Math 131A Section 4, Analysis, Spring 2015
Lecture time: MWF 11-11:50AM. Lecture room: MS 5147 .
Instructor: Huy Tran. Email: tvhuy at math dot ucla dot edu. Office: MS 6617-C.
Office hours: 1-2 MWF
Discussion session: Thursday 11-11:50AM. Room MS 5147.
Teaching Assistant: Haofei Fan. Email: ??? at math dot ucla dot edu. Office: MS 2943
Office hours: ???
Syllabus from Math department. Click here to see information about grading, homework, exam policy.
Textbook: K.A. Ross, Elementary Analysis: The Theory of Calculus, 2nd Ed.
Other resources: 131AH, Tao, Winter 2003, two, three, four
Announcement:
-3/30: Hw1 is posted. It is due this Friday.
-4/3: Hw 2 is posted. It is due on 4/10.
-4/8: For each homework, the TA will type up the solutions of three problems for you (including 2 graded problems).
Problems 4.11 and 4.15 are omitted from HW2.
-4/11: Hw 3 is posted. It is due on 4/17
-4/19: Students whose last digit of ID is even will go to MS 5147 for midterm 1. Others will go to MS 5225.
Please see the "exam preparation" page to see the instruction in the first page of Midterm 1.
-4/20: Solution is uploaded.
-4/22: We will skip limsup, liminf material. My office hour is 1-2 MWF.
The back of the book has hints and answers for odd-numbered problems. You should learn from it.
-4/23: One(1) point will be added to your final if you find an error, or typo of the textbook and send it to me. The errors should not be already in the latest errata from the publisher.
-4/26: List of errors/typos is recorded here
-4/27: I'll be out of town on Wednesday. Someone will teach for me. No office hour on that day. Email is OK.
-5/6: Office hours this week and next week:
Email is welcome.
-5/8: Material for midterm 2 is up to section 19.
-5/15: Please be careful when reading section 20. The writing is not well-organized (in my opinion). Please stick with the following definition:
lim_{x to a} f(x) = L if and only if for any e>0, there exists delta>0 such that |f(x)-L|< e for all 0< |x-a|<L and x in dom(f).
-6/1: Office hours for this week:
-6/2: You are allowed to use two sides of an A4 paper sheet for note. Other stuff (calculator, book, phone, laptop) is not allowed.
-6/3: Please spend 5 mins to fill out the teaching evaluation on Myucla. Thanks.
Tentative schedule (subject to change): (you may need to zoom out the page to see the table)
Final: Tuesday, June 09, 2015, 8AM-11AM, room BOELTER 5436
Homework problems: see schedule for due dates, "updating" means it could be changed, "updated" means there is no more changes.
-Homework 1 (updated):
+ Read https://math.berkeley.edu/~hutching/teach/proofs.pdf (I realize this is unpractical to require you to read)
+ Read S1, S2.
+ Do exercises 1.1, 1.4, 1.8, 1.11, 2.1 (for sqrt(3), 2.2 (for 4th root of 13), 2.3, 2.4,
-Homework 2 (updated):
+ Read S3, S4, S5.
+ Do exercises 2.5, 2.7, 3.1, 3.2, 3.3, 3.4, 3.7, 3.8, 4.1 & 4.3, 4.5, 4.7, 4.9, 4.11, 4.13, 4.15
+ Read some remarks on writing mathematical proofs, especially the following parts:
- Write in paragraph form.
- Use proper English.
- Write clearly (We will prove the contrapositive. We will prove this by induction)
- State what you are proving.
- Label your theorems.
- Show where your proof begin and end.
- Writing mathematical formulas (I'll explain this in class).
-Homework 3 (updated):
+ Read S5, S7, S8, S9.
+ Do exercises 4.11, 4.15, 5.2, 5.4, 7.3, 7.4, 7.5, 8.2 (a, c, e), 8.3, 8.4, 8.8, 8.10
-Homework 4 (updated):
+ Read S9
+ Relax with this http://abstrusegoose.com/230
+ Do exercises 8.5, 8.6, 8.9, 9.1, 9. 3, 9.5, 9.6, 9.12, 9. 17
-Homework 5 (updated):
+ Read S10, S11 (we skip limsup, liminf)
+ Do exercises 10.2, 10.4, 10.6, 10.10, 11.2, 11.4 (skip (c))
-Homework 6 (updated)
+ Read S14 (skip S12, S15)
+ Do exercises 11.6, 11.9, 14.2, 14.4, 14.6, 14.8, 14.9
-Homework 7 (updated):
+ Read S17, S18, S19, S20, S28, S29
+ Do exercises 18.4, 18.6, 18.7, 18.8, 20.2, 20.6, 20.18, 28.2, 28.4, 28.6, 28.14
-Homework 8 (updated):
+Read S32, S33, S34.
+ Do exercises 19.9, 19.10; 29.4, 29.10, 29.12, 29.18; 32.2, 32.6; 33.4, 33.5, 33.10