Introduction to Complex Analysis–Part 2 | UCLA Extension

The second in a series of two quarters of advanced math focusing on complex analysis
The topic for Mike Miller’s UCLA Winter math course isn’t as much a surprise as is often the case. During the summer he had announced he would be doing a two quarter sequence on complex analysis, so this Winter, we’ll be continuing on with our complex analysis studies.

I do know, however, that there were a few who couldn’t make part of the Fall course, but who had some foundation in the subject and wanted to join us for the more advanced portion in the second half. Toward that end, below are the details for the course:

Introduction to Complex Analysis: Part II | MATH X 451.41 – 350370

Course Description

Complex analysis is one of the most beautiful and practical disciplines of mathematics, with applications in engineering, physics, and astronomy, to say nothing of other branches of mathematics.  This course, the second in a two-part sequence, builds on last quarter’s development of the differentiation and integration of complex functions to extend the principles to more sophisticated and elegant applications of the theory.  Topics to be discussed include conformal mappings, Laurent series and meromorphic  functions, Riemann surfaces, Riemann Mapping Theorem, analytical continuation, and Picard’s Theorem.  The course should appeal to those whose work involves the application of mathematics to engineering problems, and to those interested in how complex analysis helps explain the structure and behavior of the more familiar real number system and real-variable calculus.

Winter 2017
Days: Tuesdays
Time: 7:00PM to 10:00PM
Dates: Jan 10, 2017 to Mar 28, 2017
Contact Hours: 33.00
Location: UCLA, Math Sciences Building
Course Fee(s): $453.00
Available for Credit: 3 units
Instructors: Michael Miller
No refund after January 24, 2017.
Class will not meet on one Tuesday to be announced.

Recommended Textbook: Complex Analysis with Applications by Richard A. Silverman, Dover Publications; ISBN 0-486-64762-5

 

Enroll Now

For many who will register, this certainly won’t be their first course with Dr. Miller–yes, he’s that good! But for the newcomers, I’ve written some thoughts and tips to help them more easily and quickly settle in and adjust: Dr. Michael Miller Math Class Hints and Tips | UCLA Extension

If you’d like additional details as well as lots of alternate textbooks, see the announcement for the first course in the series.

If you missed the first quarter and are interested in the second quarter but want a bit of review or some of the notes, let me know in the comments below.

I look forward to seeing everyone in the Winter quarter!

Michael Miller making a "handwaving argument" during a lecture on Algebraic Number Theory at UCLA on November 15, 2015. I've taken over a dozen courses from Mike in areas including Group Theory, Field Theory, Galois Theory, Group Representations, Algebraic Number Theory, Complex Analysis, Measure Theory, Functional Analysis, Calculus on Manifolds, Differential Geometry, Lie Groups and Lie Algebras, Set Theory, Differential Geometry, Algebraic Topology, Number Theory, Integer Partitions, and p-Adic Analysis.
Michael Miller making a “handwaving argument” during a lecture on Algebraic Number Theory at UCLA on November 15, 2015. I’ve taken over a dozen courses from Mike in areas including Group Theory, Field Theory, Galois Theory, Group Representations, Algebraic Number Theory, Complex Analysis, Measure Theory, Functional Analysis, Calculus on Manifolds, Differential Geometry, Lie Groups and Lie Algebras, Set Theory, Differential Geometry, Algebraic Topology, Number Theory, Integer Partitions, and p-Adic Analysis.

Introduction to Complex Analysis – Lecture 1 Notes

For those who missed the first class of Introduction to Complex Analysis on 09/20/16, I’m attaching a link to the downloadable version of the notes in Livescribe’s Pencast .pdf format. This is a special .pdf file but it’s a bit larger in size because it has an embedded audio file in it that is playable with the more recent version of Adobe Reader X (or above) installed. (This means to get the most out of the file you have to download the file and open it in Reader X to get the audio portion. You can view the written portion in most clients, you’ll just be missing out on all the real fun and value of the full file.) [Editor’s note: Don’t we all wish Dr. Tao’s class was recording his lectures this way.]

With these notes, you should be able to toggle the settings in the file to read and listen to the notes almost as if you were attending the class live. I’ve done my best to write everything exactly as it was written on the board and only occasionally added small bits of additional text.

If you haven’t registered yet, you can watch the notes as if you were actually in the class and still join us next Tuesday night without missing a beat. There are over 25 people in the class not counting several I know who had to miss the first session.

Hope to see you then!

Viewing and Playing a Pencast PDF

Pencast PDF is a new format of notes and audio that can play in Adobe Reader X or above.

You can open a Pencast PDF as you would other PDF files in Adobe Reader X. The main difference is that a Pencast PDF can contain ink that has associated audio—called “active ink”. Click active ink to play its audio. This is just like playing a Pencast from Livescribe Online or in Livescribe Desktop. When you first view a notebook page, active ink appears in green type. When you click active ink, it turns gray and the audio starts playing. As audio playback continues, the gray ink turns green in synchronization with the audio. Non-active ink (ink without audio) is black and does not change appearance.

Audio Control Bar

Pencast PDFs have an audio control bar for playing, pausing, and stopping audio playback. The control bar also has jump controls, bookmarks (stars), and an audio timeline control.

Active Ink View Button

There is also an active ink view button. Click this button to toggle the “unwritten” color of active ink from gray to invisible. In the default (gray) setting, the gray words turn green as the audio plays. In the invisible setting, green words seem to write themselves on blank paper as the audio plays.