COURSE UNIT TITLE

: GEOMETRY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
IMÖ 1005 GEOMETRY COMPULSORY 3 0 0 4

Offered By

ELEMENTARY MATHEMATICS TEACHER EDUCATION

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR CENK KEŞAN

Offered to

ELEMENTARY MATHEMATICS TEACHER EDUCATION

Course Objective

The goal is to ensure that students acquire theoretical knowledge and skills related to plane and solid geometry by grasping the fundamental concepts of geometry, its axiomatic structure, and various types of geometry. The aim is for students to understand the relationships between basic geometric elements such as points, lines, planes, angles, polygons, circles, and solid objects, and to be able to make geometric proofs using these relationships. Additionally, students will develop skills in problem-solving through area, perimeter, and volume calculations. Moreover, it is intended that students will be able to transfer the geometry knowledge they have acquired to real-life situations and mathematical modeling.

Learning Outcomes of the Course Unit

1   Defines the fundamental concepts of geometry, its axiomatic structure, and different types of geometry. Explains the basic relationships between points, lines, planes, angles, and polygons in the plane, and grasps the properties of geometric shapes.
2   Applies congruence and similarity theorems on triangles; solves geometric problems using these theorems. Explains the properties of quadrilaterals and polygonal regions, and solves problems related to area calculations.
3   Proves theorems related to circles and discs, and solves related length and angle problems.
4   Explains the relationships between points, lines, and planes in space; describes the properties of solid objects.
5   Solves application problems by calculating the surface area and volume of solid objects. Develops the ability to make geometric proofs and applies knowledge to real-life situations and problem-solving.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Definition of the science of geometry, its fundamental structure, and areas of application in daily life. The basic elements of geometry: undefined terms, propositions, axioms, theorems, and the concept of proof. Axioms of plane geometry.
2 Structure of the axiomatic system, relationship between undefined concepts and theorems. Relationships between the concepts of point, line, and plane. Euclidean and non-Euclidean geometries.
3 Basic axioms of Euclidean geometry. The concept of angle, regions of an angle, and units of measurement. Corresponding, alternate interior, alternate exterior angles, and parallel and perpendicular angles.
4 Definition of the polygon concept. The concept of triangle and its classification (based on sides and angles). Inequalities in triangles. Auxiliary elements of a triangle: angle bisector, median, altitude, perpendicular from the midpoint, and related properties.
5 Congruence axioms and theorems in triangles. Congruent triangles and their applications. Calculations of triangle areas. Triangle constructions and conditions for existence.
6 Similarity theorems in triangles and their applications. Similar figures and similarity of polygons. Geometric properties of special triangles (right, isosceles, equilateral). Theorems of Thales, Ceva, and Menelaus.
7 Carnot and Stewart theorems. Heron's theorem and its results. Relationships concerning the sum of the distances from any point in a triangle to the vertices.
8 Midterm Exam and General Review.
9 Definition, basic elements, and classification of quadrilaterals. Theorems and proofs related to trapezoids, parallelograms, rectangles, rhombuses, squares, and deltoids. Angle, length, and area calculations in quadrilaterals. Relationships and applications between quadrilaterals.
10 Concepts of circle and disc. Basic elements of a circle. Relationships between angles, chords, and arcs in a circle. The concept of tangent and positions between circles. Common tangents of circles and the power of a point theorem with respect to a circle.
11 Circumference and area of a circle. Theorems, proofs, and applications concerning angles and lengths in circles and discs.
12 Problem-solving related to circles and discs. Power of a point theorem in a circle, external center, internal center, and related applications.
13 Solid geometry: Lines and planes in space. The relative positions of lines and planes. Geometric solids: prisms, pyramids, cylinders, cones, and spheres. Cavalieri s principle and its applications.
14 Surface area and volume calculations of solid objects. Surface area and volume of prisms, pyramids, cylinders, cones, spheres, truncated pyramids, and truncated cones. Applications.
15 Final Exam.

Recomended or Required Reading

Balcı, M. (2021). Öklid Geometrisi. Palme Yayıncılık.
Hızarcı, S., Kaplan, A., Ipek, A. S., Işık, C., & Elmas, S. (2012). Düzlem Geometri. Palme Yayıncılık.
Altshiller-Court, N. (2007). College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle. Dover Publications.
Doneddu, A. (1970). Düzlem Euclide Geometrisi (N. Ersoy, Çev.). Milli Eğitim Bakanlığı Devlet Kitapları. (Öğretmen Kitapları No: 129)
Referanslar:
Diğer ders materyalleri: Internet, ders notları

Planned Learning Activities and Teaching Methods

Expository, discussion, question and answer.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Midterm
2 FN Semester final exam
3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60
4 BUT Make-up note
5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

The evaluation of students is measured through midterm and final exams in line with the learning outcomes.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

cenk.kesan@deu.edu.tr

Office Hours

Will be announced at the beginning of the semester.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 3 39
Preparation for midterm exam 1 10 10
Preparation for final exam 1 10 10
Final 1 1 1
Midterm 1 1 1
TOTAL WORKLOAD (hours) 100

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15
LO.14353544544
LO.243355554545
LO.34334534543
LO.44334534544
LO.54354534544

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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