It’s true what they say, “Complex Analysis IS for lovers.” #theoremoncanonicalproducts #HappyValentinesDay

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# Tag: complex analysis

## Checkin Mathematical Sciences Building, UCLA

## Check in Mathematical Sciences Building, UCLA

## I’m a tad under the weather, so I’m skipping complex analysis tonight.

## The best part of a rainy morning

## The first quarter of Complex Analysis is slowly drawing to a close

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## Introduction to Complex Analysis–Part 2 | UCLA Extension

## Fundamental Theorem of Algebra

## Millions of photos of legs by beaches and pools… Now you suddenly realize what they’ve all been missing.

## Just spent the last 25 minutes hanging out with Terry Tao talking about complex analysis, blogging, and math pedagogy

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## Introduction to Complex Analysis – Lecture 1 Notes

## 🔖 Complex Analysis by Elias M. Stein & Rami Shakarchi

## 📖 5.0% done with Complex Analysis by Elias M. Stein & Rami Shakarchi

## 📖 5.0% done with Complex Analysis by Lars V. Ahlfors

## 🔖 Complex Analysis by Lars Ahlfors

## Introduction to Complex Analysis | UCLA Extension

## Introduction to Complex Analysis

#### Update 9/1/16

### Textbook

### Alternate textbooks

#### Undergraduate

#### More advanced

### References

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Musings of a Modern Day Cyberneticist

It’s true what they say, “Complex Analysis IS for lovers.” #theoremoncanonicalproducts #HappyValentinesDay

Los Angeles, California, United States of America

Syndicated copies to:Clean boards before complex analysis.

Los Angeles, California, United States of America

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Photo taken at: UCLA Math Sciences Building

There’s still plenty of time to join us for the second installment in January!

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 Applicationsby Richard A. Silverman, Dover Publications; ISBN 0-486-64762-5

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!

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Dr. Tao is keeping a great set of complex analysis notes on his blog.

For those who missed the first class of 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!

Syndicated copies to:## 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.

🔖 Marked *Complex Analysis* by Elias M. Stein & Rami Shakarchi as currently reading in relation to UCLA class Introduction to Complex Analysis

📖 5.0% done with Complex Analysis by Elias M. Stein & Rami Shakarchi

A nice beginning overview of where they’re going and philosophy of the book. Makes the subject sound beautiful and wondrous, though they do use the word ‘miraculous’ which is overstepping a bit in almost any math book whose history is over a century old.

Their opening motivation for why complex instead of just real:

However, everything changes drastically if we make a natural, but misleadingly simple-looking assumption on that it is differentiable in the complex sense. This condition is called

holomorphicity, and it shapes most of the theory discussed in this book.

We shall start our study with some general characteristic properties of holomorphic functions, which are subsumed by three rather miraculous facts:

Contour integration: If is holomorphic in , then for appropriate closed paths inRegularity: If is holomorphic, then is indefinitely differentiable.Analytic continuation: If and are holomorphic functions in which are equal in an arbitrarily small disc in , then everywhere in .

This far into both books, I think I’m enjoying the elegance of Stein/Shakarchi better than Ahlfors.

Syndicated copies to:🔖 Marked *Complex Analysis* by Lars Ahlfors as currently reading in relation to UCLA class Introduction to Complex Analysis

Looking for some serious entertainment on Tuesday nights this fall? Professor Mike Miller has got you covered!

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

## 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!

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]

(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!

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:

*Complex Analysis*by Joseph Bak and Donald J. Newman [2]*Complex Analysis*by Theodore Gamelin [3]*Complex Variables and Applications*by James Brown and Ruel Churchill [4]*Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics*by Edward Saff and Arthur D. Snider (Pearson, 2014, 3rd edition) [5]

*Complex Analysis*by Lars Ahlfors [6]*Complex Analysis*by Serge Lang [7]*Functions of One Complex Variable*(Graduate Texts in Mathematics by John B. Conway (Springer, 1978) [8]*Complex Analysis*(Princeton Lectures in Analysis, No. 2) by Elias M. Stein and Rami Shakarchi (Princeton University Press, 2003) [9]

[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