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

Attending MATH X 451.43 Introduction to Algebraic Geometry: The Sequel
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!

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

MATH X 451.43 Introduction to Algebraic Geometry: The Sequel by 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 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!

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I’ve been to thousands of hours of math lectures and tonight was the first time I saw an honest to goodness math accident! There weren’t buckets of blood, but there was quite a bit. Fortunately I came prepared with band-aids.

The injury was to the professor’s hand, but I’m pretty sure it wasn’t due to excessive hand-waiving…

🔖 Ten Great Ideas about Chance by Persi Diaconis and Brian Skyrms

Ten Great Ideas about Chance by Persi Diaconis and Brian Skyrms (Princeton University Press)
In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact. Persi Diaconis and Brian Skyrms begin with Gerolamo Cardano, a sixteenth-century physician, mathematician, and professional gambler who helped develop the idea that chance actually can be measured. They describe how later thinkers showed how the judgment of chance also can be measured, how frequency is related to chance, and how chance, judgment, and frequency could be unified. Diaconis and Skyrms explain how Thomas Bayes laid the foundation of modern statistics, and they explore David Hume’s problem of induction, Andrey Kolmogorov’s general mathematical framework for probability, the application of computability to chance, and why chance is essential to modern physics. A final idea―that we are psychologically predisposed to error when judging chance―is taken up through the work of Daniel Kahneman and Amos Tversky. Complete with a brief probability refresher, Ten Great Ideas about Chance is certain to be a hit with anyone who wants to understand the secrets of probability and how they were discovered.

h/t Michael Mauboussin

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🔖 Adjoint School, ACT 2018 (Applied Category Theory)

Adjoint School, ACT 2018 (Applied Category Theory)
The Workshop on Applied Category Theory 2018 takes place in May 2018. A principal goal of this workshop is to bring early career researchers into the applied category theory community. Towards this goal, we are organising the Adjoint School. The Adjoint School will run from January to April 2018.

There’s still some time left to apply. And if nothing else, this looks like it’s got some interesting resources.

h/t John Carlos Baez

Applied Category Theory

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👓 ‘A Sort of Everyday Struggle’ | The Harvard Crimson

'A Sort of Everyday Struggle' by Hannah Natanson
Women in Harvard's math department report a bevy of inequalities—from a discouraging absence of female faculty to a culture of "math bro" condescension.

A story about math that sadly doesn’t feature equality.

Oddly not featured in the story was any reference to the Lawrence H. Summers incident of 2005. Naturally, one can’t pin the issue on him as this lack of diversity has spanned the life of the university, but apparently the math department didn’t get the memo when the university president left.

I’ve often heard that the fish stinks from the head, but apparently it’s the whole fish here.

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Video lectures for Algebraic Geometry

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

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

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📅 The Calculus of Comedy: Math in The Simpsons, Futurama, and The Big Bang Theory at UCLA’s IPAM on 10/25

The Calculus of Comedy: Math in The Simpsons, Futurama, and The Big Bang Theory (IPAM (Special Events and Conferences))
When: Wednesday, October 25, 2017, from 4:30 PM – 6:30 PM PDT Where: UCLA California NanoSystems Institute (CNSI), 570 Westwood Plaza, Los Angeles, CA 90095 While there is no mathematical formula for writing television comedy, for the writers of The Simpsons, Futurama, and The Big Bang Theory, mathematical formulas (along with classic equations and cutting-edge theorems) can sometimes be an integral part of those shows. In a lively and nerdy discussion, five of these writers (who have advanced degrees in math, physics, and computer science) will share their love of numbers and talent for producing laughter. Mathematician Sarah Greenwald, who teaches and writes about math in popular culture, will moderate the panel. The event will begin with a lecture by bestselling author Simon Singh (The Simpsons and Their Mathematical Secrets), who will examine some of the mathematical nuggets hidden in The Simpsons (from Euler’s identity to Mersenne primes) and discuss how Futurama has also managed to include obscure number theory and complex ideas about geometry. Tickets: Tickets are $15 each and seating is limited, so reserve your seat soon. Tickets can be purchased here via Eventbrite (ticket required for entry to the event). A limited number of free tickets will be reserved for UCLA students. We ask that students come to IPAM between 9:00am and 3:00pm on Friday, October 20, to present your BruinCard and pick up your ticket (one ticket per BruinCard, nontransferable). If any tickets remain, we will continue distributing free tickets to students on Monday, Oct. 23, starting at 9:00am until we run out. Both your ticket and BruinCard must be presented at the door for entry. Doors open at 4:00. Please plan to arrive early to check in and find a seat. We expect a large audience.

Okay math nerds, this looks like an interesting lecture if you’re in Los Angeles next Wednesday. I remember reading and mostly liking Singh’s book The Simpsons and Their Mathematical Secrets a few years back.

The hard core math crowd may be disappointed in the level, but it could be an interesting group to get out and be social with.

My review of The Simpsons and Their Mathematical Secrets from Goodreads:

I’m both a math junkie and fan of the Simpsons. Singh’s book is generally excellent and well written and covers a broad range of mathematical areas. I’m a major fan of his book Big Bang: The Origin of the Universe, but find myself wanting much more from this effort. Much of my problem stems from my very deep knowledge of math and its history as well as having read most of the vignettes covered here in other general popular texts multiple times. Fortunately most readers won’t suffer from this and will hopefully find some interesting tidbits both about the Simpsons and math here to whet their appetites.

There were several spots at which I felt that Singh stretched a bit too far in attempting to tie the Simpsons to “mathematics” and possibly worse, several spots where he took deliberate detours into tangential subjects that had absolutely no relation to the Simpsons, but these are ultimately good for the broader public reading what may be the only math-related book they pick up this decade.

This could be considered a modern-day version of E.T. Bell‘s Men of Mathematics but with an overly healthy dose of side-entertainment via the Simpsons and Futurama to help the medicine go down.

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📖 Read pages 63-88 of Abstract Algebra: An Introduction by Thomas W. Hungerford

📖 Read pages 63-88 of Abstract Algebra: An Introduction (First Edition) by Thomas W. Hungerford
Chapter 3: Rings, Section 3 – Chapter 4: Arithmetic in F[x], Sections 1 & 2

Reviewing over some algebra for my algebraic geometry class

Abstract Algebra: An Introduction

📖 Read chapter one of Weapons of Math Destruction by Cathy O’Neil

📖 Read chapter one of Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy by Cathy O’Neil

I don’t think she’s used the specific words in the book yet, but O’Neil is fundamentally writing about social justice and transparency. To a great extent both governments and increasingly large corporations are using these Weapons of Math Destruction inappropriately. Often it may be the case that the algorithms are so opaque as to be incomprehensible by their creators/users, but, as I suspect in many cases, they’re being used to actively create social injustice by benefiting some classes and decimating others. The evolving case of Facebook’s involvement in potentially shifting the outcome of the 2016 Presidential election especially via “dark posts” is an interesting case in point with regard to these examples.

In some sense these algorithms are like viruses running rampant in a large population without the availability of antibiotics to tamp down or modify their effects. Without feedback mechanisms and the ability to see what is going on as it happens the scale issue she touches on can quickly cause even greater harm over short periods of time.

I like that one of the first examples she uses for modeling is that of preparing food for a family. It’s simple, accessible, and generic enough that the majority of people can relate directly to it. It has lots of transparency (even more than her sabermetrics example from baseball). Sadly, however, there is a large swath of the American population that is poor, uneducated, and living in horrific food deserts that they may not grasp the subtleties of even this simple model. As I was reading, it occurred to me that there is a reasonable political football that gets pushed around from time to time in many countries that relates to food and food subsidies. In the United States it’s known as the Supplemental Nutrition Assistance Program (aka SNAP) and it’s regularly changing, though fortunately for many it has some nutritionists who help to provide a feedback mechanism for it. I suspect it would make a great example of the type of Weapon of Mass Destruction she’s discussing in this book. Those who are interested in a quick overview of it and some of the consequences can find a short audio introduction to it via the Eat This Podcast episode How much does a nutritious diet cost? Depends what you mean by “nutritious” or Crime and nourishment Some costs and consequences of the Supplemental Nutrition Assistance Program which discusses an interesting crime related sub-consequence of something as simple as when SNAP benefits are distributed.

I suspect that O’Neil won’t go as far as to bring religion into her thesis, so I’ll do it for her, but I’ll do so from a more general moral philosophical standpoint which underpins much of the Judeo-Christian heritage so prevalent in our society. One of my pet peeves of moralizing (often Republican) conservatives (who often both wear their religion on their sleeves as well as beat others with it–here’s a good recent case in point) is that they never seem to follow the Golden Rule which is stated in multiple ways in the Bible including:

He will reply, ‘Truly I tell you, whatever you did not do for one of the least of these, you did not do for me.

Matthew 25:45

In a country that (says it) values meritocracy, much of the establishment doesn’t seem to put much, if any value, into these basic principles as they would like to indicate that they do.

I’ve previously highlighted the application of mathematical game theory before briefly in relation to the Golden Rule, but from a meritocracy perspective, why can’t it operate at all levels? By this I’ll make tangential reference to Cesar Hidalgo‘s thesis in his book Why Information Grows in which he looks not at just individuals (person-bytes), but larger structures like firms/companies (firmbytes), governments, and even nations. Why can’t these larger structures have their own meritocracy? When America “competes” against other countries, why shouldn’t it be doing so in a meritocracy of nations? To do this requires that we as individuals (as well as corporations, city, state, and even national governments) need to help each other out to do what we can’t do alone. One often hears the aphorism that “a chain is only as strong as it’s weakest link”, why then would we actively go out of our way to create weak links within our own society, particularly as many in government decry the cultures and actions of other nations which we view as trying to defeat us? To me the statistical mechanics of the situation require that we help each other to advance the status quo of humanity. Evolution and the Red Queeen Hypothesis dictates that humanity won’t regress back to the mean, it may be regressing itself toward extinction otherwise.

Highlights, Quotes, & Marginalia

Chapter One – Bomb Parts: What is a Model

You can often see troubles when grandparents visit a grandchild they haven’t seen for a while.

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Upon meeting her a year later, they can suffer a few awkward hours because their models are out of date.

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Racism, at the individual level, can be seen as a predictive model whirring away in billions of human minds around the world. It is built from faulty, incomplete, or generalized data. Whether it comes from experience or hearsay, the data indicates that certain types of people have behaved badly. That generates a binary prediction that all people of that race will behave that same way.

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Needless to say, racists don’t spend a lot of time hunting down reliable data to train their twisted models.

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the workings of a recidivism model are tucked away in algorithms, intelligible only to a tiny elite.

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A 2013 study by the New York Civil Liberties Union found that while black and Latino males between the ages of fourteen and twenty-four made up only 4.7 percent of the city’s population, they accounted for 40.6 percent of the stop-and-frisk checks by police.

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So if early “involvement” with the police signals recidivism, poor people and racial minorities look far riskier.

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The questionnaire does avoid asking about race, which is illegal. But with the wealth of detail each prisoner provides, that single illegal question is almost superfluous.

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judge would sustain it. This is the basis of our legal system. We are judged by what we do, not by who we are.

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(And they’ll be free to create them when they start buying their own food.) I should add that my model is highly unlikely to scale. I don’t see Walmart or the US Agriculture Department or any other titan embracing my app and imposing it on hundreds of millions of people, like some of the WMDs we’ll be discussing.

You have to love the obligatory parental aphorism about making your own rules when you have your own house.
Yet the US SNAP program does just this. It could be an interesting example of this type of WMD.
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three kinds of models.

namely: baseball, food, recidivism
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The first question: Even if the participant is aware of being modeled, or what the model is used for, is the model opaque, or even invisible?

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many companies go out of their way to hide the results of their models or even their existence. One common justification is that the algorithm constitutes a “secret sauce” crucial to their business. It’s intellectual property, and it must be defended,

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the second question: Does the model work against the subject’s interest? In short, is it unfair? Does it damage or destroy lives?

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While many may benefit from it, it leads to suffering for others.

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The third question is whether a model has the capacity to grow exponentially. As a statistician would put it, can it scale?

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scale is what turns WMDs from local nuisances into tsunami forces, ones that define and delimit our lives.

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So to sum up, these are the three elements of a WMD: Opacity, Scale, and Damage. All of them will be present, to one degree or another, in the examples we’ll be covering

Think about this for a bit. Are there other potential characteristics?
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You could argue, for example, that the recidivism scores are not totally opaque, since they spit out scores that prisoners, in some cases, can see. Yet they’re brimming with mystery, since the prisoners cannot see how their answers produce their score. The scoring algorithm is hidden.

This is similar to anti-class action laws and arbitration clauses that prevent classes from realizing they’re being discriminated against in the workplace or within healthcare. On behalf of insurance companies primarily, many lawmakers work to cap awards from litigation as well as to prevent class action suits which show much larger inequities that corporations would prefer to keep quiet. Some of the recent incidences like the cases of Ellen Pao, Susan J. Fowler, or even Harvey Weinstein are helping to remedy these types of things despite individuals being pressured to stay quiet so as not to bring others to the forefront and show a broader pattern of bad actions on the part of companies or individuals. (This topic could be an extended article or even book of its own.)
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the point is not whether some people benefit. It’s that so many suffer.

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And here’s one more thing about algorithms: they can leap from one field to the next, and they often do. Research in epidemiology can hold insights for box office predictions; spam filters are being retooled to identify the AIDS virus. This is true of WMDs as well. So if mathematical models in prisons appear to succeed at their job—which really boils down to efficient management of people—they could spread into the rest of the economy along with the other WMDs, leaving us as collateral damage.

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Guide to highlight colors

Yellow–general highlights and highlights which don’t fit under another category below
Orange–Vocabulary word; interesting and/or rare word
Green–Reference to read
Blue–Interesting Quote
Gray–Typography Problem
Red–Example to work through

I’m reading this as part of Bryan Alexander’s online book club.

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📖 Read pages 39-62 of Abstract Algebra: An Introduction by Thomas W. Hungerford

📖 Read pages 39-62 of Abstract Algebra: An Introduction (First Edition) by Thomas W. Hungerford
Chapter 3: Rings, Sections 1 and 2

Reviewing over some algebra for my algebraic geometry class

Abstract Algebra: An Introduction

📖 Read pages 112-121 of Abstract Algebra: An Introduction by Thomas W. Hungerford

📖 Read pages 112-121 of Abstract Algebra: An Introduction (First Edition) by Thomas W. Hungerford
Chapter 5: Congruence in F[x] and Congruence-Class arithmetic, Sections 1 and 2

Reviewing over some algebra for my algebraic geometry class tonight. I always did love the pedagogic design of this textbook. The way he builds up algebraic structures is really lovely.

Abstract Algebra: An Introduction

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Reply to Reading Weapons of Math Destruction: the plan by Bryan Alexander

Reading Weapons of Math Destruction: the plan by Bryan Alexander (BryanAlexander.org)
Our new book club reading is Cathy O’Neil’s Weapons of Math Destruction. In this post I’ll lay out a reading agenda, along with ways to participate. The way people read along in this book club is through the web, essentially. It’s a distributed experience.

It occurs to me while reading the set up for this distributed online book club that posting on your own site and syndicating elsewhere (POSSE) while pulling back responses in an IndieWeb fashion is an awesome idea for this type of online activity. Now if only the social silos supported salmention!

I’m definitely in for this general schedule and someone has already gifted me a copy of the book. Given the level of comments I suspect will come about, I’m putting aside the fact that this book wasn’t written for me as an audience and will read along with the crowd. I’m much more curious how Bryan’s audience will see and react to it. But I’m also interested in the functionality and semantics of an online book club run in such a distributed way.

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