Tag: Riemann surfaces

Introduction to Complex Analysis–Part 2 | UCLA Extension

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 | UCLA Extension

Dr. Michael Miller has announced his Autumn mathematics course, and it is…

Introduction to Complex Analysis

Course Description

Complex analysis is one of the most beautiful and useful disciplines of mathematics, with applications in engineering, physics, and astronomy, as well as other branches of mathematics. This introductory course reviews the basic algebra and geometry of complex numbers; develops the theory of complex differential and integral calculus; and concludes by discussing a number of elegant theorems, including many–the fundamental theorem of algebra is one example–that are consequences of Cauchy’s integral formula. Other topics include De Moivre’s theorem, Euler’s formula, Riemann surfaces, Cauchy-Riemann equations, harmonic functions, residues, and meromorphic functions. The course should appeal to those whose work involves the application of mathematics to engineering problems as well as individuals who are interested in how complex analysis helps explain the structure and behavior of the more familiar real number system and real-variable calculus.

Prerequisites

Basic calculus or familiarity with differentiation and integration of real-valued functions.

Details

MATH X 451.37 – 268651  Introduction to Complex Analysis
Fall 2016
Time 7:00PM to 10:00PM
Dates Tuesdays, Sep 20, 2016 to Dec 06, 2016
Contact Hours 33.00
Location: UCLA, Math Sciences Building
Standard credit (3.9 units) $453.00
Instructor: Michael Miller
Register Now at UCLA

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

I often recommend people to join in Mike’s classes and more often hear the refrain: “I’ve been away from math too long”, or “I don’t have the prerequisites to even begin to think about taking that course.” For people in those categories, you’re in luck! If you’ve even had a soupcon of calculus, you’ll be able to keep up here. In fact, it was a similar class exactly a decade ago by Mike Miller that got me back into mathematics. (Happy 10th math anniversary to me!)

I look forward to seeing everyone in the Fall!

Update 9/1/16

Textbook

Dr. Miller is back from summer vacation and emailed me this morning to say that he’s chosen the textbook for the class. We’ll be using Complex Analysis with Applications by Richard A. Silverman.  [1]

Complex Analysis with Applications by Richard A. Silverman

(Note that there’s another introductory complex analysis textbook from Silverman that’s offered through Dover, so be sure to choose the correct one.)

As always in Dr. Miller’s classes, the text is just recommended (read: not required) and in-class notes are more than adequate. To quote him directly, “We will be using as a basic guide, but, as always, supplemented by additional material and alternate ways of looking at things.”

The bonus surprise of his email: He’s doing two quarters of Complex Analysis! So we’ll be doing both the Fall and Winter Quarters to really get some depth in the subject!

Alternate textbooks

If you’re like me, you’ll probably take a look at some of the other common (and some more advanced) textbooks in the area. Since I’ve already compiled a list, I’ll share it:

Undergraduate

More advanced

References

[1]
R. A. Silverman, Complex Analysis with Applications, 1st ed. Dover Publications, Inc., 2010, pp. 304–304 [Online]. Available: http://amzn.to/2c7KaQy
[2]
J. Bak and D. J. Newman, Complex Analysis, 3rd ed. Springer, 2010, pp. 328–328 [Online]. Available: http://amzn.to/2bLPW89
[3]
T. Gamelin, Complex Analysis. Springer, 2003, pp. 478–478 [Online]. Available: http://amzn.to/2bGNQct
[4]
J. Brown and R. V. Churchill, Complex Variables and Applications, 8th ed. McGraw-Hill, 2008, pp. 468–468 [Online]. Available: http://amzn.to/2bLQWcu
[5]
E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3rd ed. Pearson, 2003, pp. 563–563 [Online]. Available: http://amzn.to/2f3Nyj6
[6]
L. V. Ahlfors, Complex Analysis, 3rd ed. McGraw-Hill, 1979, pp. 336–336 [Online]. Available: http://amzn.to/2bMXrxm
[7]
S. Lang, Complex Analysis, 4th ed. Springer, 2003, pp. 489–489 [Online]. Available: http://amzn.to/2c7OaR0
[8]
J. B. Conway, Functions of One Complex Variable, 2nd ed. Springer, 1978, pp. 330–330 [Online]. Available: http://amzn.to/2cggbF1
[9]
El. M. Stein and R. Shakarchi, Complex Analysis. Princeton University Press, 2003, pp. 400–400 [Online]. Available: http://amzn.to/2bGOG9c