Brief Information

• Name : Introduction to Analysis 1 해석학1
• Lecturer : 허민?Min Her
• Semester : 2016 Spring
• Major?: BS, Mathematics
• Textbook
  • 맨프레드 스톨 (2015) 『실 해석학 입문』. 2판. 오혜영·허민(역). 경문사(경문북스)
  • Stoll, M. (2000) Introduction to Real Analysis. 2nd Ed.?Pearson
• Syllabus : Syllabus_2016-5-1__Introduction to Analysis 1.pdf
• In?short

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Assignments

1. Submit all notes where you have learned before the midterm exam.
2. Solve again problems that you solved incorrectly.

Tests

The 1st Test

• Chapter 1: The Real Number System
• set, function, mathematical induction, the least upper/lower bound property, the Archimedian property, binary/tenary expansion, countable set, uncountable set

The 2nd Test

• Chapter 2: Sequences of Real Numbers
• Section 2.1 to 2.6
• convergent sequence, limit theorem, monotone sequence, subsequence, the Bolzano-Weierstrass theorem, limit superior, limit inferior, Cauchy sequence

The 3rd Test

Lectures

1. 2016-03-03 Thu.

• Orientation
• Range
  • Section 1.1
• Section 1.1: Set

2. 2016-03-08 Tue.

• Range
  • Section 1.1~1.2
• The start of mathematical analysis: Questioning how we can be convinced our intuition.?해석학의 시작: 인간의 직관을 얼마나 신뢰할 수 있는가.
• Section 1.1:?Sets
• Homework
  • Miscellaneous exercise 1.1
    • 3-b, 5, 7-c, 9
  • Example 1.2.4 (b)
• Section 1.2: Functions
• 관계를 보존한다. 보존 = preserve.

3. 2016-03-10 Thu.

• Range
  • Section 1.2~1.3
• Homework
  • Exercise 1.2
    • 6-(a,e), 7, 11
  • Exercise 1.3
    • 5-(b,c), 6, 8
• 직접 증명할 줄 알아야 한다.
• Generalized Bernoulli’s inequality: 최대한 이해하길 바랍니다.

4. 2016-03-15 Tue.

• 문제풀이 (For the exercises that the professor chose)
  • Exercises 1.2
  • Exercises 1.3
• Chapter 3: The Least Upper Bound Property
  • The 8 properties of the real numbers

5. 2016-03-17 Thu.

 

6. 2016-03-22 Tue.

 

7. 2016-03-24 Thu.

 

8. 2016-03-29 Tue.

9. 2016-03-31 Thu.

 

10. 2016-04-05 Tue.

11. The 1st Test | 2016-04-07 Thu.

 

12. 2016-04-12 Tue.

13. 2016-04-14 Thu.

 

15. 2016-04-19 Tue.

16. 2016-04-21 Thu.

 

17. 2016-04-26 Tue.

18. 2016-04-28?Thu.

 

19. 2016-05-03 Tue.

20. 2016-05-05 Thu.

 

21. 2016-05-10 Tue.

22. The 2nd Test | 2016-05-12 Thu.

 

23. 2016-05-17 Tue.

24. 2016-05-19 Thu.

 

24. 2016-05-24 Tue.

25. 2016-05-26 Thu.

 

26. 2016-05-31 Tue.

27. 2016-06-02 Thu.

 

28. 2016-06-07 Tue.

29. 2016-06-09 Thu.

 

30. 2016-06-14 Tue.

31. The 3rd Test(Final) | 2016-06-16 Thu.