# Introduction to Algebraic Geometry | UCLA Extension in Fall 2017

MATH X 451.42 Introduction to Algebraic Geometry (UCLA Extension)
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):

1. 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
2. Algebraic Geometry: An Introduction (Universitext) by Daniel Perrin
3. An Invitation to Algebraic Geometry (Universitext) by Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves
4. 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.)

Syndicated copies to:

## Author: Chris Aldrich

I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, theoretical mathematics, and big history. I'm also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.

## 23 responses on “Introduction to Algebraic Geometry | UCLA Extension in Fall 2017”

1. I actually ordered the book. But I’m spending a lot of time studying machine learning! So I’m not sure, but I’d like to.

2. I originally made this compilation on May 31, 2016 to share with some friends and never got around to posting it. Now that I’m actually in the midst of a class on the topic, I thought I’d dust it off and finally publish it for those who are interested.
If you’re aware of things I’ve missed, or which have appeared since, please do let me know in the comments.
A List of video lectures for Algebraic Geometry

Harpreet Bedi (YouTube) 68 lectures (Note: His website also has some other good lectures on Galois Theory and Algebraic Topology)

Algebraic geometry for physicists by Ugo Bruzzo
Lectures on Algebraic Geometry by L. Goettsche (ICTP)

Classical Algebraic Geometry Today (MSRI Workshop 2009)

Some other places with additional (sometimes overlapping resources), particularly for more advanced/less introductory lectures:

Video Lectures for Algebraic Geometry (MathOverflow)

Sites to Learn Algebraic Geometry (MathOverflow)

Syndicated copies to:

### Reposts

• Jenis Kelamin :
• UCLA Extension

### Mentions

• Chris Aldrich
• Now: August 2017
• Now: September 2017
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• Rama Kunapuli
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