Math 110b  
Analysis, I  
Winter 20142015  
MWF
11:00
//
159
Sloan



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Math 110b is our graduate course in complex analysis, the second in the required graduate analysis sequence. Topics include Cauchy's integral theorem (in great generality: contractible rectifiable contours) with applications, some discussion of complex functional analysis (uniform convergence, Vitali, Montel, Hurwitz theorems), conformal maps (linear fractional transformations, the Riemann mapping theorem), the Weierstrass and MittagLeffler theorems (representations of entire functions as products, resp. meromorphic functions as sums), and some theory of special functions (the Gamma function, as well as an introduction to elliptic functions). Further topics as time allows will probably include Picard's theorem, PaleyWiener theorems, global analytic functions and the Poincare metric. 

Grading:
Based
on
homework;
no
exams. Homework: There will be four homeworks due roughly every two weeks. They will definitely be longer than a oneweek homework. The first three homeworks will have roughly equal weight and the last homework, which will have a threeweek time period, will be longer and be worth somewhat more. Until one week before the homework is due, you may not collaborate but you may use any books. For the last week you may collaborate with others in the class or ask leading questions of the TA or Professor. The spirit of this is that you should be making significant effort to do the homework yourself before speaking to others (so if you leave the homework for the last few days, you really shouldn't collaborate until a day after you seriously start). Also, this should be primarily your own efforts. So it is contrary to the spirit (but not technically the letter) of the collaboration policy for two or more students to sit down and do the homework as a joint project. Included in "use any books" is googling on the Internet. However, posting the homework on a chat site is definitely an example of collaboration NOT with others in the class and is therefore not allowed. Late homework policy: If you get a note from the Dean's Office (personal problems) or infirmary (medical problems) requesting a postponement, it will be honored. Otherwise, late homework will not be accepted EXCEPT ONE time (per term) you may email me PRIOR to the due time requesting an extension of up to one week (for the last HW up to two days) and it will granted. 

We will use a draft book by Barry Simon on Complex Analysis (that covers both Ma 110b and 111b). We are getting this 920page manuscript "printed" by Caltech graphic arts at a cost of to be determined per copy. 









