Math 405 - Complex Analysis - Fall 2016

General Information:

Meeting Time:	MWF 9 - 9:50
Location:	Jones 113
Instructor:	Ryan Vinroot Office: Jones 100D Office Hours: M 3:30-5, T 10:30-12, Th 3:30-5 (also by appointment).
Textbook:	Complex Variables and Applications (9th Edition) by James Ward Brown and Ruel V. Churchill
Grade Breakdown:	Class Participation - 5%, Midterm - 30%, Homework - 35%, Final Exam - 30%. The grading scale will be the standard 10 percentage point scale, so that a final score of 93 or higher is an A, 90-92 is an A-, 87-89 is a B+, 83-86 is a B, 80-82 is a B-, 77-79 is a C+, 73-76 is a C, 70-72 is a C-, etc.
Attendance & Lecture Policy:	It is expected that you attend all lectures, with exceptions minimized. It is greatly appreciated when you are on time. Please do your best to stay awake and attentive during lecture, please do not email or text during lecture, and keep all cell phones/hand held devices/tablets/laptops put away during lecture. While it is understandable that you may miss a lecture here and there, or be sleepy in class once in awhile, repeated absences, late arrivals, naps, or general non-attentiveness will negatively affect your class participation score.
Prerequisites:	Math 311 Elementary Analysis. It is extremely important to have a thorough knowledge of the topics from Math 214 Foundations of Mathematics, and to have a firm grasp of the main concepts from Math 311.

Course Summary: Complex analysis is the study of functions and Calculus of a complex variable. We will study and develop many of the most important notions from Calculus 1 and 2, as well as Elementary Analysis, including limits, derivatives, integrals, and power series. While proofs will not be the primary focus of the course, we will give proofs (or outlines of proofs) of most of the Theorems we develop and use. You will be expected to prove some things as well, but the main focus will be on the concepts and computations.

Dates & Course Announcements:

Midterm and Final Exams:

There will be one midterm (details will be determined later). The final exam will be timed. The midterm and the final will each count as 30% of your final grade. The final exam will be on Fri, Dec 9, from 9 AM until 12 Noon.

Exam Calendar (Tentative):

Exam	Date	Time/Due	Location
Midterm	Fri, Oct 28	8:35 - 9:50 AM	Jones 113
Final Exam	Fri, Dec 9	9 AM - 12 Noon	Jones 113

All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
Important Dates and Class Holidays:
- Fri, Sep 2: ADD/DROP DEADLINE
- Sat, Oct 8 - Tues, Oct 11: NO CLASS (Fall Break)
- Fri, Oct 21: WITHDRAW DEADLINE
- Fri, Oct 28, 8:35 AM - MIDTERM
- Wed, Nov 23 - Sun, Nov 27: NO CLASS (Thanksgiving Break)
- Fri, Dec 9, 9:00 AM - 12 Noon - FINAL EXAM
(8/24) My office hours during the first short week of classes are as follows: W 1:30-3, Th 3:30-5, F 1-2.
(8/29) The next HW is due next Mon, Sept 5, and is a group HW. During class time on Mon, Sept 5, you will have the chance to discuss all of the problems together. The HW (one for each group) will be due at 5 PM that day, on my door.
(8/29) My office hours this week are as follows: M 3-4:30, T 1-2:30, Th 10:30-12.
(9/2) Homework 2 (the group HW) will be due on my office door (Jones 100D) by 4:30 pm on Monday, Sept 5. The outer door of Jones 100 is usually locked by 5 pm, or sometimes earlier, which is why I say 4:30 is the due time. There should be one HW per group, with all of your names on the paper turned in. I will make a copy of the graded HW for each individual in the group. Class begins at 9 AM on Mon, Sept 5, as usual, and it will be an open discussion on any HW problem. Groups should have already discussed and written up all of the HW unless your are stuck on something. Professor Bolotnikov will be there to make sure everyone is there and that the discussion stays on track.
(9/2) My office hours during the week of Sept 5-9 are as follows: T 10:30-12 and 3-4:30, W 1:30-3, Th 3:30-5.
(9/12) My permanent weekly office hours are set as follows: M 3:30-5, T 10:30-12, Th 3:30-5 (you can also email me to try to make an appointment for another time).
(9/20) For those of you who are interested, I will finish the proof of the sufficiency conditions for a complex-valued function to be differentiable at about 8:30 on Wed morning, before class. This is a completely unrequired half-lecture. However, if you have missed a class or two, then your presence would be noted in terms of your participation in the class (which is 5% of your total grade).
(9/29) On Fri, Sept 30, at 8:30 I'll talk a bit about connectedness in the complex plane, and I will continue that topic at another time. This is a completely optional lecture.
(9/29) On Mon, Oct 3, and on Wed, Oct 5, we will start class officially at 8:35 on both mornings. This will be normal class material, and not extra optional material. We will then not have class on Fri, Oct 7.
(10/12) I will continue the extra (optional) lecture on connectedness at 8:30 AM this Friday (Oct 14).
(10/21) Here are some problems from each chapter of the book which is covered on the Midterm:
Chapter 1: pgs. 13-14 #3, 6, pg. 16 #7, 9, pg. 24 #8, pg. 31 #4, 5, pg. 35 #5
Chapter 2: pg. 44 #6, pgs. 54-55 #1, 9, 12, pg. 61 #1, 2, 6, pgs. 70-71 #1(a,b,d), 3, 4, pgs. 76-77 #1(a,c), 2(b), 4, 5
Chapter 3: pg. 89 #1, 2, 4, pg. 95 #1, 2, pg. 99 #3, pg. 103 #1, 2, pg. 108 #9, 10, pg. 111 #7, 8 , pg. 114 #1, 3
Chapter 4: pgs. 119-120 #2, 5, pg. 124 #2, 4, pgs. 132-133 #1, 2, 6
Chapter 8: pg. 301 #3, 4, pg. 306 #7, 10, pgs. 325 #2, 7
(10/25) The Midterm will be this Fri, Oct 28, in the normal classroom. You may start the midterm as early as 8:35 AM.
(10/31) As I stated in class, you may turn in corrections to any problems on your midterm where you missed points, for up to 50% of your points back. This work is due in 2 weeks, on Mon, Nov 14, at 9 AM in class. You should complete new solutions on clean pieces of paper, and attach those to your original exam to turn in. You may not discuss any of the problems with anyone except for me, and I am happy to help you if you are stuck on a problem.
(11/8) Tomorrow (Wed, Nov 9), there will be an optional half-lecture at 8:30.
(11/10) Tomorrow (Fri, Nov 11), there will be another optional half-lecture at 8:30, continuing the proof we started during the Wed optional half-lecture.
(11/21) There is an optional HW 12 due on Fri, Dec. 2 (the last day of class) at 9 AM in class. The material on this HW will be covered on the final, so even if you don't turn it in you should make sure you understand the problems. Since this is optional, no late homework will be accepted, so anything you would like credit for should be turned in by class time on the last day of class. Your HW grade can only increase from turning in the optional homework, so any problems you turn in will help. You will be able to pick up your optional homework any time before the final exam.
(11/28) I fixed a typo in the optional HW 12. It should be pg. 237 #1(d,e), not (d,f).
(12/2) The Final Exam is on Friday, Dec. 9, 9 AM-12 Noon, in Jones 113 (our normal classroom). The final exam will be roughly twice as long as the midterm, and will be commulative, with a very slight emphasis on the second half of the semester's material (something like 40% first half, 60% second half). There will be problems not unlike the ones on the midterm, along with some TRUE/FALSE problems based on definitions, concepts, and main theorems.
(12/2) The following Chapters/sections are exactly what are covered on the Final exam:
Chapter 1 - Sec. 1-12 (all of Chapter 1)
Chapter 2 - Sec. 13-27 (all but the last 2 sections)
Chapter 3 - Sec. 30-40 (all of Chapter 3)
Chapter 4 - Sec. 41-50 and 52-59 (all but section 51)
Chapter 5 - Sec. 60-68 (just first 9 sections)
Chapter 6 - Sec. 74-77 (just first 4 sections)
(12/2) My office hours next week will be as follows:
Tues, Dec. 6: 12-2 pm
Wed, Dec. 7: 9-10 am and 12-2 pm
Thurs, Dec. 8: 9-10 am and 12-3 pm.
(12/2) Here are practice problems from material covered since the midterm. For practice problems from the first half of the class, do all of the midterm review problems that you haven't done yet (and go over the homework problems as well):
Chapter 4: pgs. 138-139 #1, 2, 3, pg. 147 #1, 2, 3, pgs. 159-160 #1(a, b, e), 2, pgs. 170-171 #1, 2, 7, pgs. 177-178 #4, 5, 6
Chapter 5: pg. 185 #1, 6, 7, pgs. 195-197 #1, 2, 3, 11, pgs. 205-206 #1, 2, 3, 5
Chapter 6: pgs. 237-238 #1(a, b, c), 2(a, d), 4
Harmonic Functions (Sec. 27): pg. 90 #13, pg. 97 #11, pg. 112 #15, pg. 178 #7

Homework:

Homework problems will be a very important part of the course, and there will be homework assigned almost every week. Proofs and computations should be written carefully and neatly, with attention paid to the completeness of your argument and clarity of your steps. Individual homework assignments should be written up by yourself, although some collaboration while working on the homework is OK. You should not, under any circumstances, attempt to look up solutions or hints to problems online. I will consider this plagiarism, an honor offense.

Homework is due at the beginning of class on the due date of the assignment, and if you like you may email me a pdf of your homework if you LaTex it. Homework that is turned in or in my email inbox after the beginning of the class is considered late. Late penalties are:
10% off if it is turned in after the beginning of class, but it is in my hands, or in my email inbox as a pdf by 5 pm on the day it is due.
20% off if it is turned in by 5 pm the next weekday after the due date.
20% more off for each (week)day late, turned in by 5 pm, thereafter.
Everything is easier, of course, if you turn in the homework on time!

Homework scores will each be out of 50 points. Your lowest homework score of the semester will be dropped.

Assignment	Problems	Due Date
1	pg. 8 #8, pg. 13 #5, pg. 17 #14, 15	Mon, Aug 29
2	Individual (Don't turn in): pg. 31 #3, 5, pg. 43 #1-4 Group (Turn in): pg. 24 #9, pg. 31 #7, pg. 35 #10, pg. 44 #5, 8	Mon, Sept 5
3	pg. 301 #2, 5, pgs. 54-55 #2, 5, 7	Mon, Sept 12
4	pg. 35 #6, pg. 55 #10, 11 pg. 61 #4, 8, 9	Mon, Sept 19
5	pgs. 70-71 #1(c), 2(c), 6, 8 pg. 76 #1(b,d), 2(a,c)	Mon, Sept 26
6	pg. 77 #6, pg. 90 #7, 10 pgs. 96-97 #5, 10, pg. 99 #1	Mon, Oct 3
7	pg. 103 #6, pg. 108 #11, pg. 111 #11 pg. 114 #6, pg. 325 #4, 8	Fri, Oct 14
8	pg. 119 #3, 4, pgs. 124-125 #1, 6 pgs. 133-134 #9, 10	Fri, Oct 21
9	pg. 139 #4, 5, pg. 147 #4 pgs. 159-161 #1(c,d,f), 5, 7	Mon, Nov 7
10	pgs. 170-171 #3, 4, 5, 9 pg. 79 #1, pg. 177 #1	Mon, Nov 14
11	pg. 177 #2, 3, pg. 186 #8 pgs. 196-197 #8, 9, 10	Mon, Nov 21
12 (Optional)	pgs. 205-207 #6, 7, 10 pg. 237 #1(d,e), 2(b,c), 3	Fri, Dec. 2

Math Major Writing Requirement (Math 300):

If you are a math major, and you would like to complete your major writing requirement through a writing assignment in this class, please let me know in the first week of class. This writing assignment will not count towards your grade in this class, but will rather just serve as your Major Writing Requirement (Math 300). If you decide to do this, you must write your paper on a topic in Complex Analysis (or a closely related subject) approved by me, and you must keep to a schedule of turning in drafts that is set at the beginning of the semester in order to get credit.