Introduction to Analysis 1 | MA | Course

Brief Information

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.

 

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