"...now lastly, set \(x=10\), ..."
#proofinatoot that if a finite poset has a unique maximal \(x\), then \(x\) is maximum.
If not, there is a \(y_1||x\). \(y_1\) is not maximal, so there is \(y_2>y_1\); we cannot have \(y_2<x\), else transitivity would give \(y_1<x\), and we cannot have \(y_2>x\) because \(x\) is maximal, so \(y_2||x\). Continuing, we build a chain \(y_1<y_2<\dotsb\) (with \(y_i||x\) for all \(i\)), contradicting finiteness.
(This proof also suggests a construction of an infinite poset without the property.)
“To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space and say 'fourteen' to yourself very loudly. Everyone does it.”
In summer 2019, my department is hosting a workshop on mathematical and statistical perspectives of data science:
If you know anyone who would be interested in attending, please let them know!
"Nate's Silver Guarantee:
We 100% guarantee that these results are
at minimum 50% accuracte per race"
So I've been exposed to R / SAS / SPSS for several weeks in this stats computation course now, and I reckon R to probably be the most useful pursuing further beyond the course (being completely free definitely helps).
Honestly though, is SAS and SPSS still in hot demand by companies as tools for stats/data work? Seems like Python and R are the more prominent options nowadays.
Symmetric graphs constructed as the state spaces of rolling dice of different shapes: https://math.stackexchange.com/questions/2972454/rolling-icosahedron-hamiltonian-path
It doesn't say so in the post, but Ed Pegg pointed out separately to me that if you do this with a regular octahedron (d8) you get the Nauru graph. A dodecahedron (d12) should get you a nice 5-regular 120-vertex graph (because each face has 10 orientations) – anyone have any idea what's known about this graph?
Inspired by an article in @chalkdustmag, I wrote code to generate Truchet tiles for any even number of sides. Then I looked up which tilings of even-sided polygons exist, and here we are: http://somethingorotherwhatever.com/truchet-polygons/
"Help! I need a doctor!"
"He was shot!"
"I have a PhD in topology."
"Can you examine the bullet hole?"
"Still path connected, the homology is trivial."
A few tips on how to speak proper Mathlish from J.S Milne's webpage http://www.jmilne.org/math/words.html
Inspired by a line in a textbook about imagining people standing in circles to show set membership, I've made a @glitch simulation of people spontaneously forming a Venn diagram: https://spontaneous-venning.glitch.me/
Combinatorist (esp. graph theorist) turned Data Scientist
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
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