Introduction to Algebraic Geometry | UCLA Extension in Fall 2017

Bookmarked 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.)

Mathematical Sciences Building, 520 Portola Plaza, Los Angeles, CA 90095

Published by

Chris Aldrich

I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, IndieWeb, 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.

16 thoughts on “Introduction to Algebraic Geometry | UCLA Extension in Fall 2017”

  3. 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. [http://boffosocko.com/2015/09/22/dr-michael-miller-math-class-hints-and-tips-ucla-extension/]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.)+Rama Kunapuli, +Dave Sneadhttp://boffosocko.com/2017/07/25/introduction-to-algebraic-geometry-ucla-extension/



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  9. 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:
    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.
    Lecture 1 – Part 1
    If possible, click to play, otherwise your browser may be unable to play this audio file.
    Lecture 1 – Part 2
    If possible, click to play, otherwise your browser may be unable to play this audio file.
    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.
    Syndicated copies to:


    <em>Related</em>

    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.
    View all posts by Chris Aldrich

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  11. Somewhere between the granularity of following my daily updates and my about page here’s a quick outline of things I’ve been doing within the past month or plan to do in the coming weeks.
    What am I focused on Now?

    Buying a new house / Selling my current house

    Physically moving and setting up new home and office

    Continuing work with IndieWeb.org Community

    Learning

    Gearing up for Algebraic Geometry in September

    Events

    WordCamp Los Angeles 9/29-10/1/2017

    Reading

    American Amnesia: How the War on Government Led Us to Forget What Made America Prosper by Jacob S. Hacker and Paul Pierson (Simon & Schuster, March 29, 2016)

    For up-to-the-day updates on what I’m reading, see my reading updates, or, if you prefer, the syndicated copies I send to GoodReads.com. I now also post online articles I’ve been reading lately too.

    Listening

    Podcasts: This Week in Google

    Spotify: The Bridge, Relaxing Breakfast Classics (in mornings), various playlists
    Amazon Music (typically via Amazon Echo): various artists
    Radio: Morning news (most week days): 89.3FM KPCC–Local NPR affiliate

    Watching

    Television

    Cheers (Netflix), Season 10 Episode 17 -Season 11 Episode 2
    The Vietnam War, Episode 1 (of 10)

    PBS News Hour (PBS)
    The Daily Show (Comedy Central), Season 2 Episode 151, 153, 154
    College Football

    Movies

    Silk
    Tango & Cash
    Keeping Up With the Jonses
    Herbie: Fully Loaded
    The Accountant
    National Treasure (2x)
    National Treasure: Book of Secrets
    Central Intelligence
    Now You See Me
    Now You See Me 2
    Moana
    The Prestige
    Bowfinger

    Internet

    TBD

    Last updated October 9, 2017. (Updated after-the-fact due to move.)
    This page is inspired by Derek Sivers‘ /now project.
    Syndicated copies to:

    Syndicated copies:

    Reply

  12. Somewhere between the granularity of following my daily updates and my about page here’s a quick outline of things I’ve been doing within the past month or plan to do in the coming weeks.
    What am I focused on Now?

    Buying a new house / Selling my current house
    Continuing work with IndieWeb.org Community
    Learning

    Gearing up for Algebraic Geometry in September

    Events

    Onanoue Japanese Library, Sunday, August 27, 2017 from 10am – 12pm
    DrupalCamp Los Angeles 8/5-6/2017 (Sadly skipped due to House purchase responsibilities)

    WordCamp Los Angeles 9/29-10/1/2017

    Reading

    American Amnesia: How the War on Government Led Us to Forget What Made America Prosper by Jacob S. Hacker and Paul Pierson (Simon & Schuster, March 29, 2016)

    For up-to-the-day updates on what I’m reading, see my reading updates, or, if you prefer, the syndicated copies I send to GoodReads.com. I now also post online articles I’ve been reading lately too.

    Listening

    Spotify: The Bridge, Relaxing Breakfast Classics (in mornings), various playlists
    Amazon Music (typically via Amazon Echo): various artists
    Radio: Morning news (most week days): 89.3FM KPCC–Local NPR affiliate

    Watching

    Television

    Cheers (Netflix), Season 9 Episode 19 – Season 10 Episode 16
    West Wing (Netflix/NBC), Season 5 Episodes 20, 21
    Friday Night Lights (Netflix), Season 1 Episode 1 – Season 2 Episode 7
    House Hunters (miscellaneous episodes)
    The Daily Show, Season 2 Episode 144

    Doubt (CBS), Season 1 Episodes 4-13 (cancelled after 2 episodes in the Winter)
    Face the Nation (CBS)
    This Week with George Stephanopolous (ABC)
    Meet the Press (NBC)

    PBS News Hour (PBS)
    Flip or Flop (Atlanta, Palm Springs)

    Movies

    TBD

    Internet

    TBD

    Last updated October 9, 2017 (too busy to have done this previously due to move.)
    This page is inspired by Derek Sivers‘ /now project.

    Syndicated copies to:

    Syndicated copies:

    Reply

  13. 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)

    Miles Reed(How to Download Miles Reid’s Algebraic Geometry videos)

    Basic Algebraic Geometry: Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity (NPTEL)

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

    2007/2008 Lectures
    2008/2009 Lectures
    2009/2010 Lectures
    2010/2011 Lectures

    Talks given at the AMS Summer Institute in Algebraic Geometry (2015)

    Classical Algebraic Geometry Today (MSRI Workshop 2009)

    Lectures by Harris, Hartshorne, Maclagan, and Beelen at ELGA2011

    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)

    Video lectures of Algebraic Geometry-Hartshorne-Shafarevich (MathOverflow)

    Syndicated copies:

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  14. 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. [http://boffosocko.com/2015/09/22/dr-michael-miller-math-class-hints-and-tips-ucla-extension/]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.)+Rama Kunapuli, +Dave Sneadhttp://boffosocko.com/2017/07/25/introduction-to-algebraic-geometry-ucla-extension/

    Reply

  15. Replied to A (very) gentle comment on Algebraic Geometry for the faint-hearted by Ilyas Khan (LinkedIn)

    This short article is the result of various conversations over the course of the past year or so that arose on the back of two articles/blog pieces that I have previously written about Category Theory (here and here). One of my objectives with such articles, whether they be on aspects of quantum computing or about aspects of maths, is to try and de-mystify as much of the associated jargon as possible, and bring some of the stunning beauty and wonder of the subject to as wide an audience as possible. Whilst it is clearly not possible to become an expert overnight, and it is certainly not my objective to try and provide more than an introduction (hopefully stimulating further research and study), I remain convinced that with a little effort, non-specialists and even self confessed math-phobes can grasp some of the core concepts. In the case of my articles on Category Theory, I felt that even if I could generate one small gasp of excited comprehension where there was previously only confusion, then the articles were worth writing.

    I just finished a course on Algebraic Geometry through UCLA Extension, which was geared toward non-traditional math students and professionals, and wish I had known about Smith’s textbook when I’d started. I did spend some time with Cox, Little, and O’Shea’s Ideals, Varieties, and Algorithms which is a pretty good introduction to the area, but written a bit more for computer scientists and engineers in mind rather than the pure mathematician, which might recommend it more toward your audience here as well. It’s certainly more accessible than Hartshorne for the faint-of-heart.
    I’ve enjoyed your prior articles on category theory which have spurred me to delve deeper into the area. For others who are interested, I thought I’d also mention that physicist and information theorist John Carlos Baez at UCR has recently started an applied category theory online course which I suspect is a bit more accessible than most of the higher graduate level texts and courses currently out. For more details, I’d suggest starting here: https://johncarlosbaez.wordpress.com/2018/03/26/seven-sketches-in-compositionality/
    Syndicated copies to:

    Syndicated copies:

    Reply

  16. Replied to A (very) gentle comment on Algebraic Geometry for the faint-hearted by Ilyas Khan (LinkedIn)

    This short article is the result of various conversations over the course of the past year or so that arose on the back of two articles/blog pieces that I have previously written about Category Theory (here and here). One of my objectives with such articles, whether they be on aspects of quantum computing or about aspects of maths, is to try and de-mystify as much of the associated jargon as possible, and bring some of the stunning beauty and wonder of the subject to as wide an audience as possible. Whilst it is clearly not possible to become an expert overnight, and it is certainly not my objective to try and provide more than an introduction (hopefully stimulating further research and study), I remain convinced that with a little effort, non-specialists and even self confessed math-phobes can grasp some of the core concepts. In the case of my articles on Category Theory, I felt that even if I could generate one small gasp of excited comprehension where there was previously only confusion, then the articles were worth writing.

    I just finished a course on Algebraic Geometry through UCLA Extension, which was geared toward non-traditional math students and professionals, and wish I had known about Smith’s textbook when I’d started. I did spend some time with Cox, Little, and O’Shea’s Ideals, Varieties, and Algorithms which is a pretty good introduction to the area, but written a bit more for computer scientists and engineers in mind rather than the pure mathematician, which might recommend it more toward your audience here as well. It’s certainly more accessible than Hartshorne for the faint-of-heart.
    I’ve enjoyed your prior articles on category theory which have spurred me to delve deeper into the area. For others who are interested, I thought I’d also mention that physicist and information theorist John Carlos Baez at UCR has recently started an applied category theory online course which I suspect is a bit more accessible than most of the higher graduate level texts and courses currently out. For more details, I’d suggest starting here: https://johncarlosbaez.wordpress.com/2018/03/26/seven-sketches-in-compositionality/

    Syndicated copies to:

    Syndicated copies:

    Reply

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