GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
ALGEBRA OF SETS/MAT1014
Course Title: ALGEBRA OF SETS
Credits 3 ECTS 3
Course Semester 2 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
To understand how to set up the language of set theory.
To understand and use the concepts of transfinite cardinal and ordinal arithmetic.
Demonstrate a working knowledge of set notation and elementary set theory, recognize the connection between set operations and logic.
Use bijections to compare the cardinality of finite and infinite sets, and explain the difference between countable and uncountable sets.
Formulate and interpret statements presented in disjunctive normal form.
Reformulate statements from common language to formal logic using the rules of propositional and predicate calculus.
Formulate short proofs using the following methods: direct proof, indirect proof, proof by contradiction, and case analysis.
Determine when a relation is reflexive, symmetric, antisymmetric, or transitive, apply the properties of equivalence relations and partial orderings.
Provide grounding in the basic concepts of abstract algebra, including set theory, binary operations and algebraic structures.

 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 --WEEKLY SCHEDULE
1. Week  The historical development of the concept of set, Russell Paradox
2. Week  Logic and propositional calculus.
3. Week  Mathematical structures
4. Week  Boole algebras, sigma algebra, topology
5. Week  Families of sets, lower limit sets and upper limit sets
6. Week  Sequences, nets, filters
7. Week  Ordered sets, order types
8. Week  Lattices, Dedekind completion, Archimedean property and Mid-Term Exam
9. Week  Lattices, Dedekind completion, Archimedean property
10. Week  Infinite sets, countable sets, Cantor set
11. Week  The axiom of choice and its equivalents
12. Week  Cardinal numbers, cardinal arithmet
13. Week  Hamel ve Schauder bases
14. Week  Heine-Borel Theorem, Bolzano-Weierstrass Theorem
15. Week  Fuzzy logic and fuzzy sets
16. Week  Final Exam
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
30
 Assignment
2
5
 Application
2
5
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Percent of In-term Studies  
40
 Percentage of Final Exam to Total Score  
60
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
3
42
 Weekly Tutorial Hours
0
 Reading Tasks
1
3
3
 Searching in Internet and Library
2
3
6
 Material Design and Implementation
5
2
10
 Report Preparing
0
 Preparing a Presentation
0
 Presentation
0
 Midterm Exam and Preperation for Midterm Exam
2
3
6
 Final Exam and Preperation for Final Exam
2
4
8
 Other (should be emphasized)
0
 TOTAL WORKLOAD: 
75
 TOTAL WORKLOAD / 25: 
3
 Course Credit (ECTS): 
3
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To train individuals who are contemporary, entrepreneur and have unique and aesthetic values, self-confidence and capable of independent decision-making.X
2To give good education in the program fields as algebra, geometry, applied mathematics, topology and analysis in order to be equipped with enough mathematics.X
3To teach mathematical thinking methods in order to improve the ability to express mathematics both orally and in writing.X
4To train individuals who are knowledgeable about the history of mathematics and the production of scientific knowledge and can follow developments in these disciplines.X
5To provide necessary equipments to take positions such areas as banking, finance, econometrics, and actuarial.X
6To acquire ability to solve problems encountered in real life by means of mathematical modeling using mathematical methods.X
7To provide ability to do necessary resource researches in the areas of mathematics and to use accessed information.X
8To give appropriate training in such areas as in computer programming and creating algorithms in order to take parts in developing IT sector.X
9To gain substructure to be able to study at graduate level.X
10To enable the student to gain the ability of relating mathematics with the other sciences.X
 -- NAME OF LECTURER(S)
   (Prof. Bahri TURAN , Assoc.Prof. Cüneyt ÇEVİK)
 -- WEB SITE(S) OF LECTURER(S)
   (websitem.gazi.edu.tr/site/bturan , http://websitem.gazi.edu.tr/site/ccevik)
 -- EMAIL(S) OF LECTURER(S)
   (bturan@gazi.edu.tr , ccevik@gazi.edu.tr)