Architecture (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

ARCH109

Course Name:

Mathematics in Architecture

Semester:

Fall

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Dr. Öğr. Üy. ZEHRA TONBUL

Course Lecturer(s):

Kadri Uğur Çakıroğlu

Course Assistants:

Course Objective and Content

Course Objectives:	Firming a foundation for Descriptive Geometry lectures. Enhancing problem-solving skills. Acquisition of a powerful spatial perception.
Course Content:	Basic tools of mathematics: Matrices, Vectors. Metric problems. Mathematical background for computer graphics.

Learning Outcomes

The students who have succeeded in this course;
1) Gets a better understanding of space and of relations of objects in space
2) Learns the calculative methods for metric problems like lengths, angles etc., so forms a basis for the Descriptive Geometry program that solves similar problems via graphical methods.
3) Develops abstraction skills.
4) Develops creative thinking and problem solving skills.

Course Flow Plan

Week	Subject	Related Preparation
1)	Basic definitions: Point; line; jeodesic; surface. Classification of surfaces
2)	Matrices. Addition, multiplication by a scalar, multiplication of two matrices. Special matrices: Null matrix; square matrix; identity matrix; transpose of a matrix; cofactor matrix; adjoint matrix; echolon matrix; reduced echolon matrix Systems of Linear Equations.
3)	Vectors. Addition, multiplication by a scalar, dot product, angle between two vectors. Linear combination; basis of a vector space; orientation; orthonormal basis
4)	Vector product, triple product. Vector equations of lines and planes
5)	Vector equations of sphere, conical and cylindrical surfaces. Projection of a vector on another vector. Distance problems: Distance of a point from a point, from a line, from a plane; distance between parallel lines; distance between skew lines; distance of a line from a plane parallel to it; distance between parallel planes. Vector equation of hyperbolic paraboloidal surface
6)	Vector differentiation. Tangent line of a curve. Tangent surface of a curve
7)	Mathematical elements for computer graphics. Linear transformation. 2D transformations: Scaling along the x and y axes; reflection about the x and y axes; shearing along the x and y axes; rotation about the origin. Compound transformations. Transformation of the unit square. Homogenious coordinates; translation. Rotation about an arbitrary point; reflection about an arbitrary axis
8)	Central projection. Global scaling. 3D transformations: Scaling along x, y, z axes; reflection about coordinate planes; shearing along x, y, z axes; rotation about x, y, z axes. orthographic pojections on coordinate planes. Rotation about an axis parallel to a coordinate axis; rotation about an arbitrary axis; reflection about an arbitrary plane.
9)	Central projection. Vanishing point. One-point perspective. Two-point perspective. Three-point perspective
10)	Golden ratio. Regular figures; Platonic solids. Semi-regular solids; Archimedean solids. Principle of duality of space. Polytopes.
11)	Intrinsic properties of curves: Curvature and torsion. Vector integration. Arc length a natural parameter.
12)	Minimal surfaces. Geodesic. Catenary curve.
13)	Linear programming. Graphic solution. Simplex method.
14)	General overview.

Sources

Course Notes / Textbooks:	"Architectural Geometry", Helmut Pottmann, Andreas Asperl, Michael Hofer, and Axel Kilian
References:	The Geometry of Design: Studies in Proportion and Composition", Kimberly Elam

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4
Program Outcomes
1) She/he gains knowledge of and develops values on technical, aesthetic, cultural, historical, social and ethical dimensions of architecture with a scientific and critical approach.
2) She/he integrates architectural practice with environmental, economic and social sustainability principles.
3) She/he has the knowledge and ability to provide and implement interactions between urban planning, urban design and architectural projects.
4) Gains the ability to identify architectural potentials and problems based on data collection, analysis, interpretation and critical thinking, in order to cultivate concepts and determine strategies for action.	1	3	2	3
5) She/he is able to interrelate theory, design and construction practices.
6) She/he will be able to produce architectural design, presentation, implementation, management and supervision stages both independently and collectively for different contexts and scales and through a responsive approach to social, functional, technical and aesthetic requirements.	2	2	2	3
7) In addition to traditional methods, she/he interactively uses the emerging information technologies required by the field.	3	3	2	3
8) To analyze and document the historical and conservation characteristics of the built environment; taking into account of the balance between protection and use, she/he has the ability and necessary knowledge in renovation and restoration issues.
9) She / he gains the ability to cooperate with different disciplines on the conception and design of the built environment, as an individual and/or as a team member.
10) Has knowledge on and comprehension of professional ethics and codes of conduct, legal and managerial regulations, standards, rights and responsibilities and processes in the field of architecture.
11) Can produce design, know-how and knowledge for the improvement of different and changing social needs, and for the enhancement of life quality.
12) She/he has the knowledge and responsibility to design solidly built structures and takes into account of the risks of natural disaster.
13) She/he monitors new developments in architectural theory and practice and is open to lifelong learning.		2	2	3
14) She/he takes responsibility for the improvement of social consciousness in the field of architecture, and for the endorsement and defense of ecological and urban rights.
15) Has architectural communication skills in a foreign language.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	She/he gains knowledge of and develops values on technical, aesthetic, cultural, historical, social and ethical dimensions of architecture with a scientific and critical approach.
2)	She/he integrates architectural practice with environmental, economic and social sustainability principles.
3)	She/he has the knowledge and ability to provide and implement interactions between urban planning, urban design and architectural projects.
4)	Gains the ability to identify architectural potentials and problems based on data collection, analysis, interpretation and critical thinking, in order to cultivate concepts and determine strategies for action.	3
5)	She/he is able to interrelate theory, design and construction practices.
6)	She/he will be able to produce architectural design, presentation, implementation, management and supervision stages both independently and collectively for different contexts and scales and through a responsive approach to social, functional, technical and aesthetic requirements.	2
7)	In addition to traditional methods, she/he interactively uses the emerging information technologies required by the field.	3
8)	To analyze and document the historical and conservation characteristics of the built environment; taking into account of the balance between protection and use, she/he has the ability and necessary knowledge in renovation and restoration issues.
9)	She / he gains the ability to cooperate with different disciplines on the conception and design of the built environment, as an individual and/or as a team member.
10)	Has knowledge on and comprehension of professional ethics and codes of conduct, legal and managerial regulations, standards, rights and responsibilities and processes in the field of architecture.
11)	Can produce design, know-how and knowledge for the improvement of different and changing social needs, and for the enhancement of life quality.
12)	She/he has the knowledge and responsibility to design solidly built structures and takes into account of the risks of natural disaster.
13)	She/he monitors new developments in architectural theory and practice and is open to lifelong learning.	3
14)	She/he takes responsibility for the improvement of social consciousness in the field of architecture, and for the endorsement and defense of ecological and urban rights.
15)	Has architectural communication skills in a foreign language.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Workload
Course Hours	14	56
Study Hours Out of Class	14	28
Midterms	1	8
Final	1	8
Total Workload		100