Course Name
Code
Semester
Theory
(hour/week)
Application/Laboratory
(hour/week)
Local Credits
ECTS
Fundamentals of Mathematics
MATH 103
Fall
3
0
3
5

 
Prerequisites
None

 
Course Language
English
Course Type
Required
Course Level
First Cycle
Course Coordinator -
Course Lecturer(s)
Course Assistants -
Course Objectives To introduce fundamental concepts of mathematics which are essential for mathematical thinking and to provide most common methods of mathematical proofs.
Course Learning Outcomes The students who succeeded in this course;
  • will be able to describe proof methods.
  • will be able to conclude validity of propositions.
  • will be able to apply concepts of logic to proof methods.
  • will be able to formulate and develop mathematical statements.
  • will be able to distinguish mathematical implications.
  • will be able to use proof techniques such as direct proof,induction,contrapositive,contradiction effectively.
  • will be able to adapt proof techniques to fundamental topics:set theory, relations, functions,construct sets and relations of given property.
  • will be able to compare sets (cardinality),compare functions (injection, surjection, bijection, inverse, preimage),demonstrate basic abstract structures.
Course Content In this course symbolic logic, set theory, cartesian product, relations, functions, equivalence relations, equivalence classes and partitions, order relations: partial order, total order and well ordering will be discussed. Mathematical induction and recursive definitions of functions will be taught.

 

Week Subjects Related Preparation
1 Notation and Assumptions. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 1:7.
2 Introduction to Logic. IfThen Statements. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 11:23.
3 Universal and Existential Quantifiers. Negations of Statements. Proof Methods. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 27:42.
4 Properties of Real Numbers. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 45:59.
5 Sets and Their Properties. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 63:77.
6 The Principle of Mathematical Induction. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 78:90.
7 Equivalence Relations. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 91:101.
8 Building the Rational Numbers. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 102:105.
9 Relations. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 111:118.
10 Functions. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 119:138.
11 Cardinality. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 139:150.
12 Introduction to Groups. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 243:259.
13 Quotient Groups. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 260:267.
14 Permutation Groups. “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier, 268:274.
15 Review  
16 Review of the Semester  

 

Course Notes / Textbooks “A Transition to Abstract Mathematics” by Randall B. Maddox, 2/e, Elsevier.
References “Chapter Zero: Fundamental Notions of Abstract Mathematics” by Carol Schumacher, AddisonWesley.

 

Semester Requirements Number Percentage of Grade
Attendance/Participation
-
-
Laboratory
-
-
Application
-
-
Field Work
-
-
Special Course Internship (Work Placement)
-
-
Quizzes/Studio Critics
-
-
Homework Assignments
3
15
Presentation/Jury
-
-
Project
-
-
Seminar/Workshop
-
-
Midterms/Oral Exams
3
45
Final/Oral Exam
1
40
Total
7
100

 
PERCENTAGE OF SEMESTER WORK
-
60
PERCENTAGE OF FINAL WORK
-
40
Total 0 100

 

Course Category

 Core Courses
X
Major Area Courses
 
Supportive Courses
 
Media and Managment Skills Courses
 
Transferable Skill Courses
 

 

#
 Program Qualifications / Outcomes
* Level of Contribution
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics.         X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics,         X
3 To be able to define and analyze problems and to find solutions based on scientific methods,         X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials,         X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,         X
6 To be able to criticize and renew her/his own models and solutions,         X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way,       X  
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

         X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

          
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

         X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,          
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

         X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

          
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

     X    
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

          

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
16
3
48
Laboratory
-
-
-
Application
-
-
-
Special Course Internship (Work Placement)
-
-
-
Field Work
-
-
-
Study Hours Out of Class
15
2
30
Presentations / Seminar
-
-
-
Project
-
-
-
Homework Assignments
3
5
15
Quizzes
-
-
-
Midterms / Oral Exams
3
10
30
Final / Oral Exam
1
20
20
    Total Workload
143