# Category: Mathematics

## 👓 Flu Vaccines and the Math of Herd Immunity | Quanta Magazine

*(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.

Syndicated copies to:## 📖 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

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.

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.

more butter given the chance! Reminiscent of the Paula Deen phrase: “Mo’e butta is mo’e betta.”

Added on Sunday, February 4, 2018

Syndicated copies to:

## 👓 Losing Count | The Paris Review

*(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

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.

Syndicated copies to:## 📺 Proving Brouwer’s Fixed Point Theorem | PBS Infinite Series on YouTube

*PBS Infinite Series | 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)

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.

Syndicated copies to:## 📺 Introduction to Category Theory 1 by Steven Roman | YouTube

*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.

Syndicated copies to:## 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

Syndicated copies to: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

*(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.

Syndicated copies to:

## 🔖 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.

Syndicated copies to:## RSVP to 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.

I’m definitely attending the Winter Quarter!

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

*(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!

Syndicated copies to:## Checkin UCLA Mathematical Sciences Building

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

*(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.