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Course Code: 
MATH 101
Semester: 
Fall
Course Type: 
Core
P: 
3
Lab: 
2
Laboratuvar Saati: 
0
Credits: 
4
ECTS: 
8
Course Language: 
English
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:Question-answer, 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

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

100

Quizzes

-

-

Assignments

-

-

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

40

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

60

Total

 

100

 

COURSE CATEGORY

Core Courses

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 self-development 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 off-the-classroom study (Pre-study, practice)

14

5

70

Mid-terms (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