Substrate

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!

The completed edition is out now!

We’re proud and incredibly excited to announce reMarkable 2. A paper tablet that redefines note-taking, reading, and reviewing documents…

the light moving at its own speed

I wear black turtlenecks. Black panties. My lunch—mustard. Straight from the packet. No one sits next to me. Keep working my skills.

More CRSSD: https://www.crssdfest.com More NORA EN PURE: https://soundcloud.com/noraenpure Enjoy this? Please Subscribe: http://mixm.ag/L8j8ta About CRSSD Fest: Known for its sunny, oceanside views and roster of talent that ranges from driving techno to powerful displays on its live stage, the bi-annual event has consistently solidified its reputation as one of California's top electronic music occasions. Continuously developing their commitment to bringing cutting-edge selectors and live acts to Southern California, the initial line-up for this year's edition features some of the most promising and talked about talent in the world of dance music today.

Consider Your Space and Discover Beautiful, Functional Furniture for Everyday Life. Designed and Handcrafted in the USA.

Group of symmetries of a regular polygon. di-hedral in that you have to consider both rotations and reflections ⇒ if we’re considering _n_ sides, there are _2n_ members of the group. One for each possible rotation, reflection of said rotation, and identity.

Two diametrically opposed perspectives of the world. And both were both true.

how venture capital, in its essence, is a call option and how that explains the odd ways startups sometimes behave. I’d write about, in my most financially-ambitious piece, how the maniacal focus on the upside is why companies build their technologies as generally throw-away, how people constantly change jobs after 2-3 years, and other such things. ​ But one of the reasons I had moved to the U.S. more than 15 years ago was [...] a sense of sanity. A place to not just live, but breathe.

As a team of only seven people operating solely off revenue and not VC funding, we are judicious about what we prioritize and focus on. Now, our priorities have been changed for us, and our new focus is clear: We must build an excellent, online-only version of RC.

Pay attention up to the point where it’s useful, then stop. And please, please, please don’t stop making art. Especially weird shit. We need you right now more than ever.

I’ve committed to donating at least 20% of Buttondown’s profits to the software that enables it. This is a relatively low number in absolute terms—I'm certainly not changing anyone’s life—but I think it’s still important.

I worry that the closer the world gets to our fingertips, the further it gets from our hearts. It’s not an either/or—being “anti-technology” is perhaps the only thing more foolish than being unquestioningly “pro-technology”—but a question of balance that our lives hang upon.

I’m a better teacher when I focus on what students experience first, and my actions as a teacher second.

…what did I know of love’s austere and lonely offices?

The “Some More Inspiration” slide is great. https://speakerdeck.com/alisoftware/and-thats-a-wrap?slide=23

It is one thing to be sick. It is another not to know your chances of getting well. Americans who have had the virus share their experiences.

I spent last week relatively offline in Mexico, which became an interesting experiment in how the internet shapes perception: During the vacation, alarm about coronavirus in the United States escalated, but I didn’t really know because nothing in my offline environment reflected that sentiment. Since returning to the US and resuming my normal internet intake, it feels like my panic instinct missed a formative period in its development. As of now, I’m still less concerned about coronavirus than others seem to be, and while I feel a vague need, if not a civic duty, to step my worry up, I’m mainly just thankful to care less about something than I’m supposed to, for once. Regardless of how I feel, though, the coronavirus discourse is providing an interesting lesson in how these two different layers of reality can handle certain information so differently, and either amplify or suppress it: Usually the internet seems to overamplify things, but right now it seems to be properly amplifying something (although there’s nothing to check that against).

What I’m missing is the identity of an academic. An academic is an intellectual, a truth-seeker and truth-teller, a lifelong learner. Whereas I only do those things, if I feel like it. An identity gives you permission to do all the above. External permission, such as being allowed in a laboratory if that’s where your interests are pursued. But it’s also about allowing yourself to engage in intellectual pursuits. Or even: being afraid that without the external pressure of people expecting (predicting) novel intellectual output from you, you would not create any.

inside the perfect closeness

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

A celebration of minor, automatic graciousness within a community, which can shine a penetrating light.