Analysis

Course Description and Grading Breakdown
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 Mittag-Leffler 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, Paley-Wiener theorems, global analytic functions and the Poincare metric.  

The grade will be based entirely on homework sets due roughly every other week (most likely four over the course of the term), with no exams. Students are allowed one free extension, to be used by sending an e-mail to the professor.  This free extension will last one week, except that if there is a homework set due the last week of term, that extension will at most last until the day before finals.  No further extensions will be granted without a recommendation from the relevant Dean to do so.

Collaboration is encouraged, to the extent of figuring out how to approach problems; each student is of course responsible for understanding the solution and writing it up in their own words.  (Also see table below.)


Course Meeting Time and Location
Monday, Wednesday and Friday
11:00 - 11:55 am
104 Math Building (Building 15)

Course Instructor Contact Information and Office Hours
219 Math Building (Building 15)

TA Contact Information and Office Hours
2-I Math Building (Building 15)

Course Schedule and Textbook

 DateTopic 
  
  


Course Policies
Late work - 


Assignments
 Date PostedAssignment Due Date 
 1/16/18HW1 1/26/18 in class
 1/24/18HW2 2/9/18 in class
 2/9/18HW3 2/23/18 in class
 2/23/18HW4  3/9/18 in class


Collaboration Table

 

Homework

You may consult:

 

Course textbook (including answers in the back)

YES

Other books

YES

Solution manuals

NO

Internet

YES

Your notes (taken in class)

YES

Class notes of others

YES

Your hand copies of class notes of others

YES

Photocopies of class notes of others

YES

Electronic copies of class notes of others

YES

Course handouts

YES

Your returned homework / exams

YES

Solutions to homework / exams (posted on webpage)

YES

Homework / exams of previous years

NO

Solutions to homework / exams of previous years

NO

Emails from TAs

YES

You may:

Discuss problems with others

YES

Look at communal materials while writing up solutions

YES

Look at individual written work of others

NO

Post about problems online

NO

For computational aids, you may use:

Calculators

YES*

Computers

YES*

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.

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HW01.pdf
(46k)
Caltech Math,
Jan 16, 2018, 12:00 PM
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HW02.pdf
(59k)
Caltech Math,
Jan 24, 2018, 11:54 AM
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HW03.pdf
(146k)
Caltech Math,
Feb 9, 2018, 12:27 PM
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HW04.pdf
(44k)
Caltech Math,
Feb 23, 2018, 10:30 AM