Course Name	Analysis Ⅰ
Credits	3
Professor(s)	Name	Yeol Je Cho
	Department/School	Department of Mathematics Education

COURSE DESCRIPTION

Course Objectives

It is to give the following topics :

(1) Sets and functions

(2) The real number systems

(3) Convergence of sequences and series in ℝ

(4) Limit and continuity of functions

(5) Metric spaces

(6) Derivatives of functions

MAIN TEXTBOOK and FURTHER READINGS

Main Textbook: Yeol Je Cho et al., Basic Analysis (2007).

Further Reading:

- K. A. Ross, Elementary Analysis the Theory of Calculus.

- W. Rudin, Principles of Mathematical Analysis.

TASKS AND GRADING

Tasks
- Solutions of Exercises of each section
Grading Scheme
- Attendance (10%), Mid-term Exam (30%), Final Exam (40%), Tasks (20%)

COURSE SCHEDULE

Course Outline
Week 1 : Sets and functions

Week 2 : The real number systems

Week 3 : Completeness axiom, countable sets

Week 4 : Limit of sequences

Week 5 : Bolzano-Weierstrazz theorem

Week 6 : Convergence of series

Week 7 : Power series

Week 8 : Mid-term Exam.

Week 9 : Limit of functions

Week 10 : Conituity of functions

Week 11 : Exameples of metric spaces

Week 12 : Topologies of metric spaces

Week 13 : Continuity of functions on metric spaces

Week 14 : Compactness, connectedness of metric spaces

Week 15 : Final Exam.

CONTACT DETAILS

Tel.: +82 55 751 5673

e-mail : yjcho@gsnu.ac.kr