Mathematics | Chris Aldrich

🔖 Nonlinear Dynamics 1 & 2: Geometry of Chaos by Predrag Cvitanovic

Bookmarked Nonlinear Dynamics 1 & 2: Geometry of Chaos by

Predrag Cvitanovic (Georgia Institute of Technology)

The theory developed here (that you will not find in any other course :) has much in common with (and complements) statistical mechanics and field theory courses; partition functions and transfer operators are applied to computation of observables and spectra of chaotic systems. Nonlinear dynamics 1: Geometry of chaos (see syllabus) Topology of flows - how to enumerate orbits, Smale horseshoes Dynamics, quantitative - periodic orbits, local stability Role of symmetries in dynamics Nonlinear dynamics 2: Chaos rules (see syllabus) Transfer operators - statistical distributions in dynamics Spectroscopy of chaotic systems Dynamical zeta functions Dynamical theory of turbulence The course, which covers the same material and the same exercises as the Georgia Tech course PHYS 7224, is in part an advanced seminar in nonlinear dynamics, aimed at PhD students, postdoctoral fellows and advanced undergraduates in physics, mathematics, chemistry and engineering.

An interesting looking online course that appears to be on a white-labeled Coursera platform.

I’ve come across Predrag Cvitanovic’s work on Group Theory and Lie Groups before, so this portends some interesting work. I’ll have to see if I can carve out some time to sample some of it.

👓 Everyone Should Have the Right To Bear Mathematical Arms | Slate | Edward Frenkel

Read Don’t Let Economists and Politicians Hack Your Math: Of course kids need to learn algebra by Edward Frenkel (Slate)

Imagine a world in which it is possible for an elite group of hackers to install a “backdoor” not on a personal computer but on the entire U.S. economy. Imagine that they can use it to cryptically raise taxes and slash social benefits at will. Such a scenario may sound far-fetched, but replace “backdoor” with the Consumer Price Index (CPI), and you get a pretty accurate picture of how this arcane economics statistic has been used.

Tax brackets, Social Security, Medicare, and various indexed payments, together affecting tens of millions of Americans, are pegged to the CPI as a measure of inflation. The fiscal cliff deal that the White House and Congress reached a month ago was almost derailed by a proposal to change the formula for the CPI, which Matthew Yglesias characterized as “a sneaky plan to cut Social Security and raise taxes by changing how inflation is calculated.” That plan was scrapped at the last minute. But what most people don’t realize is that something similar had already happened in the past. A new book, The Physics of Wall Streetby James Weatherall, tells that story: In 1996, five economists, known as the Boskin Commission, were tasked with saving the government $1 trillion. They observed that if the CPI were lowered by 1.1 percent, then a $1 trillion could indeed be saved over the coming decade. So what did they do? They proposed a way to alter the formula that would lower the CPI by exactly that amount!

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

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

Bookmarked MATH X 451.43 Introduction to Algebraic Geometry: The Sequel (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!

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

Bookmarked Ten Great Ideas about Chance (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

📺 Are University Admissions Biased? | Simpson’s Paradox Part 2 | YouTube

Watched Are University Admissions Biased? | Simpson's Paradox Part 2 by Henry Reich from youtube.com

Simpson's Paradox Part 2. This video is about how to tell whether or not university admissions are biased using statistics: aka, it's about Simpson's Paradox again!

REFERENCES:
Original Berkeley Grad Admissions Paper
Interactive Simpson’s Paradox Explainer
No Lawsuit, But Yes, Berkeley Study on Gender Bias

Statistics on college majors by gender:
https://nces.ed.gov/programs/digest/2016menu\_tables.asp
http://www.npr.org/sections/money/2014/10/28/359419934/who-studies-what-men-women-and-college-majors
http://www.randalolson.com/2014/06/14/percentage-of-bachelors-degrees-conferred-to-women-by-major-1970-2012/

Earnings by college major

Wall Street Journal Article on Simpson’s Paradox

🔖 Adjoint School, ACT 2018 (Applied Category Theory)

Bookmarked 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

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

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)
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)