Course Language:
İngilizce
Course Objectives:
To teach the usage of analytical tools for mathematical thinking.
Course Content:
Propositional and predicate calculus. Introduction to logic. Methods of proof. Axioms of set theory. Cartesian product, relations and functions. Partial and total orderings. Zorn's lemma. Cardinality, finite, countable and uncountable sets. Arithmetic of cardinals and ordinals.
Course Methodology:
1: Lecture, 2: Problem Solving, 3:Questionanswer, 4: Homework
Course Evaluation Methods:
A: Written examination, B: Homework
Vertical Tabs
Course Learning Outcomes
Learning Outcomes  Program Learning Outcomes  Teaching Methods  Assessment Methods 
1) Thinks like a mathematician.  1,2,3,4  A  
2) Applies laws of logic in reasoning.  1,2,3,4  A  
3) Tests the validity of an argument by using laws of logic.  1,2,3,4  A  
4) Identifies the properties of a given function, relation or an ordering.  1,2,3,4  A  
5) Understands that there are different sizes of infinity.  1,2,3,4  A  
6) Applies set theory axioms to deduce results about denumerable and uncountable sets.  1,2,3,4  A 
Course Flow
Week  Topics  Study Materials 
1  Intro. to propositional logic, logical equivalence and tautologies  Textbook 
2  Rules of inference  Textbook 
3  Proof techniques  Textbook 
4  Mathematical induction  Textbook 
5  Predicates and quantifiers  Textbook 
6  The Algebra of sets  Textbook 
7  Arbitrary unions and intersections  Textbook 
8  Product sets, functions  Textbook 
9  Compositions, bijections and inverse functions  Textbook 
10  Images and inverse images of sets  Textbook 
11  Relations, equivalence relations  Textbook 
12  Partially ordered sets  Textbook 
13  The cardinality of finite sets  Textbook 
14  The cardinality of infinite sets  Textbook 
Recommended Sources
Textbook  Introduction to Advanced Mathematics, William Barnier Norman Feldman. 
Additional Resources 
Material Sharing
Documents  
Assignments  
Exams 
Assessment
INTERM STUDIES  NUMBER  PERCENTAGE 
Midterms  2  100 
Quizzes     
Assignments     
Total  100  
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE  40  
CONTRIBUTION OF INTERM STUDIES TO OVERALL GRADE  60  
Total 
100

Course’s Contribution to Program
No  Program Learning Outcomes  Contribution  
1  2  3  4  5  
1  The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)  x  
2  Acquiring fundamental knowledge on fundamental research fields in mathematics  x  
3  Ability form and interpret the relations between research topics in mathematics  x  
4  Ability to define, formulate and solve mathematical problems  x  
5  Consciousness of professional ethics and responsibilty  x  
6  Ability to communicate actively  x  
7  Ability of selfdevelopment in fields of interest  x  
8  Ability to learn, choose and use necessary information technologies  x  
9  Lifelong education  x 
ECTS
Activities  Quantity 
Duration (Hour) 
Total Workload (Hour) 
Course Duration (14x Total course hours)  14  5  70 
Hours for offtheclassroom study (Prestudy, practice)  14  5  70 
Midterms (Including self study)  2  15  30 
Quizzes       
Assignments       
Final examination (Including self study)  1  20  20 
Total Work Load  190  
Total Work Load / 25 (h)  7.60  
ECTS Credit of the Course  8 