COURSE UNIT TITLE

: ARTS AND MATHEMATICS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
GKD 6000 ARTS AND MATHEMATICS ELECTIVE 2 0 0 3

Offered By

Buca Faculty Of Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR YUSUF ERKUŞ

Offered to

Music Teacher Education
Turkish Language Teacher Education
Computer and Instructional Technologies Teacher Education
Chemistry Teacher Education
Biology Teacher Education
Turkish Language and Literature Teacher Education
Geography Teacher Education
Physics Teacher Education
Special Teacher Education
ELEMENTARY MATHEMATICS TEACHER EDUCATION
PRE - SCHOOL TEACHER EDUCATION
Mathematics Teacher Education
Elementary Teacher Education
FINE ARTS TEACHER EDUCATION
Guidance and Psychological Counseling
Social Studies Teacher Education
History Teacher Education
Science Teacher Education

Course Objective

The main purpose of this course is to enable prospective teachers to explore the effects of mathematical concepts and ways of thinking on artistic creativity, aesthetic understanding and different art forms. It is aimed that students, even if they do not have prior knowledge of mathematics, will notice the mathematical structures hidden in works of art, understand how these structures contribute to artistic expression and use these principles consciously in their own artistic productions. In addition to theoretical knowledge, the course aims to develop both analytical and creative skills of students through practical workshops.

Learning Outcomes of the Course Unit

1   1. Describe the basic concepts, historical connections, and interdisciplinary relationships between art and mathematics.
2   2. Can distinguish and analyze basic mathematical principles (symmetry, proportion, pattern, perspective, fractal, geometric shapes, etc.) found in different works of art (painting, sculpture, architecture, textile, digital art, etc.) and in nature.
3   3. Understand the mathematical foundations of cultural heritage, such as geometric patterns in Islamic art, and interpret the aesthetic value of these patterns.
4   4. Able to design and produce own original artistic works using basic geometric and mathematical concepts (e.g. symmetry, tessellation, origami, Islamic geometric pattern drawing).
5   5. Explain how mathematical thinking contributes to the processes of artistic expression, problem solving, and aesthetic perception.
6   6. Can think critically about the relationship between art and mathematics, evaluate different perspectives, and develop and present his/her own artistic project in this context.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Introduction and Introduction to the Course The purpose of the course, its scope, learning objectives, assessment methods, expectations. Meeting with students and obtaining their preliminary expectations about the course.
2 An Overview of the Relationship Between Mathematics and Art Historical and conceptual intersections of art and mathematics. A general perspective on important figures and works. Examples of how mathematical thinking fosters artistic creativity.
3 Symmetry and Balance in Art Types of symmetry (reflection, rotation, translation), elements of balance. Analysis with examples from nature and art (architecture, painting, textile). *Activity: Creating simple symmetrical patterns or photographing and presenting examples of symmetry in the environment.*
4 Golden Ratio and Fibonacci Sequence Definition of the golden ratio, its relationship with the Fibonacci sequence. Examining examples of its use in nature (sunflower, pine cone, etc.) and art (Parthenon, Mona Lisa, etc.). *Activity: Creating simple compositions using the golden ratio or searching for the golden ratio in a known work.*
5 Perspective and Space Perception Fundamentals of one- and two-point perspective. Examples of how to create the illusion of depth and three-dimensional space in art. *Activity: One-point perspective drawing exercises with simple geometric objects.*
6 Tilings and Tessellations Periodic and aperiodic tilings, Escher's works. Mathematical principles of shapes that cover the plane without gaps. *Activity: A simple tessellation (tiling) design workshop using own motifs. *
7 Fractals and Patterns in Nature Basic concepts of fractal geometry, repeating patterns. Examples from nature (snowflake, broccoli, tree branches) and art (Pollock etc.). *Activity: Simple fractal drawing study (e.g. Koch snowflake or the first steps of the Sierpinski triangle). *
8 Midterm Exam A midterm exam covering the topics of the first 7 weeks, measuring students' ability to understand basic concepts and relate them to artistic examples.
9 Origami Art and Mathematics Geometric principles of folding art. Mathematics behind creating three-dimensional forms from flat paper. *Activity: Basic origami figures (crane, box, etc.) and simple modular origami construction. *
10 Geometric Abstraction and Modern Art The use of geometric forms (line, square, circle, etc.) in abstract art. Mathematical examination of the works of artists such as Mondrian, Kandinsky, Malevich. *Activity: Creating an abstract composition using certain geometric forms.*
11 Geometric Patterns in Islamic Art The importance of geometry in Islamic art, the use of basic geometric shapes (stars, polygons), symmetry and repetition. An introduction to girih patterns and the mathematical foundations of Islamic decorative art. *Activity: Workshop on drawing a basic Islamic geometric pattern (e.g. a 6 or 8 star motif) using compasses and ruler.
12 Mathematical Transformations in Art The use of basic geometric transformations such as translation, rotation, reflection, scaling in works of art (especially in patterns, ornaments, and modern art). *Activity: Creating new patterns by applying various transformations to a motif.*
13 Use of Mathematics in Digital Art and Project Workshop Introduction to algorithmic art, generative art. Producing art in a digital environment with mathematical formulas. *Activity: Workshop on creating geometric patterns with a simple digital art tool (free software or web-based tools) and developing ideas for the final project.*
14 Student Projects Presentation and Exhibition Presentation, discussion and mini exhibition of artistic projects (drawing, design, model, digital work, etc.) based on a mathematical concept prepared by students throughout the semester.
15 Final Evaluation and Course Closing Project submissions and/or final exam. An overall evaluation of the course, reinforcement of what has been learned, a general discussion on the relationship between art and mathematics, and feedback.

Recomended or Required Reading

Recommended Resources for the Course :
1. Basic Lecture Notes and Presentations:
* Lecture notes and visual presentations (PowerPoint, PDF, etc.) prepared by the instructor, covering each week's topic.
2. Books (Examples, both Turkish and English sources can be considered):
* Coxeter, HSM Introduction to Geometry (Relevant sections)
* El-Said, Issam & Parman, Ayşe. Geometric Concepts in Islamic Art .
* Broug, Eric. Islamic Geometric Patterns .
* Livio, Mario. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number .
* Doczi, György. The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture .
* Kaplan, Craig S. Introductory Tesselation Theory for Computer Graphics . (More digitally oriented, but useful for basic concepts)
* Lang, Robert J. Origami Design Secrets: Mathematical Methods for an Ancient Art .
* Mandelbrot, Benoît B. The Fractal Geometry of Nature . (Conceptually)
* Sections containing mathematical analysis in various art history books. * Popular science and mathematics books (for example, relevant ones among TUBITAK publications).
3. Articles and Web Resources:
* Academic Articles: Articles that can be found on platforms like JSTOR, Academia.edu, Google Scholar with keywords like "mathematics and art", "geometry in art", "Islamic patterns".
* Websites:
* The Mathematical Art Galleries (bridgesmathart.org)* Art of Islamic Pattern (artofislamicpattern.com)* Wolfram MathWorld (mathworld.wolfram.com) - For mathematical concepts. * Khan Academy (Art History and Mathematics departments)* Museum websites (Metropolitan Museum of Art, Louvre, British Museum, etc. - for art reviews). * GeoGebra (geogebra.org) - for geometric drawings and explorations. * Videos:
* Relevant videos from math-focused YouTube channels like Numberphile, 3Blue1Brown. * Documentaries or TED Talks on art and math.
4. Software and Tools (For Activities):
* GeoGebra: Dynamic geometry software (free).
* Free Drawing Programs: Krita, GIMP, Inkscape (for digital art and pattern design).
* Web-Based Tools: Various fractal generators, tessellation creation tools, online geometric drawing platforms.
* Origami Simulators: (Optional)
5. Art Materials (For Workshops):
* Drawing papers (A4, A3, sketchbook) * Pencils (various hardnesses), eraser * Compass, ruler (30cm, T-ruler), set square (45 and 30-60 degrees) * Colored pencils, markers, felt-tip pens * Origami papers (different colors and sizes) * Scissors, utility knife, cutting mat, glue * Optional: Watercolor, gouache, acrylic paint and brushes * Graph paper

Planned Learning Activities and Teaching Methods

In this course, various learning and teaching methods will be used with an integrated approach so that students can deeply understand and experience the relationship between art and mathematics. Theoretical knowledge will be conveyed through rich visual presentations and analysis of works of art, and will be reinforced with discussions that encourage active participation of students. On this theoretical basis, students will have the opportunity to discover and create by using mathematical principles in their own artistic production processes through applied workshops. At the end of the term, it will be aimed to transform what they have learned into an original artistic expression through individual projects.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE Midterm Exam
2 DTK Other Activity
3 FN Semester final exam
4 BNS BNS Student examVZ * 0.30 + Student examDTK * 0.10 + FN * 0.60
5 BUT Make- up note
6 BBN End of make-up grade Student examVZ * 0.30 +Student examDTK * 0.10 + BUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

yusuf.erkus@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 2 26
Preparations before/after weekly lectures 13 1 13
Preparation for midterm exam 1 10 10
Preparation for final exam 1 10 10
Preparing assignments 2 7 14
Midterm 1 1 1
Final 1 1 1
TOTAL WORKLOAD (hours) 75

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16
LO.154
LO.254
LO.354
LO.435
LO.535
LO.635

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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