Introduction to Algebraic Geometry | UCLA Extension in Fall 2017

MATH X 451.42 Introduction to Algebraic Geometry by Dr. Michael Miller (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

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🔖 A Course in Game Theory by Martin J. Osborne, Ariel Rubinstein | MIT Press

A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein (MIT Press)
A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.

Tangentially suggested after reading In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)

Free, personal copy is downloadable in .pdf format with registration here.

A Course in Game Theory

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🔖 Subjectivity and Correlation in Randomized Strategies by Robert J. Aumann | Journal of Mathematical Economics

Subjectivity and Correlation in Randomized Strategies by Robert J. Aumann (Journal of Mathematical Economics 1 (1974) 67-96. North-Holland Publishing Company)
(.pdf download) Subjectivity and correlation, though formally related, are conceptually distinct and independent issues. We start by discussing subjectivity. A mixed strategy in a game involves the selection of a pure strategy by means of a random device. It has usually been assumed that the random device is a coin flip, the spin of a roulette wheel, or something similar; in brief, an ‘objective’ device, one for which everybody agrees on the numerical values of the probabilities involved. Rather oddly, in spite of the long history of the theory of subjective probability, nobody seems to have examined the consequences of basing mixed strategies on ‘subjective’ random devices, i.e. devices on the probabilities of whose outcomes people may disagree (such as horse races, elections, etc.).

Suggested by In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)

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🔖 Communication complexity of approximate Nash equilibria | arXiv

Communication complexity of approximate Nash equilibria by Yakov Babichenko, Aviad Rubinstein (arXiv)
For a constant ϵ, we prove a poly(N) lower bound on the (randomized) communication complexity of ϵ-Nash equilibrium in two-player NxN games. For n-player binary-action games we prove an exp(n) lower bound for the (randomized) communication complexity of (ϵ,ϵ)-weak approximate Nash equilibrium, which is a profile of mixed actions such that at least (1−ϵ)-fraction of the players are ϵ-best replying.

Suggested by In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)

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WPCampus 2017 (WPCampus.com)
A two-day event filled with sessions, networking, and social events covering a variety of topics, all dedicated to the confluence of WordPress in higher education. The second annual WPCampus conference will take place July 14-15, 2017 at Canisius College in lovely Buffalo, New York.

How did I manage to miss this? I know they livestreamed the sessions, but did they manage to record them?

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🔖 A relatively comprehensive list of Indieweb sites

The 2300+ sites in the public IndieWeb social graph and dataset by Ryan Barrett (Indie Map Project)
Indie Map is a complete crawl of 2300 of the most active IndieWeb sites, sliced and diced and rolled up in a few useful ways: Social graph API and interactive map. SQL queryable dataset and GUI analytics. Raw crawl data in WARC format: 2300 sites, 5.7M pages, 380GB HTML + mf2. Indie Map is free, open source, and placed into the public domain via the CC0 public domain dedication. Crawled content remains the property of each site's owner and author, and subject to their existing copyrights.

So you’re looking to start an Indieweb blogroll? This is a reasonably large place to start…

cc: Richard MacManus

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🔖 A Mind at Play: How Claude Shannon Invented the Information Age by Jimmy Soni, Rob Goodman

A Mind at Play: How Claude Shannon Invented the Information Age by Jimmy Soni and Rob Goodman (Simon & Schuster)
The life and times of one of the foremost intellects of the twentieth century: Claude Shannon—the neglected architect of the Information Age, whose insights stand behind every computer built, email sent, video streamed, and webpage loaded. Claude Shannon was a groundbreaking polymath, a brilliant tinkerer, and a digital pioneer. He constructed a fleet of customized unicycles and a flamethrowing trumpet, outfoxed Vegas casinos, and built juggling robots. He also wrote the seminal text of the digital revolution, which has been called “the Magna Carta of the Information Age.” His discoveries would lead contemporaries to compare him to Albert Einstein and Isaac Newton. His work anticipated by decades the world we’d be living in today—and gave mathematicians and engineers the tools to bring that world to pass. In this elegantly written, exhaustively researched biography, Jimmy Soni and Rob Goodman reveal Claude Shannon’s full story for the first time. It’s the story of a small-town Michigan boy whose career stretched from the era of room-sized computers powered by gears and string to the age of Apple. It’s the story of the origins of our digital world in the tunnels of MIT and the “idea factory” of Bell Labs, in the “scientists’ war” with Nazi Germany, and in the work of Shannon’s collaborators and rivals, thinkers like Alan Turing, John von Neumann, Vannevar Bush, and Norbert Wiener. And it’s the story of Shannon’s life as an often reclusive, always playful genius. With access to Shannon’s family and friends, A Mind at Play brings this singular innovator and creative genius to life.

I can’t wait to read this new biography about Claude Shannon! The bio/summer read I’ve been waiting for.

With any luck an advanced reader copy is speeding it way to me! (Sorry you can’t surprise me with a belated copy for my birthday.) A review is forthcoming.

You have to love the cover art by Lauren Peters-Collaer.

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Resources from Domains 2017

Domains 2017 Conference (Reclaim Hosting)
Indie EdTech and Other Curiosities, June 5-6, 2017 at University of Oklahoma

Twitter Stream for #Domains17

Keynote: Neither Locked out nor locked in by Martha Burtis

Live-streamed videos from Virtually Connecting

DoOO Curriculum on Github

JBJ blogpost: Looking back at #Domains17

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🔖 Feed reader revolution: it’s time to embrace open & disrupt social media

Feed reader revolution: it’s time to embrace open & disrupt social media
By supporting Micropub, indie-config, and/or action URLs, current feed readers can make it far easier for people on the open web to not only read content the way they currently do on siloed social media services like Facebook, Twitter, Instagram, et al. Increased ease-of-use to allow these functionalities with beautiful user interface will help to move users out of walled-gardens where they’re trapped into the larger universe of the free and open internet. Individuals with their own websites can support the acceptance of these posts to save their interactions with what they’ve read, be they comments, likes, bookmarks, or other interactions. They can also close the loop by supporting Webmentions so that their comments can be sent to (and potentially displayed) on others’ websites. All of these pieces combined make for a more open and democratic web.

The article about feed readers that I wrote for the new AltPlatform tech blog is out now. I hope everyone will take a look.

When this publication from Richard MacManus (the founder of ReadWriteWeb.com, one of my old favorite standbys) popped up a few weeks ago with the tagline “A non-profit tech blog about the open web”, I immediately bookmarked it and knew it would be at the top of my subscription list. When I read his founding manifesto for the blog, I was hooked and bumped it to the top of my list and tipped off others:

There’s also some great articles up by Emre Sokullu, Brian Hendrickson, and Richard MacManus on a variety of other great topics. I hope you’ll take a look at what they’re doing and subscribe.

I’m pleased that they’ve taken something I was planning on posting here on my site and are giving it some wider exposure.

If you’re a journalist, blogger, or writer in the space, do feel free to connect with them to pitch ideas.​​

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Twitter List from #Domains17

Twitter List from #Domains17 by Chris Aldrich (Twitter)
Teachers, educators, researchers, technologists using open technologies in education #openEd, #edTech, #DoOO, #indieweb

I’ve compiled a twitter list of people related to #openEd, #edTech, #DoOO, #indieweb, and related topics who tweeted about #domains17 in the past week. The list has multiple views including members and by tweets.

Feel free to either subscribe to the list (useful when adding streams to things like Tweetdeck), or for quickly scanning down the list and following people on a particular topic en-masse. Hopefully it will help people to remain connected following the conference. I’ve written about some other ideas about staying in touch here.

If you or someone you know is conspicuously missing, please let me know and I’m happy to add them. Hopefully this list will free others from spending the inordinate amount of time to create similar bulk lists from the week.

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🔖 dokieli

dokie.li (dokie.li)
dokieli is a clientside editor for decentralised article publishing, annotations and social interactions.

dokieli envisions research results, analysis and data all being produced interactively on the Web and seamlessly linked to and from articles. Through annotations and notifications, the academic process of peer-review can be open, transparent and decentralised for researchers.

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🔖 Can entropy be defined for and the Second Law applied to the entire universe? by Arieh Ben-Naim | Arxiv

Can entropy be defined for and the Second Law applied to the entire universe? by Arieh Ben-Naim (arXiv)
This article provides answers to the two questions posed in the title. It is argued that, contrary to many statements made in the literature, neither entropy, nor the Second Law may be used for the entire universe. The origin of this misuse of entropy and the second law may be traced back to Clausius himself. More resent (erroneous) justification is also discussed.
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🔖 The hidden simplicity of biology by Paul C W Davies and Sara Imari Walker | Reports on Progress in Physics

The hidden simplicity of biology by Paul C W Davies and Sara Imari Walker (Reports on Progress in Physics)
Life is so remarkable, and so unlike any other physical system, that it is tempting to attribute special factors to it. Physics is founded on the assumption that universal laws and principles underlie all natural phenomena, but is it far from clear that there are 'laws of life' with serious descriptive or predictive power analogous to the laws of physics. Nor is there (yet) a 'theoretical biology' in the same sense as theoretical physics. Part of the obstacle in developing a universal theory of biological organization concerns the daunting complexity of living organisms. However, many attempts have been made to glimpse simplicity lurking within this complexity, and to capture this simplicity mathematically. In this paper we review a promising new line of inquiry to bring coherence and order to the realm of biology by focusing on 'information' as a unifying concept.

Downloadable free copy available on ResearchGate.

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🔖 The “Hard Problem” of Life by Sara Imari Walker & Paul C.W. Davies

The "Hard Problem" of Life by Sara Imari Walker, Paul C.W. Davies (arXiv)
Chalmer's famously identified pinpointing an explanation for our subjective experience as the "hard problem of consciousness". He argued that subjective experience constitutes a "hard problem" in the sense that its explanation will ultimately require new physical laws or principles. Here, we propose a corresponding "hard problem of life" as the problem of how `information' can affect the world. In this essay we motivate both why the problem of information as a causal agent is central to explaining life, and why it is hard - that is, why we suspect that a full resolution of the hard problem of life will, similar to as has been proposed for the hard problem of consciousness, ultimately not be reducible to known physical principles. Comments: To appear in "From Matter to Life: Information and Causality". S.I. Walker, P.C.W. Davies and G.F.R. Ellis (eds). Cambridge University Press
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