MATHEMATICS PROGRAMME COURSE DESCRIPTION

Code	Name of the Course Unit	Semester	In-Class Hours (T+P)	Credit	ECTS Credit
MAT151	MATHEMATICS	1	3	3	4

GENERAL INFORMATION
Language of Instruction :	Turkish
Level of the Course Unit :	ASSOCIATE DEGREE, TYY: + 5.Level, EQF-LLL: 5.Level, QF-EHEA: Short Cycle
Type of the Course :	Compulsory
Mode of Delivery of the Course Unit	-
Coordinator of the Course Unit	Lecturer DAMLA YAĞCI
Instructor(s) of the Course Unit	Lecturer KÜBRA ÇETİNBERK
Course Prerequisite	No

OBJECTIVES AND CONTENTS
Objectives of the Course Unit:	It is aimed to learn the mathematics used in the basic calculations required for the department.
Contents of the Course Unit:	Basic Concepts (Numbers), Rational Numbers and Decimal Fractions, Number Systems and Digit Concept, Prime Factors and Exact Divisors, Division and Divisibility Rules, Factorial - Base Arithmetic, Obeb (Ebob) and Okek (Ekok), Solving Equations - Problems, Simple Inequalities - Absolute Value, Exponents - Square Root Numbers, Factorization and Identities, Permutation - Combination - Probability, Operation - Modular Arithmetic, Geometric concepts - Volume Calculus.

KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to)
Provides analytical solutions to the problems encountered.
Makes calculations for the solution of technical problems.
Makes geometric area and volume calculations.
Analyzes and evaluates problems by using materials related to mathematics based on the competencies gained in secondary education.
Evaluates the concepts, theories and data in mathematics science with scientific methods, identifies, analyzes, discusses, and develops proposals based on evidence and research.
Have knowledge of computer software at the level required by mathematics science.
To have social, scientific and ethical values in the stages of collecting, interpreting and announcing data related to mathematics science. Uses the ability of abstract thinking.

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week	Preparatory	Topics(Subjects)	Method
1	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. Express the repeated product of a natural number with itself as an exponential quantity and determine the value of exponential quantities. 2. Performs four operations with natural numbers taking into account the priority of operations. 3. Performs operations to apply the property of common factor bracketing and dispersion in natural numbers. 4. Solves problems that require four operations with natural numbers. 5. Relates number sets to each other. a) Introduces the symbols of natural number, whole number, rational number, irrational number and real number sets and emphasizes the relationship between these number sets. 1. Divides a natural number by a unit fraction and a unit fraction by a natural number and makes sense of this operation. 6. Solves numbers given in decimal representations. 7. Converts numbers given in decimal notation to rational numbers. 8. Multiplies a natural number by a fraction and makes sense of this operation. 9. Solves problems that require operations with fractions.	Lecture, Question and Answer, Illustration, Problem solving
2	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. Interprets whole numbers and displays them on the number line. 2. Compares and sorts whole numbers. 3. Performs addition and subtraction operations with whole numbers; solves related problems. 4. Understands that subtraction of whole numbers means adding with the opposite sign of the negative. 5. Solves problems related to the divisibility rules of whole numbers. (Divisibility rules of 2, 3, 4, 5, 8, 9, 10, 11 and the numbers obtained from these numbers such as 6, 12, 15)	Lecture, Question and Answer, Illustration, Problem solving
3	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1.Makes applications about EBOB and EKOK in integers. a) Real life problems are included. b) EBOB and EKOK functions in spreadsheets are used.	Lecture, Question and Answer, Illustration, Problem solving
4	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. Expresses the rule of arithmetic sequences with a letter; finds the desired term of the sequence whose rule is expressed with a letter. 2. Writes an algebraic expression appropriate to a given verbal situation and a verbal situation appropriate to a given algebraic expression. 3. Calculates the values of the algebraic expression for different natural number values of the variable. 4. Explains the meaning of simple algebraic expressions. 5. Performs addition and subtraction operations with algebraic expressions.	Lecture, Question and Answer, Illustration, Problem solving
5	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	First Order Equations and Inequalities 1. Finds the solution sets of first order equations and inequalities with one unknown. a) Remind students to solve first order equations and inequalities with one unknown.	Lecture, Question and Answer, Illustration, Problem solving
6	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. Solves equations involving exponential expressions. a) The concept of exponential expression is reminded. b) Applications are made about the integer power of a real number. c) The properties of exponential expressions are emphasized. 2. Determines the absolute value of an integer and makes sense of it. 3. Explains the absolute value of a real number and states the properties related to absolute value. 4. Finds the solution sets of equations and inequalities involving one or two absolute value terms in a first-order unknown.	Lecture, Question and Answer, Illustration, Problem solving
7	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. Determines the relationship between perfect square natural numbers and their square roots. 2. Performs multiplication and division operations with square root expressions. 3. Performs four operations with cube root expressions. 4. performs operations with nth order roots. 5. Finds conjugates in rooted expressions. 6. Makes ordering in rooted expressions. 7. Factors a polynomial. a) Factorization applications are made using common factor bracketing and variable substitution methods. b) Factorization applications are made using identities of perfect square, difference of two squares, cube of sum and difference of two terms, sum and difference of cubes of two terms. c) Expressions of the form 𝑎x2 + 𝑏x + 𝑐𝑐 are factored.	Lecture, Question and Answer, Illustration, Problem solving
8	-	MID-TERM EXAM	-
9	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. Uses ratio in comparing multiplicities and shows the ratio in different forms. 2. Determines the ratio of two multiplicities in the same or different units. 3. Solves problems related to direct and inverse proportion. 4. Finds the quantity corresponding to a given percentage of a quantity; finds the quantity given a given percentage. 5. Calculates one quantity as a percentage of another quantity.	Lecture, Question and Answer, Illustration, Problem solving
10	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1.Collects data about real life problems. 2.Translates the real life problem into mathematical language. 3.Solves the real life problem translated into mathematical language and applies it to real life.	Lecture, Question and Answer, Illustration, Problem solving
11	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. The basic concepts related to sets are reminded. a) Real life examples about sets are given. b) Different representations of sets are given. c) Cantor's works are given. 2. Performs operations using a subset. a) The concept of subset and its properties are discussed. b) Real-life examples about the concept of subset are given. c) Problems requiring combination are not included. 3. Performs operations using the equality of two sets. a) The concept of equality of two sets is associated with the concept of subset. b) The concept of equivalent set is not given. 4. Solves problems with the help of union, intersection, difference and complement operations in sets. a) The properties of union, intersection, difference and integration operations of sets are given. b) The concept of disjoint set is given. c) Relationships that give the number of elements of the union of at most three sets are emphasized. ç) Associations are made between operations with sets and symbols, notations and operations expressed with them used in symbolic logic.	Lecture, Question and Answer, Illustration, Problem solving
12	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. Solves problems related to functions. a) The concept of function is explained. b) Only functions defined on real numbers are discussed. c) Implicit function, implicit function, one-to-one function, equal function, unit (identity) function, constant function, linear function, odd function, even function and partially defined function are explained. ç) The equality of two functions is explained with examples. d) Using the functions f and g, operations 𝑓 + 𝑔, 𝑓 - 𝑔, 𝑓. 𝑔, 𝑓/𝑔, 𝑓/𝑔, but these operations are not performed for piecewise defined functions. e) Real life problems and the use of tables and graphs are included. 2. Draws the graphs of functions. a) Applications related to the graphs of functions of the form f(x) = ax + b are made. b) The graphs of the functions given in piecewise defined form are drawn. c) The graph of the functions of the type f(x) = ax + b is drawn with the help of information and communication technologies and the relationship between the coefficients a and b and the function graph is discussed. 3. Interpret the graphs of functions. a) The definition and image sets of the functions whose graphs are given are shown. b) In a function graph, it is pointed out that the lines drawn parallel to the y-axis from each point where the function is defined on the x-axis intersect the graph at only one point (vertical/vertical line test). c) Emphasize that the graph of a function f is the graph of the equation y = f(x) and that the points (if any) where the graph crosses the x-axis are the solution set of the equation f(x) = 0 in real numbers. 4. Make graphical representations of real-life situations that can be expressed by linear functions. 3. Makes applications related to one-to-one and covering functions. a) The one-to-one and covering of a function is examined on the graph with the horizontal line test and is related algebraically. b) With the help of information and communication technologies, it is determined whether a function is one-to-one and covering. 4. Performs operations related to the operation of composition in functions. a) The operation of composition is handled by associating it with algebraic and graphical representations of functions. b) It is stated that the operation of composition in functions has the property of unification, and it is shown with examples that it does not change. c) The composition of piecewise defined functions is not entered. 5. Finds the inverse of a given function. a) The necessary conditions for the inverse of a function to be a function are stated. b) The graph of the inverse of only a one-to-one and continuous linear function is drawn; it is shown that the graph of the function and its inverse are symmetric with respect to the y=x line. c) The inverse of piecewise defined functions is not given.	Lecture, Question and Answer, Illustration, Problem solving
13	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1.Defines operations with functions of two or more variables and solves examples. 2.Demonstrate the properties of modular arithmetic and make applications using them.	Lecture, Question and Answer, Illustration, Problem solving
14	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1. Calculates the number of occurrences of events using addition and multiplication methods. a) The historical development process of counting is mentioned and the works of SâbitİbnKurrâ, who played a role in this process, are included. b) The concept of factorial is given and associated with the basic principle of counting. 2. Calculates how many different permutations (permutations) can be made with n kinds of objects. 3. Solves problems by explaining the permutations of a limited number of repetitive objects. a) The number of all different permutations of objects with at least two identical objects is discussed in the context of examples/problems. b) Real life problems are included. 4. Calculates how many different ways r elements of a set of n elements can be chosen. a) The concept of combination is associated with the number of subsets. b) The following basic properties of the concept of combination are examined: - 𝐶(𝑛, 𝑟) = 𝐶(𝑛, 𝑛 - 𝑟) - 𝐶(𝑛, 0) + 𝐶(𝑛, 1) + ⋯ + 𝐶(𝑛, 𝑛) = 2𝑛 5. It is emphasized that Pascal's triangle was discussed by mathematicians and thinkers in Indian, Chinese and Islamic civilizations, including Omar Khayyam, long before Pascal; in this context, the role of different cultures and scientists in the formation of mathematical knowledge is emphasized. 6. Explains the concepts of sample space, experiment, output, complement of an event, definite event, impossible event, discrete event and non-discrete event. a) The concepts of sample space, experiment, output are exemplified and defined for non-discrete cases based on equiprobable cases. b) Discrete event and non-discrete event are emphasized. c) The works of Al-Kindī and Laplace are included. 7. Makes applications related to the concept of probability. a) Calculate the probabilities of equiprobable and non-probable events. b) Calculate the probabilities of complementary, discrete and non-discrete events. c) Real life problems are included.	Lecture, Question and Answer, Illustration, Problem solving
15	Studies the new subject that has been covered and will be covered from the DGS and TYT resources with lectures. Examines the questions that they can solve or interpret.	1.Creates its own analytical thinking style with numerical logic exercises in preparation for DGS-KPSS-ALES exams.	Lecture, Question and Answer, Illustration, Problem solving
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

SOURCE MATERIALS & RECOMMENDED READING
Türkyılmaz, U.(2017). DGS Subject Explained Solved Question Bank.
Tasarı Academic Publications.(2019).DGS Lecture. Kayhan Matbaacılık.
Akdeniz,H.(2019). Math Question Bank Special for our Teacher. Mf Kazanım Publishing.
Başay,İ.B. and Öztürk,M.(2019). Emergency Mathematics TYT Question Bank. Acil Publications.
Başay,İ.B. and Öztürk,M.(2019). Emergency Mathematics AYT Question Bank. Acil Publications.
Koç,M.(2019). Active Mathematics 0'dan Başlayanlara. Yorum Matbaacılık.
Özcan,S. and Özcan,K.(2018). Mathematics from Zero to Infinity.

ASSESSMENT
Assessment & Grading of In-Term Activities	Number of Activities	Degree of Contribution (%)	Description

Level of Contribution
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Have basic knowledge and skills of hybrid and electric vehicles.
2	Know and apply the next generation of design and technologies.
3	Generate solutions to problems related to the field and implement them.
4	An ability to transfer knowledge from theoretical to practical.
5	Creates ideas that are open to innovation and change.

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Know functions and tasks of hardware such as sensors, batteries, etc. which to be used in electric vehicles.
2	Understand functions of parts used in hybrid and electric vehicles (e.g. Crankshaft-camshaft-valve mechanism, battery systems, electric and gasoline engines, etc.) and how it is produced and understands its operation.

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Have knowledge about ethical issues required by their profession.
2	Know and apply the importance of working individually and as a team in production and laboratory studies.
3	Identify problems related to unforeseen situations and seeks solutions in working conditions in areas where hybrid and electric vehicle technology is used.

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Have a competence to take responsibility for the given works.
2	Have an ability to solve problems and take risks in hybrid and electric vehicle technology.
3	Have an ability to bring the jobs/projects given to from the initial stage to the maturity stage.

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Know how to use two and three dimensional design programs related to the profession.
2	Have an ability general information for using computer; can use programs very well.

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Adopt an importance of learning lifetime and also have an ability to develop socially, technologically and culturally.
2	Can work as a team; have an ability to prepare projects and presentations.

WORKLOAD & ECTS CREDITS OF THE COURSE UNIT
Workload for Learning & Teaching Activities
Type of the Learning Activites	Learning Activities (# of week)	Duration (hours, h)	Workload (h)
Lecture & In-Class Activities	0	0	0
Preliminary & Further Study	0	0	0
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	0	0	0
Assignment (Homework)	0	0	0
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	0	0	0
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	0	0	0
Preparation for the Final Exam	0	0	0
Mid-Term Exam	0	0	0
Preparation for the Mid-Term Exam	0	0	0
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	0	0	0