https://www.uclaextension.edu/sciences-math/math-statistics/course/introduction-differential-topology-math-x-45148

https://www.uclaextension.edu/sciences-math/math-statistics/course/introduction-differential-topology-math-x-45148

Skip to content
# Tag: UCLA Extension

## Differential Topology—Two quarter sequence at UCLA Extension for Fall/Winter 2021

## 🔖 Introduction to Category Theory | UCLA Continuing Education

Bookmarked Introduction to Category Theory *(UCLA Continuing Education)*
## Gems And Astonishments of Mathematics: Past and Present—Lecture One

## Reply to Stephanie Hurlburt on Twitter

## RSVP to MATH X 451.43 Introduction to Algebraic Geometry: The Sequel | UCLA Extension

RSVPed Attending
## MATH X 451.43 Introduction to Algebraic Geometry: The Sequel | UCLA Extension

Bookmarked MATH X 451.43 Introduction to Algebraic Geometry: The Sequel *(UCLA Extension)*
## Algebraic Geometry Lecture 1

## 🔖 Elementary Algebraic Geometry by Klaus Hulek

Bookmarked Elementary Algebraic Geometry (Student Mathematical Library, Vol. 20) *(American Mathematical Society)*
## Introduction to Algebraic Geometry | UCLA Extension in Fall 2017

Bookmarked MATH X 451.42 Introduction to Algebraic Geometry *(UCLA Extension)*
## Introduction to Complex Analysis–Part 2 | UCLA Extension

## Introduction to Complex Analysis – Lecture 1 Notes

## Introduction to Complex Analysis | UCLA Extension

@UCLAExtension I know a follow up course to the first half of Differential Topology is being offered for Winter 2022, but it doesn’t seem to be on the site yet to register. Can someone fix this?

https://www.uclaextension.edu/sciences-math/math-statistics/course/introduction-differential-topology-math-x-45148

https://www.uclaextension.edu/sciences-math/math-statistics/course/introduction-differential-topology-math-x-45148

It hasn’t been announced officially in the UCLA Extension catalog, but Dr. Mike Miller’s anticipated course topic for Fall 2021 is differential topology. The anticipated recommended text is *Differential Topology: An Introduction* by David B. Gauld (M. Dekker, 1982 or Dover, 1996 (reprint)).

The offering is naturally dependent on potential public health measures in September, which may also create a class limit on the number of attendees, so be sure to register as soon as it’s announced. For those who are interested in mathematics, but have never attended any of Dr. Miller’s lectures, I’ve previously written some details about his stye of presentation, prerequisites (usually very minimal despite the advanced level of the topics), and other details.

A few of us have already planned weekly Thursday night topology study sessions through the end of Spring and into Summer for those interested in attending. Just leave a comment with your contact information and I’ll be in touch with details.

I hope to see everyone in the fall.

Last night saw the wrap up of Dr. Michael Miller’s excellent Winter quarter class *Introduction to Category Theory*. As usual he passed out a short survey to accept ideas for the Fall and Winter quarters this coming year at UCLA Extension.

If you didn’t get a chance to weigh in, feel free to email him directly, or respond here with your suggestions (in order of preference) and I’ll pass them along.

I keep a list of his past offerings (going back to 2006, but he’s been doing this since 1973) on my site for reference. He’s often willing to repeat courses that have been previously offered, particularly if there’s keen interest in those topics.

Some of the suggestions on last night’s list included:

combinatorics

combinatorial group theory

number theory

game theory

group theory

ring theory

field theory

Galois theory

real analysis

point set topology

differential equations

differential geometry

Feel free to vote for any of these or suggest your own topics. Keep in mind that many of the topics in the past decade have come about specifically because of lobbying on behalf of students.

This course is an introduction to the basic tenets of category theory, as formulated and illustrated through examples drawn from algebra, calculus, geometry, set theory, topology, number theory, and linear algebra.

Category theory, since its development in the 1940s, has assumed an increasingly center-stage role in formalizing mathematics and providing tools to diverse scientific disciplines, most notably computer science. A category is fundamentally a family of mathematical obejcts (e.g., numbers, vector spaces, groups, topological spaces) along with “mappings” (so-called morphisms) between these objects that, in some defined sense, preserve structure. Taking it one step further, one can consider morphisms (so-called functors) between categories. This course is an introduction to the basic tenets of category theory, as formulated and illustrated through examples drawn from algebra, calculus, geometry, set theory, topology, number theory, and linear algebra. Topics to be discussed include: isomorphism; products and coproducts; dual categories; covariant, contravariant, and adjoint functors; abelian and additive categories; and the Yoneda Lemma. The course should appeal to devotees of mathematical reasoning, computer scientists, and those wishing to gain basic insights into a hot area of mathematics.

January 8, 2019 - March 19, 2019

Tuesday 7:00PM - 10:00PM

Location: UCLA

Instructor: Michael Miller

Fee: $453.00

The new catalog is out today and Mike Miller’s Winter class in Category Theory has been officially announced.

Oddly, it wasn’t listed in the published physical catalog, but it’s available online. I hope that those interested in mathematics will register as well as those who are interested in computer science.

Last night was the first lecture of Dr. Miller’s *Gems And Astonishments of Mathematics: Past and Present* class at UCLA Extension. There are a good 15 or so people in the class, so there’s still room (and time) to register if you’re interested. While Dr. Miller typically lectures on one broad topic for a quarter (or sometimes two) in which the treatment continually builds heavy complexity over time, this class will cover 1-2 much smaller particular mathematical problems each week. Thus week 11 won’t rely on knowing all the material from the prior weeks, which may make things easier for some who are overly busy. If you have the time on Tuesday nights and are interested in math or love solving problems, this is an excellent class to consider. If you’re unsure, stop by one of the first lectures on Tuesday nights from 7-10 to check them out before registering.
## Lecture notes

## Course Description

### Suggested Prerequisites

## Renovated Classrooms

## Category Theory for Winter 2019

For those who may have missed last night’s first lecture, I’m linking to a Livescribe PDF document which includes the written notes as well as the accompanying audio from the lecture. If you view it in Acrobat Reader version X (or higher), you should be able to access the audio portion of the lecture and experience it in real time almost as if you had been present in person. (Instructions for using Livescribe PDF documents.)

We’ve covered the following topics:

- Class Introduction
- Erdős Discrepancy Problem
- n-cubes
- Hilbert’s Cube Lemma (1892)
- Schur (1916)
- Van der Waerden (1927)

- Sylvester’s Line Problem (partial coverage to be finished in the next lecture)
- Ramsey Theory
- Erdős (1943)
- Gallai (1944)
- Steinberg’s alternate (1944)
- DeBruijn and Erdős (1948)
- Motzkin (1951)
- Dirac (1951)
- Kelly & Moser (1958)
- Tao-Green Proof

- Homework 1 (homeworks are generally not graded)

Over the coming days and months, I’ll likely bookmark some related papers and research on these and other topics in the class using the class identifier MATHX451.44 as a tag in addition to topic specific tags.

Mathematics has evolved over the centuries not only by building on the work of past generations, but also through unforeseen discoveries or conjectures that continue to tantalize, bewilder, and engage academics and the public alike. This course, the first in a two-quarter sequence, is a survey of about two dozen problems—some dating back 400 years, but all readily stated and understood—that either remain unsolved or have been settled in fairly recent times. Each of them, aside from presenting its own intrigue, has led to the development of novel mathematical approaches to problem solving. Topics to be discussed include (Google away!): Conway’s Look and Say Sequences, Kepler’s Conjecture, Szilassi’s Polyhedron, the ABC Conjecture, Benford’s Law, Hadamard’s Conjecture, Parrondo’s Paradox, and the Collatz Conjecture. The course should appeal to devotees of mathematical reasoning and those wishing to keep abreast of recent and continuing mathematical developments.

Some exposure to advanced mathematical methods, particularly those pertaining to number theory and matrix theory. Most in the class are taking the course for “fun” and the enjoyment of learning, so there is a huge breadth of mathematical abilities represented–don’t not take the course because you feel you’ll get lost.

I’ve written some general thoughts, hints, and tips on these courses in the past.

I’d complained to the UCLA administration before about how dirty the windows were in the Math Sciences Building, but they went even further than I expected in fixing the problem. Not only did they clean the windows they put in new flooring, brand new modern chairs, wood paneling on the walls, new projection, and new white boards! I particularly love the new swivel chairs, and it’s nice to have such a lovely new environment in which to study math.

As I mentioned the other day, Dr. Miller has also announced (and reiterated last night) that he’ll be teaching a course on the topic of Category Theory for the Winter quarter coming up. Thus if you’re interested in abstract mathematics or areas of computer programming that use it, start getting ready!

As I get amped up for the start of Mike Miller’s Fall math class Gems and Astonishments of Mathematics, which is still open for registration, I’m even more excited that he’s emailed me to say that he’ll be teaching Category Theory for the Winter Quarter in 2019!!

It’s not specifically femme yet does involve tea, but I’ve noticed something informal like this at the Starbucks just two blocks West of CalTech in Pasadena.

Separately but related, “adults” looking for a varied advanced math outlet in the Los Angeles area are welcome to join Dr. Mike Miller’s classes at UCLA Extension on Tuesday nights from 7-10pm. We’re working on Algebraic Geometry this quarter. For those who might need notes to play catch up, I’ve got copies, with full audio recordings, that I’m happy to share.

Algebraic geometry is the study, using algebraic tools, of geometric objects defined as the solution sets to systems of polynomial equations in several variables. This course is the second in a two-quarter introductory sequence that develops the basic theory of this classical mathematical field. Whereas the fall-quarter course focused more on the subject’s algebraic underpinnings, this quarter will concentrate on geometric interpretations and applications. Topics to be discussed include Bézout’s Theorem, rational varieties, cubic curves and surfaces (including the remarkable 27-line theorem), and the connection between varieties and manifolds. The theoretical discussion will be supported by a large number of examples and exercises. The course should appeal to those with an interest in gaining a deeper understanding of the mathematical interplay among algebra, geometry, and topology.

I’m definitely attending the Winter Quarter!

Algebraic geometry is the study, using algebraic tools, of geometric objects defined as the solution sets to systems of polynomial equations in several variables. This course is the second in a two-quarter introductory sequence that develops the basic theory of this classical mathematical field. Whereas the fall-quarter course focused more on the subject’s algebraic underpinnings, this quarter will concentrate on geometric interpretations and applications. Topics to be discussed include Bézout’s Theorem, rational varieties, cubic curves and surfaces (including the remarkable 27-line theorem), and the connection between varieties and manifolds. The theoretical discussion will be supported by a large number of examples and exercises. The course should appeal to those with an interest in gaining a deeper understanding of the mathematical interplay among algebra, geometry, and topology.

Alright math nerds, it’s that time again! Be sure to register for Mike Miller’s excellent follow-on course for Algebraic Geometry.

Don’t forget to use the coupon code EARLY to save 10% with an early registration–time is limited!

For those who are still on the fence about taking Algebraic Geometry this quarter (or the follow on course next quarter), here’s a downloadable copy of the written notes with linked audio that will allow you to sample the class:
### Lecture 1 – Part 1

### Lecture 1 – Part 2

**Algebraic Geometry-Lecture 1 notes [.pdf file with embedded and linked audio]**

I’ve previously written some notes about how to best access and use these types of notes in the past. Of particular note, one must download the .pdf file and open in a recent version of Adobe Acrobat to take advantage of the linked/embedded audio file. (Trust me, it’s worth doing as it will be like you were there with the 20 of us who showed up last night!)

For those who prefer just the audio files separately, they can be listened to here, or downloaded.

Again, the recommended text is *Elementary Algebraic Geometry* by Klaus Hulek (AMS, 2003) ISBN: 0-8218-2952-1.

For those new to Dr. Miller’s classes, I’ve written up some hints/tips about them in the past as well.

This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

Dr. Miller emailed me yesterday to confirm that the textbook for his Fall UCLA Extension course *Elementary Algebraic Geometry* by Klaus Hulek (AMS, 2003) ISBN: 0-8218-2952-1.

will be Sadly, I totally blew the prediction of which text he’d use. I was so far off that this book wasn’t even on my list to review! I must be slipping…

Algebraic geometry is the study, using algebraic tools, of geometric objects defined as the solution sets to systems of polynomial equations in several variables. This introductory course, the first in a two-quarter sequence, develops the basic theory of the subject, beginning with seminal theorems—the Hilbert Basis Theorem and Hilbert’s Nullstellensatz—that establish the dual relationship between so-called varieties—both affine and projective—and certain ideals of the polynomial ring in some number of variables. Topics covered in this first quarter include: algebraic sets, projective spaces, Zariski topology, coordinate rings, the Grassmannian, irreducibility and dimension, morphisms, sheaves, and prevarieties. The theoretical discussion will be supported by a large number of examples and exercises. The course should appeal to those with an interest in gaining a deeper understanding of the mathematical interplay among algebra, geometry, and topology. Prerequisites: Some exposure to advanced mathematical methods, particularly those pertaining to ring theory, fields extensions, and point-set topology.

Dr. Michael Miller has announced the topic for his Fall math class at UCLA Extension: Algebraic Geometry!!

Yes math fans, as previously hinted at in prior conversations, we’ll be taking a deep dive into the overlap of algebra and geometry. Be sure to line up expeditiously as registration for the class won’t happen until July 31, 2017.

While it’s not yet confirmed, some sources have indicated that this may be the first part of a two quarter sequence on the topic. As soon as we have more details, we’ll post them here first. As of this writing, there is no officially announced textbook for the course, but we’ve got some initial guesses and the best are as follows (roughly in decreasing order):

*Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra*(Undergraduate Texts in Mathematics) 4th ed. by David A. Cox, John Little, and Donal O’Shea*Algebraic Geometry: An Introduction*(Universitext) by Daniel Perrin*An Invitation to Algebraic Geometry*(Universitext) by Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves*Algebraic Geometry*(Dover Books on Mathematics) by Solomon Lefschetz (Less likely based on level and age, but Dr. Miller does love inexpensive Dover editions)

For those who are new to Dr. Miller’s awesome lectures, I’ve written some hints and tips on what to expect.

Most of his classes range from about 20-30 people, many of them lifelong regulars. (Yes, there are dozens of people like me who will take almost everything he teaches–he’s that good. This class, my 22nd, will be the start of my second decade of math with him.)

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!

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.*]

on 09/20/16, I’m attaching a 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.

Dr. Michael Miller has announced his Autumn mathematics course, and it is…
## Introduction to Complex Analysis

#### Update 9/1/16

### Textbook

### Alternate textbooks

#### Undergraduate

#### More advanced

### References

## 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