications of Derivatives,Second order indeterminate equation,Higher-order derivatives, Maximum-Minimum,Graphic Drawings. |
| Course Learning Outcomes | Teaching Methods | Assessment Methods |
| understand the relationships between clusters, cartesian product and graph. | 12, 9 | A |
| Comprehends simple functions, types of functions and graphic drawings. | 12, 9 | A |
| Learns limits, special limits and uncertainties in functions. | 12, 9 | A |
| Learns continuity- discontinuity and the types of discontinuity in functions. | 12, 9 | A |
| Learns the importance of derivatives in higher mathematics, geometric interpretation of derivatives and applications of the derivative. | 12, 9 | A |
| Knows the concept of extremum and the extremum derivative relationship in single-variable functions. | 12, 9 | A |
| Manages graphic drawing in the light of the knowledge and experience gained. | 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 | Sets, Number Sets | [1], [2], [3] |
| 2 | Cartesian Product | [1], [2], [3] |
| 3 | Cartesian coordinate system | [1], [2], [3] |
| 4 | Basıc Graphs Drawing | [1], [2], [3] |
| 5 | Function concept, Polynomials, Polynomial functions | [1], [2], [3] |
| 6 | Rational functions, Trigonometric functions, Exponential and logarithmic functions | [1], [2], [3] |
| 7 | Limits | [1], [2], [3] |
| 8 | First order indeterminate equation | [1], [2], [3] |
| 9 | Special Lİmits | [1], [2], [3] |
| 10 | Continuity-Discontinuity, Types of Discontinuity | [1], [2], [3] |
| 11 | Derivatives, Geometric Interpretation of Derivatives, Applications of Derivatives | [1], [2], [3] |
| 12 | Second order indeterminate equation | [1], [2], [3] |
| 13 | Higher-order derivatives, Maximum-Minimum | [1], [2], [3] |
| 14 | Graphic Drawings | [1], [2], [3] |
| Resources |
| [1] General Mathematics, Prof. Dr. Ahmet Dernek [2] General Mathematics, Prof. Dr. Ekrem Kadioglu, Prof. Dr. Muhammet Kamali [3] Analysis I, Prof. Dr. Mustafa Balci |
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 | 2 | 3 | 6 | |||
| Guided Problem Solving | 1 | 2 | 2 | |||
| 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 | 1 | 1 | 1 | |||
| General Exam | 0 | 0 | 0 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 9 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(9/30) | 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 |
|---|---|---|---|---|---|
| ANALYSIS I | İM1114938 | Fall Semester | 3+0 | 3 | 7 |
| 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. Hüseyin KOCAMAN |
| Name of Lecturer(s) | Assist.Prof. Hüseyin KOCAMAN |
| Assistant(s) | |
| Aim | Clusters and number systems; correlation, types of functions, exponential functions and logarithmic functions; limit, continuity concepts and applications; derivative, derivative applications and graphic drawings |
| Course Content | This course contains; Sets, Number Sets,Cartesian Product,Cartesian coordinate system,Basıc Graphs Drawing,Function concept, Polynomials, Polynomial functions,Rational functions, Trigonometric functions, Exponential and logarithmic functions,Limits,First order indeterminate equation,Special Lİmits,Continuity-Discontinuity, Types of Discontinuity,Derivatives, Geometric Interpretation of Derivatives, Applications of Derivatives,Second order indeterminate equation,Higher-order derivatives, Maximum-Minimum,Graphic Drawings. |
| Course Learning Outcomes | Teaching Methods | Assessment Methods |
| understand the relationships between clusters, cartesian product and graph. | 12, 9 | A |
| Comprehends simple functions, types of functions and graphic drawings. | 12, 9 | A |
| Learns limits, special limits and uncertainties in functions. | 12, 9 | A |
| Learns continuity- discontinuity and the types of discontinuity in functions. | 12, 9 | A |
| Learns the importance of derivatives in higher mathematics, geometric interpretation of derivatives and applications of the derivative. | 12, 9 | A |
| Knows the concept of extremum and the extremum derivative relationship in single-variable functions. | 12, 9 | A |
| Manages graphic drawing in the light of the knowledge and experience gained. | 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 | Sets, Number Sets | [1], [2], [3] |
| 2 | Cartesian Product | [1], [2], [3] |
| 3 | Cartesian coordinate system | [1], [2], [3] |
| 4 | Basıc Graphs Drawing | [1], [2], [3] |
| 5 | Function concept, Polynomials, Polynomial functions | [1], [2], [3] |
| 6 | Rational functions, Trigonometric functions, Exponential and logarithmic functions | [1], [2], [3] |
| 7 | Limits | [1], [2], [3] |
| 8 | First order indeterminate equation | [1], [2], [3] |
| 9 | Special Lİmits | [1], [2], [3] |
| 10 | Continuity-Discontinuity, Types of Discontinuity | [1], [2], [3] |
| 11 | Derivatives, Geometric Interpretation of Derivatives, Applications of Derivatives | [1], [2], [3] |
| 12 | Second order indeterminate equation | [1], [2], [3] |
| 13 | Higher-order derivatives, Maximum-Minimum | [1], [2], [3] |
| 14 | Graphic Drawings | [1], [2], [3] |
| Resources |
| [1] General Mathematics, Prof. Dr. Ahmet Dernek [2] General Mathematics, Prof. Dr. Ekrem Kadioglu, Prof. Dr. Muhammet Kamali [3] Analysis I, Prof. Dr. Mustafa Balci |
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 | |