Reply to Stephanie Hurlburt on Twitter

a tweet by Stephanie HurlburtStephanie Hurlburt (Twitter)
Okay so right now I go to coffee shops to solve math problems alone, it's peaceful, I like it But someone mentioned they do cute tea parties with their girl squad & I said wow I want something like that but we all bring math textbooks & solve problems next to each other (1/2)

It’s not specifically femme yet does involve tea, but I’ve noticed something informal like this at the Starbucks just two blocks West of CalTech in Pasadena.

Separately but related, “adults” looking for a varied advanced math outlet in the Los Angeles area are welcome to join Dr. Mike Miller’s classes at UCLA Extension on Tuesday nights from 7-10pm. We’re working on Algebraic Geometry this quarter. For those who might need notes to play catch up, I’ve got copies, with full audio recordings, that I’m happy to share.

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📺 Introduction to Category Theory 1 by Steven Roman | YouTube

Introduction to Category Theory 1 by Steven Roman from YouTube
Lecture one of six in an introductory set of lectures on category theory.

Take Away from the lecture: Morphisms are just as important as the objects that they morph. Many different types of mathematical constructions are best described using morphisms instead of elements. (This isn’t how things are typically taught however.)

Would have been nice to have some more discussion of the required background for those new to the broader concept. There were a tremendous number of examples from many areas of higher math that many viewers wouldn’t have previously had. I think it’s important for them to know that if they don’t understand a particular example, they can move on without much loss as long as they can attempt to apply the ideas to an area of math they are familiar with. Having at least a background in linear algebra and/or group theory are a reasonable start here.

In some of the intro examples it would have been nice to have seen at least one more fully fleshed out to better demonstrate the point before heading on to the multiple others which encourage the viewer to prove some of the others on their own.

Thanks for these Steven, I hope you keep making more! There’s such a dearth of good advanced math lectures on the web, I hope these encourage others to make some of their own as well.

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Why More Linear Algebra? by David Austin

Why More Linear Algebra? by David Austin (More Linear Algebra)
The main purpose of this blog is to share updates about the open-access, open-source textbook Understanding Linear Algebra. Though work is continuing on this project, the HTML version of the text is now freely available, the forthcoming PDF version will also be free, and low-cost print options will be provided. The PreTeXt source code will be posted on GitHub as well.

h/t Robert Talbert

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👓 Limits and Colimits, Part 1 (Introduction) | Math3ma

Limits and Colimits, Part 1 (Introduction) by Tai-Danae BradleyTai-Danae Bradley (Math3ma)
I'd like to embark on yet another mini-series here on the blog. The topic this time? Limits and colimits in category theory! But even if you're not familiar with category theory, I do hope you'll keep reading. Today's post is just an informal, non-technical introduction. And regardless of your categorical background, you've certainly come across many examples of limits and colimits, perhaps without knowing it! They appear everywhere - in topology, set theory, group theory, ring theory, linear algebra, differential geometry, number theory, algebraic geometry. The list goes on. But before diving in, I'd like to start off by answering a few basic questions.

A great little introduction to category theory! Can’t wait to see what the future installments bring.

Interestingly I came across this on Instagram. It may be one of the first times I’ve seen math at this level explained in pictorial form via Instagram.

Given a bunch of sets, what are some ways to construct a new set? Some options include: intersections, unions, Cartesian products, preimages, and quotients. And these are all examples of “limits and colimits” in #categorytheory! Notice how the examples come in two flavors? An intersection, a preimage, a product are all formed by picking out a sub-collection of elements from given sets, contingent on some condition. These are examples of limits. On the other hand, unions and quotients are formed by assembling or 'gluing' things together. These are examples of colimits. . In practice, limits tend to have a "sub-thing" feel to them, whereas colimits tend to have a "glue-y" feel to them. And these constructions are two of the most frequent ways that mathematicians build things, so they appear ALL over mathematics. But what are (co)limits, exactly? I’ve just posted a non-technical introduction on my blog. It’s Part 1 of the latest mini-series on Math3ma. Link in profile!

A post shared by Tai-Danae Bradley (@math3ma) on

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

Nonlinear Dynamics 1 & 2: Geometry of Chaos by Predrag CvitanovicPredrag 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.

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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 (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 (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