Some awesome news just as I’ve wrapped up a class on Algebraic Geometry and was actively looking to delve into some category theory over the summer. John Carlos Baez announced that he’s going to offer an online course in applied category theory. He’s also already posted some videos and details!
Category: Mathematics
👓 Robert P. Langlands Is Awarded the Abel Prize, a Top Math Honor | New York Times
Maybe yet another hint that working on the Langlands program over the summer might be a fun diversion?
👓 G. W. Peck | Wikipedia
G. W. Peck is a pseudonymous attribution used as the author or co-author of a number of published mathematics academic papers. Peck is sometimes humorously identified with George Wilbur Peck, a former governor of the US state of Wisconsin. Peck first appeared as the official author of a 1979 paper entitled "Maximum antichains of rectangular arrays". The name "G. W. Peck" is derived from the initials of the actual writers of this paper: Ronald Graham, Douglas West, George B. Purdy, Paul Erdős, Fan Chung, and Daniel Kleitman. The paper initially listed Peck's affiliation as Xanadu, but the editor of the journal objected, so Ron Graham gave him a job at Bell Labs. Since then, Peck's name has appeared on some sixteen publications, primarily as a pseudonym of Daniel Kleitman.
I’d known about Bourbaki, but this one is a new one on me.
👓 Stephen Hawking, Who Examined the Universe and Explained Black Holes, Dies at 76 | The New York Times
A physicist and best-selling author, Dr. Hawking did not allow his physical limitations to hinder his quest to answer “the big question: Where did the universe come from?”
Some sad news after getting back from Algebraic Geometry class tonight. RIP Stephen Hawking.
There's no need to go out tonight for a movie. There are 100s of math videos on every conceivable 'math' topic' at --> https://www.pinterest.com/mathematicsprof/
👓 Science’s Inference Problem: When Data Doesn’t Mean What We Think It Does | New York Times
Three new books on the challenge of drawing confident conclusions from an uncertain world.
Not sure how I missed this when it came out two weeks ago, but glad it popped up in my reader today.
This has some nice overview material for the general public on probability theory and science, but given the state of research, I’d even recommend this and some of the references to working scientists.
I remember bookmarking one of the texts back in November. This is a good reminder to circle back and read it.
Checkin UCLA Mathematical Sciences Building
Algebraic Geometry
👓 Flu Vaccines and the Math of Herd Immunity | Quanta Magazine
Simple math shows how widespread vaccination can disrupt the exponential spread of disease and prevent epidemics.
This is a very clear and lucid article with some very basic math that shows the value of vaccines. I highly recommend it to everyone.
📖 Read pages 163-194 of Ratio by Michael Ruhlman
📖 Read pages 163-194, Part 4: Fat-Based Sauces, of Ratio: The Simple Codes Behind the Craft of Everyday Cooking by (Scribner, , ISBN: 978-1-4165-661-3)
Mayonnaise: 20 parts oil: 1 part liquid: 1 part yolk
Hollandaise: 5 parts butter: 1 part liquid: 1 part yolk
Vinaigrette: 3 parts oil: 1 part vinegar
Rule of thumb: You probably don’t need as much yolk as you thought you did.
I like that he provides the simple ratios with some general advice up front and then includes some ideas about variations before throwing in a smattering of specific recipes that one could use. For my own part, most of these chapters could be cut down to two pages and then perhaps even then cut the book down to a single sheet for actual use in the kitchen.
Highlights, Quotes, & Marginalia
Part 4: Fat-Based Sauces
But what greatly helps the oil and water to remain separate is, among other things, a molecule in the yolk called lecithin, which, McGee explains, is part water soluble and part fat soluble.
Highlight (yellow) – Mayonnaise > Page 168
Added on Sunday, February 4, 2018
The traditional ratio, not by weight, is excellent and works beautifully: Hollandaise = 1 pound butter: 6 yolks. This ratio seems to have originated with Escoffier. Some cookbooks call for considerably less butter per yok, as little as 3 and some even closer to 2 to 1, but then you’re creeping into sabayon territory; whats more, I believe it’s a cook’s moral obligation to add more butter given the chance.
Highlight (yellow) – Hollandaise> Page 185
more butter given the chance! Reminiscent of the Paula Deen phrase: “Mo’e butta is mo’e betta.”
Added on Sunday, February 4, 2018
👓 Losing Count | The Paris Review
How do nonsensical counting-out rhymes like these enter the lexicon?
I’d read this a year or two ago for a specific purpose and revisited it again today just for entertainment. There’s some interesting history hiding in this sort of exercise.
I also considered these rhymes as simple counting games, but the’re not really used to count up as if they were ordinals. Most people couldn’t even come close to saying how many things they’d have counted if they sang such a song. I also find that while watching children sing these while “counting” they typically do so with a choice for each syllable, but this often fails in the very young so that they can make their own “mental” choice known while still making things seem random. For older kids, with a little forethought and some basic division one can make something seemingly random and turn it into a specific choice as well.
So what are these really and what purpose did they originally serve?
Reply to Stephanie Hurlburt on Twitter
Stephanie 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.
📺 Proving Brouwer’s Fixed Point Theorem | PBS Infinite Series on YouTube
There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra. Analogous to the relationship between geometry and algebra, there is a mathematical “portal” from a looser version of geometry -- topology -- to a more “sophisticated” version of algebra. This portal can take problems that are very difficult to solve topologically, and recast them in an algebraic light, where the answers may become easier. Written and Hosted by Tai-Danae Bradley; Produced by Rusty Ward; Graphics by Ray Lux; Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington; Made by Kornhaber Brown (www.kornhaberbrown.com)
https://www.youtube.com/watch?v=djaSbHKK5yc
I had originally started following Tai-Danae Bradley on Instagram having found her account via the #math tag. Turns out she’s burning up the world explaining some incredibly deep and complex mathematics in relatively simple terms. If you’re into math and not following her work already, get with the program. She’s awesome!
Personal Website: http://www.math3ma.com/
Twitter: @math3ma
Instagram: @math3ma
YouTube series: PBS Infinite Series
While this particular video leaves out a masters degree’s worth of detail, it does show some incredibly powerful mathematics by analogy. The overall presentation and descriptions are quite solid for leaving out as much as they do. This may be some of the best math-based science communication I’ve seen in quite a while.
I must say that I have to love and laugh at the depth and breadth of the comments on the video too. At best, this particular video, which seems to me to be geared toward high school or early college viewers and math generalists, aims to introduce come general topics and outline an incredibly complex proof in under 9 minutes. People are taking it to task for omitting “too much”! To completely understand and encapsulate the entirety of the topics at hand one would need coursework including a year’s worth of algebra, a year’s worth of topology including some algebraic topology, and a minimum of a few months worth of category theory. Even with all of these, to fill in all the particular details, I could easily see a professor spending an hour at the chalkboard filling in the remainder without any significant handwaving. The beauty of what she’s done is to give a very motivating high level perspective on the topic to get people more interested in these areas and what can be done with them. For the spirit of the piece, one might take her to task a bit for not giving more credit to the role Category Theory is playing in the picture, but then anyone interested is going to spend some time on her blog to fill in a lot of those holes. I’d challenge any of the comments out there to attempt to do what she’s done in under 9 minutes and do it better.
📺 Introduction to Category Theory 1 by Steven Roman | YouTube
Lecture one of six in an introductory set of lectures on category theory.
https://www.youtube.com/watch?v=If6VUXZIB-4&list=PLiyVurqwtq0Y40IZhB6T1wM2fMduEVe56&index=1
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.
Why More Linear Algebra? by David Austin
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
My awesome colleague @davidaustinm is unveiling his new, open-source linear algebra text at the JMM, but you can access it NOW at his (new!) blog, the aptly named "More Linear Algebra": https://t.co/AAreqGk8DW
— Robert Talbert (@RobertTalbert) January 9, 2018
👓 Limits and Colimits, Part 1 (Introduction) | Math3ma
Tai-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.
https://www.instagram.com/p/Bdd8vmfBQvG/