Cisco Updated 2025-07-16
Nerds 2.0.1 excerpt about Cisco (1998)
Source. - youtu.be/mhz24AR3nIc?t=45 the founders both worked at Stanford University but because they were in different departments they couldn't send an email to one another.
- youtu.be/mhz24AR3nIc?t=54 Sandy Lerner is very nice and chilled. She says how she was amazed by Leonard's manners!
- youtu.be/mhz24AR3nIc?t=86 "sincerity begins at a little over 100 hours a week". The dude is a robot.
- youtu.be/mhz24AR3nIc?t=279 earthquake!!!
- youtu.be/d0ya8DggDYs?list=PLn7AqqWS1I_9EHEHy6sw-v6hUMhbeOTRW&t=3268 she bought a manor house, probably in Chawton Hampshire, England, possibly Chawton House
- youtu.be/d0ya8DggDYs?list=PLn7AqqWS1I_9EHEHy6sw-v6hUMhbeOTRW&t=3312 he started donating to search for extraterrestrial intelligence
Cis-trans isomerism Updated 2025-07-16
Exist because double bonds don't rotate freely. Have different properties of course, unlike enantiomer.
City in California Updated 2025-07-16
City in Germany Updated 2025-07-16
City in Japan Updated 2025-07-16
City in Taiwan Updated 2025-07-16
City of London Updated 2025-07-16
The City of London is an obscene thing. Its existence goes against the will of the greater part of society. All it takes is one glance to see how it is but a bunch of corruption. See e.g.: The Spiders' Web: Britain's Second Empire.
Clade Updated 2025-07-16
Cladogram Updated 2025-07-16
TODO vs Phylogenetic tree? www.visiblebody.com/blog/phylogenetic-trees-cladograms-and-how-to-read-them:
Cladograms and phylogenetic trees are functionally very similar, but they show different things. Cladograms do not indicate time or the amount of difference between groups, whereas phylogenetic trees often indicate time spans between branching points.
Classical computer Updated 2025-07-16
Classical group Updated 2025-07-16
Classification (mathematics) Updated 2025-07-16
Examples:
- classification of finite simple groups
- classification of regular polytopes
- classification of closed surfaces, and more generalized generalized Poincaré conjectures
- classification of associative real division algebras
- classification of finite fields
- classification of simple Lie groups
- classification of the wallpaper groups and the space groups
Classification of 2-transitive groups Updated 2025-07-16
Classification of 4-transitive groups Updated 2025-07-16
en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Multiply_transitive_groups is a nice characterization of 4 of the Mathieu groups.
Classification of 5-transitive groups Updated 2025-07-16
Apparently only Mathieu group and Mathieu group .
www.maths.qmul.ac.uk/~pjc/pps/pps9.pdf mentions:Hmm, is that 54, or more likely 5 and 4?
The automorphism group of the extended Golay code is the 54-transitive Mathieu group . This is one of only two finite 5-transitive groups other than symmetric and alternating groups
scite.ai/reports/4-homogeneous-groups-EAKY21 quotes link.springer.com/article/10.1007%2FBF01111290 which suggests that is is also another one of the Mathieu groups, math.stackexchange.com/questions/698327/classification-of-triply-transitive-finite-groups#comment7650505_3721840 and en.wikipedia.org/wiki/Mathieu_group_M12 mentions .
Classification of closed surfaces Updated 2025-07-16
So simple!! You can either:
- cut two holes and glue a handle. This is easy to visualize as it can be embedded in : you just get a Torus, then a double torus, and so on
- cut a single hole and glue a Möbius strip in it. Keep in mind that this is possible because the Möbius strip has a single boundary just like the hole you just cut. This leads to another infinite family that starts with:
You can glue a Mobius strip into a single hole in dimension larger than 3! And it gives you a Klein bottle!
Intuitively speaking, they can be sees as the smooth surfaces in N-dimensional space (called an embedding), such that deforming them is allowed. 4-dimensions is enough to embed cover all the cases: 3 is not enough because of the Klein bottle and family.
Classification of finite fields Updated 2025-07-16
There's exactly one field per prime power, so all we need to specify a field is give its order, notated e.g. as .
It is interesting to compare this result philosophically with the classification of finite groups: fields are more constrained as they have to have two operations, and this leads to a much simpler classification!
Classification of finite groups Updated 2025-07-16
As shown in Video "Simple Groups - Abstract Algebra by Socratica (2018)", this can be split up into two steps:This split is sometimes called the "Jordan-Hölder program" in reference to the authors of the jordan-Holder Theorem.
Good lists to start playing with:
History: math.stackexchange.com/questions/1587387/historical-notes-on-the-jordan-h%C3%B6lder-program
It is generally believed that no such classification is possible in general beyond the simple groups.
Classification of finite rings Updated 2025-07-16
So we see that the classification is quite simple, much like the classification of finite fields, and in strict opposition to the classification of finite simple groups (not to mention the 2023 lack of classification for non simple finite groups!)
Classification of finite simple groups Updated 2025-07-16
Ciro Santilli is very fond of this result: the beauty of mathematics.
How can so much complexity come out from so few rules?
How can the proof be so long (thousands of papers)?? Surprise!!
And to top if all off, the awesomely named monster group could have a relationship with string theory via the monstrous moonshine?
The classification contains:
- cyclic groups: infinitely many, one for each prime order. Non-prime orders are not simple. These are the only Abelian ones.
- alternating groups of order 4 or greater: infinitely many
- groups of Lie type: a contains several infinite families
- sporadic groups: 26 or 27 of them depending on definitions
Simple Groups - Abstract Algebra by Socratica (2018)
Source. Good quick overview. There are unlisted articles, also show them or only show them.