School/Faculty/Institute Faculty of Education
Course Code MATH 231
Course Title in English Analytical Geometry
Course Title in Turkish Analytical Geometry
Language of Instruction EN
Type of Course Flipped Classroom
Level of Course Select
Semester Fall
Contact Hours per Week
Lecture: 3 hours Recitation: Lab: Other:
Estimated Student Workload 122 hours per semester
Number of Credits 5 ECTS
Grading Mode Standard Letter Grade
Pre-requisites None
Expected Prior Knowledge None
Co-requisites None
Registration Restrictions None
Overall Educational Objective
Course Description
Course Description in Turkish Düzlem analitik geometride nokta ve doğru ilişkisi, düzlemde vektörler, doğru ve temel problemler, çember ve temel problemler, elips ve temel problemler, hiperbol ve temel problemler, parabol ve temel problemler. Üç boyutlu uzayda vektörler, doğru ve düzlem denklemleri, doğru ve düzlemin vektörel denklemleri ve ilgili problemler. Uzayda konikler, düzlem ve koniklerin kesitleri. Ayrıca, geometrinin tanımı, yapısı ve gerçek hayatta kullanımı. Aksiyom, tanımsız kavram, teoremin açıklanması. Öklid ve Öklid dışı geometriler, Öklid geometrisinin temel aksiyomları. Nokta, doğru ve düzlem kavramları arasındaki ilişkiler. Açı kavramı, çeşitleri, açıların eşliği ve eşlik aksiyomları, açılar ile ilgili uygulamalar. Çokgen kavramının tanımı. Üçgen kavramının tanımı, üçgen çeşitleri, üçgenin temel ve yardımcı elemanları, üçgenler ile ilgili eşlik aksiyom ve teoremleri, üçgenlerde eşlik ile ilgili uygulamalar, üçgenler ile ilgili benzerlik teoremleri, üçgenlerde benzerlik ile ilgili uygulamalar. Yamuk, paralelkenar, eşkenar dörtgen, dikdörtgen, kare, deltoit gibi geometrik kavramlara dönük teoremlerin ispatlanması. Dörtgenler ile ilgili uygulamalar. Çember ve daire kavramları, çember ve dairede açı ve uzunluk ile ilgili teorem ve ispatları, çember ve dairede açı ve uzunluk ile ilgili uygulamalar. Uzayda cisimlerin özellikleri, katı cisimlerin alan ve hacimleri ilgili uygulamalar.

Course Learning Outcomes and Competences

Upon successful completion of the course, the learner is expected to be able to:
1) exhibit reading, writing, and questioning skills in Analytical Geometry
1) the certain elementary mathematical notions such as sets, relations, and functions;
2) the Fundamental Principle of Analytic Geometry and the notion of an equivalence relation;
3) Cartesian coordinates, lines, vectors in the plane and in three space;
4) conic sections and the general quadratic equation in two variables;
5) matrices and solution systems of linear equations by matrices;
6) fundamental properties of determinants and the Cramer’s Rule;
7) canonical equations of quadratic surfaces and general quadratic rule of three variables.
Program Learning Outcomes/Course Learning Outcomes 1 1 2 3 4 5 6 7
1) Thorough knowledge of the major concepts, theoretical perspectives, empirical findings, and historical trends in psychology.
2) Understanding of and ability to apply essential research methods in psychology, including research design, data analysis, and data interpretation.
3) Competence to use critical and creative thinking, skeptical inquiry and a scientific approach to solving problems related to behavior and mental processes.
4) Understanding and ability to apply psychological principles, skills and values in personal, social, and organizational contexts.
5) Ability to weigh evidence, to tolerate ambiguity, and to reflect other values that underpin psychology as a discipline.
6) Internalization and dissemination of professional ethical standards.
7) Demonstration of competence in information technologies, and the ability to use computer and other technologies for purposes related to the pursuit of knowledge in psychology and the broader social sciences.
8) Skills to communicate the knowledge of psychological science effectively, in a variety of formats, in both Turkish and in English (in English, at least CEFR B2 level).
9) Recognition, understanding, and respect for the complexity of sociocultural and international diversity.
10) Recognition for the need for, and the skills to pursue, lifelong learning, inquiry, and self-improvement.
11) Ability to formulate critical hypotheses based on psychological theory and literature, and design studies to test those hypotheses.
12) Ability to acquire knowledge independently, and to plan one’s own learning.
13) Demonstration of advanced competence in the clarity and composition of written work and presentations.

Relation to Program Outcomes and Competences

N None S Supportive H Highly Related
     
Program Outcomes and Competences Level Assessed by
1) Thorough knowledge of the major concepts, theoretical perspectives, empirical findings, and historical trends in psychology. N
2) Understanding of and ability to apply essential research methods in psychology, including research design, data analysis, and data interpretation. N
3) Competence to use critical and creative thinking, skeptical inquiry and a scientific approach to solving problems related to behavior and mental processes. H Exam,HW,Participation
4) Understanding and ability to apply psychological principles, skills and values in personal, social, and organizational contexts. N
5) Ability to weigh evidence, to tolerate ambiguity, and to reflect other values that underpin psychology as a discipline. N
6) Internalization and dissemination of professional ethical standards. N
7) Demonstration of competence in information technologies, and the ability to use computer and other technologies for purposes related to the pursuit of knowledge in psychology and the broader social sciences. N
8) Skills to communicate the knowledge of psychological science effectively, in a variety of formats, in both Turkish and in English (in English, at least CEFR B2 level). N
9) Recognition, understanding, and respect for the complexity of sociocultural and international diversity. S Participation
10) Recognition for the need for, and the skills to pursue, lifelong learning, inquiry, and self-improvement. S HW,Participation
11) Ability to formulate critical hypotheses based on psychological theory and literature, and design studies to test those hypotheses. N
12) Ability to acquire knowledge independently, and to plan one’s own learning. S Exam,HW
13) Demonstration of advanced competence in the clarity and composition of written work and presentations. H Exam,HW
Prepared by and Date İBRAHİM BURAK ÖLMEZ ,
Course Coordinator BENGİ BİRGİLİ
Semester Fall
Name of Instructor Prof. Dr. CENGİZ ALACACI

Course Contents

Week Subject
1) Fundamental Principles of Analytic Geometry
2) Cartesian Coordinates
3) Lines in the Plane and Review of Trigonometry
4) Polar Coordinates
5) Vectors in the Plane I
6) Vectors in the Plane II
7) The Conic Sections: Parabola and Central Conics
8) Midterm Exam or Project
9) The Conic Sections: The Ellipse and The Hyperbola
10) Vectors in Three Space
11) Systems of Linear Equations and Matrices
12) Determinants
13) Surfaces
14) Final Exam or Project
15)
Required/Recommended Readings
Teaching Methods
Homework and Projects
Laboratory Work
Computer UseAs a matter of professionalism and respect, please do not check email, text, or go online during class time; I expect you to be fully present during class. Also, please silence your cell phones during class. Opening your cameras and microphones is required in this course. If your cameras and microphones are off, you will be considered as absent from that particular class and it will be an unexcused absence. So, if there is a problem with your internet connection, camera, or microphone, please fix this problem as soon as possible.
Other Activities
Assessment Methods
Assessment Tools Count Weight
Attendance 1 % 15
Project 1 % 30
Midterm(s) 1 % 25
Final Examination 1 % 30
TOTAL % 100
Course Administration olmezi@mef.edu.tr

ECTS Student Workload Estimation

Activity No/Weeks Hours Calculation
No/Weeks per Semester Preparing for the Activity Spent in the Activity Itself Completing the Activity Requirements
Course Hours 14 1 2 1 56
Laboratory 14 0 1 14
Presentations / Seminar 2 2 10 24
Midterm(s) 1 8 2 10
Final Examination 1 16 2 18
Total Workload 122
Total Workload/25 4.9
ECTS 5