Substrate

In our math research we make countless choices. We chose a problem to work on, decide whether its claim is true or false, what tools to use, what earlier papers to study which might prove useful, w…

In her Perimeter Public Lecture webcast on May 12, 2021, mathematician Emily Riehl will examine the fascinating mathematics providing a solution to the stable marriage problem, including the sexist implications underlying it and some real-world applications. Riehl, an associate professor of mathematics at Johns Hopkins University, has published more than 20 papers and two books on higher category theory and homotopy theory. Perimeter Institute (charitable registration number 88981 4323 RR0001) is the world’s largest independent research hub devoted to theoretical physics, created to foster breakthroughs in the fundamental understanding of our universe, from the smallest particles to the entire cosmos. The Perimeter Institute Public Lecture Series is made possible in part by the support of donors like you. Be part of the equation: https://perimeterinstitute.ca/inspiring-and-educating-public Subscribe for updates on future webcasts, events, free posters, and more: https://insidetheperimeter.ca/newsletter/ facebook.com/pioutreach twitter.com/perimeter instagram.com/perimeterinstitute Donate: https://perimeterinstitute.ca/give-today

And it's also an interesting proof of concept -- it's hard to imagine that this is the end of the story. Maybe it can be worked into a simple "check your conjectures" tool that would be of great help to mathematical researchers. 6/6— Timothy Gowers (@wtgowers) May 1, 2021

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An introduction to graph theory for high-school educators or hobbyists. The videos on this channel focus on exposing the viewer to concepts in graph theory without including a lot of rigor or detail. I recommend that you view these videos with a textbook or two handy in case you would like more detail on the discussed topics.

What comes to mind when you read the word “graph”? Graph paper? Graphing calculator? High school math homework? Unfortunately, the word is overloaded with meaning, and none of the above are what a mathematician usually means when they say “a graph." They mean something like this.

A Swift package for working with GraphViz. Contribute to SwiftDocOrg/GraphViz development by creating an account on GitHub.

Since the summation of the degrees of all vertices is _double_ the size of the edge set. That means that there must exist an even number of vertices with an odd degree to keep the overall sum of degrees even.

In this video we discuss the problem of finding a tight upper bound on the number of edges a graph on n vertices can have if it is also known that the graph has no 3-cycle in it. This is known as Mantel's Theorem and it is a special case of Turan's Theorem which generalizes this problem from a 3-cycle (a complete graph on 3 vertices) to complete graphs on arbitrary numbers of vertices. #TuranGraph #MantelsTheorem #GraphTheory CHECK OUT OTHER TYPES OF VIDEOS: ================================ GRE Math Subject Test: https://www.youtube.com/playlist?list=PLBiVnG9A5gceFbk7oTBHALETI2SUmplIL Putnam Math Competition: https://www.youtube.com/playlist?list=PLBiVnG9A5gcdLg0Im3qewDrgcMxpbjcqN Math Theorem Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gccu9O8aCjVsynisfQLQyGOe Math Problems Corner: https://www.youtube.com/playlist?list=PLBiVnG9A5gcc_1Kzd2xkHMXdO8zHz-W_4 Math Insights: https://www.youtube.com/playlist?list=PLBiVnG9A5gcfHRbtZcfQdJuUMAS6v48uj Academic Advice: https://www.youtube.com/playlist?list=PLBiVnG9A5gce-PPdJQmtPNMsivAKKuXwe GET MY BOOK ON AMAZON!! ======================== "Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures" https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464 CHECK ME OUT ON THE INTERNET!! ============================== Website: www.mohamedomar.org Twitter: @ProfOmarMath Instagram: profomarmath YouTube: www.youtube.com/ProfOmarMath And of course, subscribe to my channel!

a graph is planar if and only if its crossing number is zero.

The Four Color Map Theorem (or colour!?) was a long-standing problem until it was cracked in 1976 using a "new" method... computers! A little bit of extra footage from this: https://youtu.be/laMkuPrad3s This video features Dr James Grime - http://jamesgrime.com More Grime videos: http://bit.ly/grimevideos This video supported by Squarespace: https://www.squarespace.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

A counterexample to Hedetniemi's conjecture - featuring Erica Klarreich. Get 3 months of Audible for just $6.95 a month. Visit https://www.audible.com/numberphile or text "numberphile" to 500 500 More links & stuff in full description below ↓↓↓ Read Erica Klarreich's Quanta article on this subject: https://www.quantamagazine.org/mathematician-disproves-hedetniemis-graph-theory-conjecture-20190617/ And visit her website: http://www.ericaklarreich.com/ Yaroslav Shitov's breakthrough paper: https://arxiv.org/abs/1905.02167 Thanks to Stephen Hedetniemi for providing us with photos and pages from his original dissertation. Some more graph theory on Numberphile... Four Color Maps: https://youtu.be/NgbK43jB4rQ An Unsolved Problem: https://youtu.be/niaeV_NHh-o Planar Graphs: https://youtu.be/xBkTIp6ajAg Perfect Graphs: https://youtu.be/C4Zr4cOVm9g Friends and Strangers: https://youtu.be/xdiL-ADRTxQ River Crossings: https://youtu.be/ZCVAGb1ee8A Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.

Category theory is just a special case of edge-labelled digraph theory