Discover and read the best of Twitter Threads about #MathTwitter
Most recents (6)
I'm excited to share our new paper w/ @mungowitz and @m_zavlanos introducing a decentralized mechanism for pricing and exchanging alternatives constrained by transaction costs: a thread 🧵 1/n 
Our decentralized model is based on max-plus (linear) algebra, a branch of tropical 🌴 geometry. The recipe is simple: times <- plus, plus <- max. Max-plus algebra reinvents linear algebra with varying degrees of success, e.g. eigenvalues, linear systems, regression... 2/n
We use max-plus algebra to model the effective value of alternatives (e.g. goods, even opinions 🤔), taking transaction costs with neighbors in a trade network into account. This results in the data of a max-plus matrix-weighted graph. 3/n
1/ Tell Your Kid That Infinity Comes In Different Sizes
#parenting #learnmath #mathtwitter
Your kid probably knows infinity as the “largest number ever”.
Get ready to blow their mind - there are actually different sizes of infinity.
#parenting #learnmath #mathtwitter
Your kid probably knows infinity as the “largest number ever”.
Get ready to blow their mind - there are actually different sizes of infinity.
2/ If infinity is a number greater than any assignable quantity or countable number, how can there be different sizes?
Let's work through an example:
Let's work through an example:
3/ Step 1: Ask them to imagine that they are going to count dogs and to write down the number of dogs they have
Let them start counting dogs 1, 2, 3, 4, 5... and have them write it down as they go (do a column on a piece of paper).
Let them start counting dogs 1, 2, 3, 4, 5... and have them write it down as they go (do a column on a piece of paper).
Happy New Year #MathTwitter! Let's start 2022 w/ Part 1 of a fun series: "Groups you Never Knew Existed...and others you can't POSSIBLY live without!"
Today we'll see the "diquaternions", a term you've never heard of b/c I made it up last month. Let's dig in! 🧵👇
1/17
Today we'll see the "diquaternions", a term you've never heard of b/c I made it up last month. Let's dig in! 🧵👇
1/17
We'll start with the familiar quaternion group Q_8. Shown here are several Cayley diagrams, a Cayley table, cycle diagram, subgroup lattice, its partition by conjugacy classes, and an action diagram of Aut(Q_8). Each of these highlights different structural features.
2/17
2/17
Next, have you ever wondered what would happen if you replace i=e^{2\pi i/4} in Q_8 with a larger root of unity?
These are the dicyclic groups. Here is Dic_6, for n=6. Note that n=4 gives Q_8.
The last two pictures highlight the orbit structure (cyclic subgroups).
3/17
These are the dicyclic groups. Here is Dic_6, for n=6. Note that n=4 gives Q_8.
The last two pictures highlight the orbit structure (cyclic subgroups).
3/17
EVERYTHING IS GARBAGE, NOW WHAT?
Piper H
October 19, 2021
Piper H
October 19, 2021
*awkward time*
me, to me: should i begin?
1/5 How can you calculate the estimated DAILY risk of ischemic stroke (and other events) in patients with atrial fibrillation?
#MedTwitter #HemeTwitter #CardioTwitter #MathTwitter #FOAMed #MedEd
Note: the original post was deleted due to a mathematical error
#MedTwitter #HemeTwitter #CardioTwitter #MathTwitter #FOAMed #MedEd
Note: the original post was deleted due to a mathematical error
2/5 While the CHADSVASc is helpful for annual estimation of ischemic stroke risk (and other events), what is the risk of DAILY risk? Turns out we can do some math to derive it from the annual risk estimation!
3/5 The math here doesn't EXACTLY reflect the daily risk of for patients because there are countless variables that we cannot control. @JessieCurrier17 describes the rationale using probability quite nicely.
(1/3) Thrilled to announce that my 2nd book is now out!
It is an intro to proofs and higher math, again written in long-form style: There’s lots of discussion between results, “scratch work” before the proofs, 200+ illustrations, fun examples, and jokes.
amzn.to/3oZrMNu
It is an intro to proofs and higher math, again written in long-form style: There’s lots of discussion between results, “scratch work” before the proofs, 200+ illustrations, fun examples, and jokes.
amzn.to/3oZrMNu
(2/3) Also, after every chapter is a ~2 page intro to an open question, as well as a ~7 page intro to some advanced area of math. You can see which areas in the table of contents below.
The appendices contain advanced proof methods, some beautiful proofs, and writing advice.
The appendices contain advanced proof methods, some beautiful proofs, and writing advice.
(3/3) This book will interest first-time proof writers, as well as those interested in a broad survey of math.
Big thanks to all the people who helped! The editorial board (pictured below) includes four members of #MathTwitter: @jensg0, @deliprao, @gradmathErisa & @lgpcappiello.
Big thanks to all the people who helped! The editorial board (pictured below) includes four members of #MathTwitter: @jensg0, @deliprao, @gradmathErisa & @lgpcappiello.
