Math 341, Real Analysis
Time: T/TH 1030-1145
Location: REC 307
Office hours: 1200-200 T, 1200-200 W, 800-1000 Th, and by appointment.
Book: I do not plan to have an official textbook for the class. There are many resources for analysis that are freely available online (for example, this book). I do plan to have class notes that will be updated throughout the term for the class. I will have links to web pages (mostly wikipedia) that give lengthier discussions of the various topics we cover. You should utilize the free information that abounds. The hyperlinks in the class notes are meant to make that easier. There are also several hyperlinks to YouTube videos that discuss concepts, proofs, and topics that arise in this class.
Problem sets: I will post weekly problem sets here in .pdf format. The problem sets will be due on Thursdays. I will try to post the problem sets a week before they are due.
Grades: I assign grades based on your rank within the class. I usually employ 3-4 schemes for producing a ranking. They are based on exams and homework. I give you the best grade among the different schemes. You may care about grades. The university may care about grades. I do not care about grades. For more information on grades and such, read the .pdf on grades and class logistics below.
The class: The two primary goals for the course are to introduce you to proof based mathematics and to provide you with a good working knowledge of real analysis.
Class announcements:
- I expect to have the first in class exam on September 22 on the first two chapters of the class notes. Typically I have the exams graded before the next class. I am hopeful I can do that on this first exam but have a full day of obligations on September 24.
- August 25. Office hours have been set. I will have 6 hours per week in total. Do remember that you can also email or text me with concerns, questions, .etc. I have a very limited time during lecture to provide you with intuition for the various topics we cover. Remember, I am here to help you digest the material.
- I have added two versions of the class notes. One is more printer friendly than the other. The non-print version has a greyish background that is easier on the eyes when reading on the computer. I will try to keep both up-to-date. Important: The non-print version will always be up-to-date. I only update the print version when I remember to.
- The hint on problem 7 on Pset 2 should be [Hint: De Morgan's Laws or Problem 4 on Pset 2].
- Important: I updated earlier sections of the notes. I know that they are terse notes and I will try to make them easier for students as the class progresses. The exercises in the notes are meant to help you understand the material. Presently, one of the exercises is on the first mid-term. This problem does not appear on a problem set.
- Important: Pset 5 is due on October 20.
- Review for Midterm 2 posted. I will not post a practice exam.
- Important: No Class on Tuesday November 8. I will be at Penn State. I will have regular office hours on Wednesday and Thursday.
- Important: Pset 9 posted. The third exam will cover series and integration. I will not post a review sheet. Pset 9 is meant to be a review sheet.
The lecture schedule with topic is below (this is tentative):
- Lecture 1. August 23. Sets and Functions.
- Lecture 2. August 25. Topological Spaces.
- Lecture 3. August 30. Metric Spaces.
- Lecture 4. September 1. Sequences: Topological spaces. (Problem Set 1 Due)
- Lecture 5. September 6. Sequences: Metric Spaces, I.
- Lecture 6. September 8. Sequences: Metric Spaces, II. (Problem Set 2 Due)
- Lecture 7. September 13. Sequences: Euclidean Space.
- Lecture 8. September 15. Review/Recovery (Problem Set 3 Due).
- Lecture 9. September 20. Review.
- Lecture 10. September 22. Exam 1.
- Lecture 11. September 27. Return and Review Exam 1.
- Lecture 12. September 29. Continuity, I.
- Lecture 13. October 4. Continuity, II.
- Lecture 14. October 6. Review Continuity (Problem Set 4 Due).
- October 11. No class. Fall Break.
- Lecture 15. October 13. Differentiation, I.
- Lecture 16. October 18. Differentiation, II.
- Lecture 17. October 20. Differentiation, III. (Problem Set 5 Due)
- Lecture 18. October 25. Review for Exam 2.
- Lecture 19. October 27. Exam 2.
- Lecture 20. November 1 (hand back exam and provide exam stats)
- Lecture 21. November 3, Series, I.
- Lecture 22. November 8. No class. Ben is out of town.
- Lecture 23. November 10. Series, II (Problem Set 6 Due).
- Lecture 24. November 15. Integration, I.
- Lecture 25. November 17. Integration, II (Problem Set 7 Due).
- Lecture 26. November 22. Integration, Review (Problem Set 8 Due).
- November 24. No Class. Thanksgiving Break.
- Lecture 27. November 29. Review for Exam 3.
- Lecture 28. December 1. Exam 3. (Problem Set 9 Due).
- Lecture 29. December 6. Return and Review Exam 3. Give final grades.