Real Analysis

Fall 2017

Handouts, Quizzes, and Exams

Flipped classroom activities

  • Sections 3.1 and 3.2
  • Section 3.3

Video lectures

  1. Section 0
  2. Set and notations 
  3. Set building notations
  4. Mathematical quantifiers
  5. Proofs with quantifiers
  6. Quantifiers and the empty set
  7. Double quantifiers
  8. Conditional statements
  9. More on conditional statements
  10. An example of a bad proof 
  11. How to write a rigorous mathematical definition
  12. The negation of a conditional statement 
  13. Proof by induction
  14. The sigma notation
  15. Basic proof techniques
  16. Introduction to the natural numbersIntroduction to the natural numbersIntroduction to the natural numbers
  17. Supremum and infimum
  18. Supremum and infimum of a function
  19. Denseness of the rationals
  20. Introduction to sequences and notations
  21. Examples of sequences
  22. The concept of convergence
  23. Uniqueness of a limit
  24. The epsilon-N approach to convergence
  25. An example using the epsilon-N approach
    1. An example using the epsilon-N approach Part 2
    2. Errata: In the part of the formal proof, toward the end, I should not have written for all n in the natural number right before the conclusion
    3. Examples using the epsilon-N approach Part 3
    4. Examples using the epsilon-N approach Part 4
  26. Limits Theorem (Section 3.2)
    1. Errata: At 42:35 it should have been 1/|z_n|<2/|z| 
    2. Because of the quality of the audio, please use your headphones
    3. Limit Theorems
    4. Section 3.1 and Section 3.2
  27. Monotone Sequences (Section 3.3)
  28. Subsequences and the Bolzano-Weierstrass Theorem
  29. Section 3.5 Cauchy Criteria
  30. Section 3.6 Properly Divergent Sequences
  31. Section 4.1 Limits of functions
    1. Video Lecture Part I
    2. Video Lecture Part II
    3. Notes
    4. In-class activities
  32. Section 4.2 Limits Theorems
    1. Video Lecture
    2. Notes
    3. In-class activities
  33. Section 5.1 Continuous functions
    1. Video lecture 
    2. Notes
    3. In-class activities
  34. Section 5.2 Combination of continuous functions
    1. Video lecture
    2. Notes
    3. In-class activities
  35. Section 5.3 Continuous functions on intervals
    1. Video lecture
    2. Notes
    3. In-class activities
  36. Section 5.4
    1. Video lecture
    2. Notes
    3. In-class activities

 

 




Outline of sections and homework sets

 

 

 

 

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