Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
1MATH131FUNDAMENTALS OF MATHEMATICS 4+257

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course This course provides an introduction to the basic concepts and results of mathematical logic, set theory and basic algebraic structures. The course introduces some basic notions that will be needed as background for most of the mathematics courses. Also, the course will familiarize students with mathematical thinking.
Course Content Symbolic Logic, Logical Operations. Quantifiers, Demorgan’s Law.Direct Proofs, Proof by Contradiction. Existence Proofs. Sets and set operations. Relations, equivalence relations, Partitions. Ordered sets, Partial order, total order. Functions, Injections and Surjections, bijections. Cardinality, Countability. Countable sets, Uncountability of the reals. Well-ordering Principle, Zorn’s Lemma, Axiom of Choice, Induction Principle and its applications, Basic algebraic structures:Binary Operations.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers BAŞAK AY SAYLAM
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources S. Galovich, An Introduction to Mathematical Structures , 1989.
Ralph P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson.
Michael L. O'Leary, A first course in mathematical logic and set theory, Wiley

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 30
Quizzes 11 % 30
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
14
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 50 50
Application (Homework, Reading, Self Study etc.) 1 80 80
Exams and Exam Preparations 1 44 44
Total Work Load   Number of ECTS Credits 7 210

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To relate the logic and set theory
2 To list the fundamental knowledge of theorems and proofs
3 To restate proof techniques
4 Ability to decide how to approach a problem
5 Ability to produce examples to theorems and problems
6 Ability to apply the abstract thinking to problem solving


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Symbolic Logic. Logical Operations. S. Galovich, An Introduction to Mathematical Structures , 1989.
2 Quantifiers, Demaorgan's Law S. Galovich, An Introduction to Mathematical Structures , 1989.
3 Proof Techniques S. Galovich, An Introduction to Mathematical Structures , 1989.
4 Proof Techniques S. Galovich, An Introduction to Mathematical Structures , 1989.
5 Sets and set operations S. Galovich, An Introduction to Mathematical Structures , 1989.
6 Relations. Equivalence relations. Partitions S. Galovich, An Introduction to Mathematical Structures , 1989.
7 Ordered sets, partial ordering, total ordering. S. Galovich, An Introduction to Mathematical Structures , 1989.
8 Functions. S. Galovich, An Introduction to Mathematical Structures , 1989.
9 Injective, surjective and bijective functions. Composition of functions. S. Galovich, An Introduction to Mathematical Structures , 1989.
10 Image an inverse image of a function. S. Galovich, An Introduction to Mathematical Structures , 1989.
11 Cardinality, countability. S. Galovich, An Introduction to Mathematical Structures , 1989.
12 Well-Ordering principle. Zorn's Lemma. Axion of Choice. S. Galovich, An Introduction to Mathematical Structures , 1989.
13 Induction principle and its applications. S. Galovich, An Introduction to Mathematical Structures , 1989.
14 Basic algebraic structures: Binary operations, groups, rings, fields. S. Galovich, An Introduction to Mathematical Structures , 1989.
15 Final Exam S. Galovich, An Introduction to Mathematical Structures , 1989.


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4
C2 4
C3 3
C4 4
C5 3
C6 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


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