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Course Code: 
MATH 256
Semester: 
Spring
Course Type: 
Core
P: 
3
Lab: 
2
Laboratuvar Saati: 
0
Credits: 
4
ECTS: 
8
Course Language: 
English
Course Objectives: 
Learning the basic concepts and results of real analysis in Rp. Introducing the elementary topological concepts in Rp
Course Content: 

Elements of point set theory.Functions and the Real Number System. Open and closed sets in Rp. Accumulation points. Bolzano-Weierstrass theorem in Rp.  Compactness and connectedness.Heine Borel Theorem.Convergence of sequences in Rp. Sequences of Functions, Uniform Convergence Continuity and Uniform continuity.Sequences of Continuous Functions,Limits of Functions.

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Teaching Methods

Assessment Methods

1) Knows the topology of Euclidean spaces.

1-2

A-B

2) Knows the concept of convergence of sequences and related important teorems.

1-2

A-B

3) Knows local and global properties of continuous functions.

1-2

A-B

Course Flow

Week

Topics

Study Materials

1

Introduction, Functions, the Real Number System

 

2

Suprema, Infima and Supremum Principle

 

3

Vector Spaces, Inner Product Spaces, Schwarz Inequality, The Space Rp

 

4

Open Sets, Nested Intervals Theorem,

 

5

Accumulation Points, Bolzano- Weierstrass Theorem, Connected Sets

 

6

Compactness, The Heine-Borel Theorem

 

7

Sequences in Rp, Convergence

 

8

Monotone Convergence Theorem, Bolzano-Weierstrass Theorem

 

9

Cauchy Sequences, Cauchy Convergence Criterion

 

10

Sequences of Functions,  Convergence, Uniform Convergence, Uniform Norm, Cauchy Criterion for Uniform Convergence

 

11

Continuous Functions, Local Properties of Continuous Functions

 

12

Global Properties of Continuous Functions

 

13

Sequences of Continuous Functions

 

14

Limits of Functions

 

Recommended Sources

Textbook

The Elements of Real Analysis, Robert G. Bartle

Additional Resources

 

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

80

Quizzes

5

10

Assignments

5

10

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

50

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

50

Total

 

100

 

COURSE CATEGORY

Expertise/Field 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

1

 

 

 

 

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

10

20

Quizzes

5

2

10

Assignments

5

2

10

Final examination (Including self study)

1

15

15

Total Work Load

 

 

195

Total Work Load / 25 (h)

 

 

7.8

ECTS Credit of the Course

 

 

8