Course Website

Math 6301: Analysis I

Lecture: MATH 6301-100
Room: Morton Hall 313
Time: MWF 9:40am -- 10:35am
Instructor: Marcel Bischoff
Office: Morton Hall 521
Office Phone: (740-59)3-1261
Office Hours: Mon & Wed: 10:45am-11:45am, Fri: 8:00-9:00am

Schedule

1. Mon 08/27:
• Syllabus
• Sets, Mappings, Equivalence relations
2. Wed 08/29:
• Axiom of Choice, Zorn's Lemma
• Real Numbers
• Suggested Problem: Section 1.1, Problem 1.
3. Fri 08/31:
• Section 1.1. and 1.2
• Natural Numbers, Mathematical Induction, Archimedean Property, Integers, Rational Numbers
• Suggested Problems: Section 1.1, 1.2
0. Mon 09/03: Labor Day (no class)
4. Wed 09/05:
• $\sqrt 2$ is not rational, $\mathbb Q$ is dense in $\mathbb R$
• Pigeonhole Principle, Cantor–Schröder–Bernstein Theorem, Countable Sets, Uncountable Sets
• Suggested Problems: Section 1.3
5. Fri 09/07:
• $(a,b)$ is uncountable, Topological Space, Metric Space Topology, Every open set of $\mathbb R$ is a countable disjoint union of open intervals.
6. Mon 09/10:
• Hand in: Homework 01
• Points of closure, Closure, Neighbourhoods, Compactness, Heine-Borel Theorem
7. Wed 09/12:
• The Nested Set Theorem, Sigma-algebras, Borel Sets
• Convergent sequences are bounded, the Monotone Convergence Criterion for Real Sequences
• Suggested problems: Section 1.4
8. Fri 09/14:
• Bolzano-Weierstrass Theorem, Cauchy sequence, Cauchy's convergence theorem, Linearity of the limit
• Quiz 01
9. Mon 09/17:
• Limit superior and limit inferior, Series
• Suggested problems: Section 1.5
• Continuous Functions, Extreme Value Theorem
10. Wed 09/19:
• Intermediate Value Theorem, Uniform Continuity, Heine-Cantor Theorem, Monotone Functions
• Suggested problems: Section 1.6
11. Fri 09/21:
• Outer measure
• Quiz 02
• Suggested Problem: Section 2.1
12. Mon 09/24:
• Hand in Homework 02
• Hand in Corrections of Quiz 01 if you are unhappy with your performance/score
• Lebesgue Measure
• The $\sigma$-algebra of Lebesgue measurable sets
• Suggested Problem: Section 2.2
13. Wed 09/26:
• The $\sigma$-algebra of Lebesgue measurable sets
• Suggested Problems: Section 2.3
• Outer/inner approximation of Lebesgue measurable sets
14. Fri 09/28:
• Outer/inner approximation of Lebesgue measurable sets
• Suggested Problems: Section 2.4
• Countable additivity of Lebesgue measure, Continuity of Lebesgue Measure
• Handed out: Homework 04
15. Mon 10/01:
• Hand in Corrections of Quiz 02 if you are unhappy with your performance/score
16. Wed 10/03:
• Cantor Set, Cantor-Lebesgue Function
• Slides
• Hand in Homework 03
0. Fri 10/05: Reading Day: Class does not meet
17. Mon 10/08:
• Cantor-Lebesgue Function, Lebesgue measurable functions
• Suggested Problems: Section 2.5, 2.6, 2.7
18. Wed 10/10:
• Review
19. Fri 10/12:
• Review
• Hand in Homework 04
20. Mon 10/15: Midterm
21. Wed 10/17:
    • Lebesgue measurable functions
22. Fri 10/19:
• Suggested Problems: Section 3.1
23. Mon 10/22:
• Suggested Problems: Section 3.2
• Simple Approximation
24. Wed 10/24:
25. Fri 10/26:
• Suggested Problems: Section 3.3
26. Mon 10/29:
• Suggested Problems: Section 4.1
27. Wed 10/31:
• Suggested Problems: Section 4.2
28. Fri 11/02:
• Fatou's Lemma, The Monotone Convergence Theorem
29. Mon 11/05:
• Hand in Homework 05
• Suggested Problems: Section 4.3
30. Wed 11/07:
• Suggested Problems: Section 4.4
31. Fri 11/09:
32. Mon 11/12:
33. Wed 11/14:
34. Fri 11/16:
35. Mon 11/19:
0. Wed 11/21: Thanksgiving
0. Fri 11/23: Thanksgiving
36. Mon 11/26:
37. Wed 11/28:
38. Fri 11/30:
39. Mon 12/03:
40. Wed 12/05:
41. Fri 12/07:
42. Fri 12/14: 8:00am-10am: Final Exam

Ressources

• Tao - Analysis I (free eBook access through Alden Library)
• Tao - Analysis II (free eBook access through Alden Library)

Last update: 2018-11-16 17:03:54.