"Gram" can refer to several things, depending on the context. Here are a few of the most common meanings: 1. **Unit of Mass**: A gram is a metric unit of mass equal to one thousandth of a kilogram (0.001 kg). It is commonly used to measure small weights in fields such as cooking, nutrition, and science.
The term "Maund" can refer to a few different concepts, but it is most commonly associated with "Maundy," especially in a Christian context. Specifically, Maundy Thursday is the day during Holy Week that commemorates the Last Supper of Jesus Christ with his disciples, as well as the institution of the Eucharist (Communion). It is observed on the Thursday before Easter and is part of the Paschal Triduum.
1-2 to hour long interviews, the number of Nobel Prize winners is off-the-charts. The videos have transcripts on the description!
The proper precise definition of mathematics can be found at: Section "Formalization of mathematics".
The most beautiful things in mathematics are described at: Section "The beauty of mathematics".
One of the most beautiful things in mathematics are theorems of conjectures that are very simple to state and understand (e.g. for K-12, lower undergrad levels), but extremely hard to prove.
This is in contrast to conjectures in certain areas where you'd have to study for a few months just to precisely understand all the definitions and the interest of the problem statement.
Bibliography:
- mathoverflow.net/questions/75698/examples-of-seemingly-elementary-problems-that-are-hard-to-solve
- www.reddit.com/r/mathematics/comments/klev7b/whats_your_favorite_easy_to_state_and_understand/
- mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts this one is for proofs for which simpler proofs exist
- math.stackexchange.com/questions/415365/it-looks-straightforward-but-actually-it-isnt this one is for "there is some reason it looks easy", whatever that means
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
Advantages over Riemann:
- Lebesgue integral of is complete but Riemann isn't.
- youtu.be/PGPZ0P1PJfw?t=710 you are able to switch the order of integrals and limits of function sequences on non-uniform convergence. TODO why do we care? This is linked to the Fourier series of course, but concrete example?
youtube.com/watch?v=PGPZ0P1PJfw&t=808 shows how Lebesgue can be visualized as a partition of the function range instead of domain, and then you just have to be able to measure the size of pre-images.
One advantage of that is that the range is always one dimensional.
But the main advantage is that having infinitely many discontinuities does not matter.
Infinitely many discontinuities can make the Riemann partitioning diverge.
But in Lebesgue, you are instead measuring the size of preimage, and to fit infinitely many discontinuities in a finite domain, the size of this preimage is going to be zero.
Which is why we then fall into measure theory!
The most important on in metabolism internals, everything else gets converted to it before being processed in the .
Nice result on Lebesgue measurable required for uniqueness.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact