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# Azimuth Math Book

edited March 2020

### Idea

This is a web for math content. One of the drivers for this may be the working needs of the study groups.

Schema:

• Definitions
• Examples
• Exercises and solutions
• Propositions, theorems and proofs
• Computational experiments
• Lessons
• Blogs

### Categories

Articles can be categorized by adding a line like this:

category:definition,algebra

We have the following structural categories: definition, example, exercise, solution, proposition, theorem, proof, experiment, lesson, blog.

Please be parsimonious about creating new categories; the schema is subject to revision.

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1.

This is a great idea. Thanks also for linking to John and Jacob's paper Quantum Techniques for Stochastic Mechanics in your running tutorial on stochastic Petri nets. It might be worth summarising a few key concepts in relation at least to underlying structure - motivated by the epidemiology study group. @DavidTanzer, I might have a go at getting started with putting one or two small bits and pieces up on said web in relation to such matters at some point, if that sounds reasonable to you.

Comment Source:This is a great idea. Thanks also for linking to John and Jacob's paper [Quantum Techniques for Stochastic Mechanics](https://arxiv.org/abs/1209.3632) in your running tutorial on stochastic Petri nets. It might be worth summarising a few key concepts in relation at least to underlying structure - motivated by the epidemiology study group. @DavidTanzer, I might have a go at getting started with putting one or two small bits and pieces up on said web in relation to such matters at some point, if that sounds reasonable to you.
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2.

Hi @ChrisGoddard, Sure thing, thanks for the good word.

Yes, it would be great for you (or others) to add math content to the math book!

Comment Source:Hi @ChrisGoddard, Sure thing, thanks for the good word. Yes, it would be great for you (or others) to add math content to the math book! 
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3.

@DavidTanzer would it be all right to add a category: Investigation ?

Comment Source:@DavidTanzer would it be all right to add a category: Investigation ?
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4.
edited April 2020

Hi Andrius, I'm skeptical here, though I don't exactly know what you have in mind. This is intended to be a workbook, with stuff that come up in practice for math-based study groups. Especially: when reading papers, there are lots of definitions to be hashed out. And then along with that there are examples of the definitions, theorems that say things about the definitions, proofs. Plus expository material which attempt to give the reader guided tours through the contents of the book. I.e. tutorials, possibly in a blog style.

So it's a group "math textbook," which can be fleshed out with exercises too.

It should be objective, and its contents potentially citable as a source of reference material.

So I wouldn't want to stretch it out, or dilute this focus, to include research projects, which it seems to be what you are hinting at. Of course that's important, but it's a very different gestalt. Relatedly, note that the wikipedia guidelines assert that original research doesn't fit into the encyclopedia genre.

In a sense there is more "personality" or subjectivity involved in research writings -- as one is trying to prosecute a thesis (similar considerations apply to philosophical works). The objective tenor of a math book just doesn't mix with this other kind of material.

We had begun a discussion contemplating how research projects might be "hosted" at Azimuth. It's a delicate matter. All else being equal this would be a good thing. On the other hand, I don't want to be hosting things at Azimuth which are too far out there. There's not cut and dried boundary line between these things, it's a contextual judgement call, which could be informed by our consensus based discussion process.

Sidenote: There is a further complication here, which is that our consensus based process is limited by the small number of currently active participants. Oh well, we have to work with what we have - and hope that it may grow as social circumstances evolve.

But in any case, one can always publish there research or investigations right on this forum. Look how well Paul has done that -- using just a single, long discussion thread, for an in-depth investigation of QBO and ENSO.

And as a reminder, everyone is encouraged to encouraged to create a personal page on the main wiki, and put it in category member. That page could contain an organized index of one's writings on the forum.

When I get more organized, I plan to do this for myself. The forum is a powerful medium; if you think about it, a single discussion can function as an entire "mini-blog," e.g., Paul's thread.

Note if any of these blog-like discussions turn out to be truly expository articles about math concepts, then that could potentially be included as blog-like tutorials in the mathbook.

Comment Source:Hi Andrius, I'm skeptical here, though I don't exactly know what you have in mind. This is intended to be a workbook, with stuff that come up in practice for math-based study groups. Especially: when reading papers, there are lots of definitions to be hashed out. And then along with that there are examples of the definitions, theorems that say things about the definitions, proofs. Plus expository material which attempt to give the reader guided tours through the contents of the book. I.e. tutorials, possibly in a blog style. So it's a group "math textbook," which can be fleshed out with exercises too. It should be objective, and its contents potentially citable as a source of reference material. So I wouldn't want to stretch it out, or dilute this focus, to include research projects, which it seems to be what you are hinting at. Of course that's important, but it's a very different gestalt. Relatedly, note that the wikipedia guidelines assert that original research doesn't fit into the encyclopedia genre. In a sense there is more "personality" or subjectivity involved in research writings -- as one is trying to prosecute a thesis (similar considerations apply to philosophical works). The objective tenor of a math book just doesn't mix with this other kind of material. We had begun a discussion contemplating how research projects might be "hosted" at Azimuth. It's a delicate matter. All else being equal this would be a good thing. On the other hand, I don't want to be hosting things at Azimuth which are too far out there. There's not cut and dried boundary line between these things, it's a contextual judgement call, which could be informed by our consensus based discussion process. Sidenote: There is a further complication here, which is that our consensus based process is limited by the small number of currently active participants. Oh well, we have to work with what we have - and hope that it may grow as social circumstances evolve. But in any case, one can always publish there research or investigations right on this forum. Look how well Paul has done that -- using just a single, long discussion thread, for an in-depth investigation of QBO and ENSO. And as a reminder, everyone is encouraged to encouraged to create a personal page on the main wiki, and put it in category member. That page could contain an organized index of one's writings on the forum. When I get more organized, I plan to do this for myself. The forum is a powerful medium; if you think about it, a single discussion can function as an entire "mini-blog," e.g., Paul's thread. Note if any of these blog-like discussions turn out to be truly expository articles about math concepts, then that could potentially be included as blog-like tutorials in the mathbook. 
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5.

One caveat about posting a lot of content to the forum: it's good to be mindful of "horizontal" versus "vertical" space on the forum. If I broke my tutorial on Petri nets into too many small articles, it would take up a lot of horizontal space, and could dilute the main view of the forum -- and many people might not be interested in this topic. So I took a cue from Paul's approach, which is to concentrate the content into larger "vertical threads."

There are no rules about this. It's just something to be aware of in a social setting like this.

Comment Source:One caveat about posting a lot of content to the forum: it's good to be mindful of "horizontal" versus "vertical" space on the forum. If I broke my tutorial on Petri nets into too many small articles, it would take up a lot of horizontal space, and could dilute the main view of the forum -- and many people might not be interested in this topic. So I took a cue from Paul's approach, which is to concentrate the content into larger "vertical threads." There are no rules about this. It's just something to be aware of in a social setting like this. 
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6.

@AndriusKulikausas, Let me return to your question now. The above were my general thoughts surrounding research projects.

But could you say more about the investigations that you have in mind?

Perhaps even better than answering that here, why not start a discussion for the investigation you are thinking of. That way you could also get some real feedback from colleagues.

I personally like to "think out loud" on the forum -- even if nobody replies -- as it feels less lonely, knowing that at least what I write will be read/considered by somebody somewhere.

Comment Source:@AndriusKulikausas, Let me return to your question now. The above were my general thoughts surrounding research projects. But could you say more about the investigations that you have in mind? Perhaps even better than answering that here, why not start a discussion for the investigation you are thinking of. That way you could also get some real feedback from colleagues. I personally like to "think out loud" on the forum -- even if nobody replies -- as it feels less lonely, knowing that at least what I write will be read/considered by *somebody* somewhere. 
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7.
edited April 2020

@ChrisGoddard wrote:

Thanks also for linking to John and Jacob's paper Quantum Techniques for Stochastic Mechanics

Related work:

Comment Source:@ChrisGoddard wrote: > Thanks also for linking to John and Jacob's paper [Quantum Techniques for Stochastic Mechanics](https://arxiv.org/abs/1209.3632) Related work: * John Baez, [Network Theory](http://math.ucr.edu/home/baez/networks/). See the blog articles in the section called Chemical reaction networks, Petri nets and Markov processes. These blogs were the starting point for the book. As blogs, they have a more informal tone, freewheeling tone. * [Network Theory (part 12) - Comparing quantum mechanics and stochastic mechanics](http://math.ucr.edu/home/baez/networks/networks_12.html). This article is a conceptual kernel. As part of the comparison, it presents an incisive mathematical synopsis of quantum mechanics. 
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8.

@DavidTanzer thank you for explaining. I have created a couple of pages at the wiki for investigations into a Hierarchy of Classifiers and into Deriving Hamiltonians. I expect they will have forum threads, too.

Comment Source:@DavidTanzer thank you for explaining. I have created a couple of pages at the wiki for investigations into a Hierarchy of Classifiers and into Deriving Hamiltonians. I expect they will have forum threads, too.
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9.
edited April 2020

@AndriusKulikausas, Great! Sure add that category to the articles on the main wiki that you wrote. It makes sense.

To be clear, I was talking about the category schema for the new Math Book, which is a "satellite web" of the main wiki. It is only there that I want to keep things structured for a math book.

Comment Source:@AndriusKulikausas, Great! Sure add that category to the articles on the main wiki that you wrote. It makes sense. To be clear, I was talking about the category schema for the new Math Book, which is a "satellite web" of the main wiki. It is only _there_ that I want to keep things structured for a math book. 
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10.

Regarding new categories on the main wiki, I would say, aim for parsimony. See if your material fits in with something already there. But if not, then go for it, and post a note to the forum saying what you did. That will give the idea a chance to circulate. On the other hand, be prepared for articles to be reclassified as part of our general group editing process.

Comment Source:Regarding new categories on the main wiki, I would say, aim for parsimony. See if your material fits in with something already there. But if not, then go for it, and post a note to the forum saying what you did. That will give the idea a chance to circulate. On the other hand, be prepared for articles to be reclassified as part of our general group editing process.
• Options
11.

David said:

.. which is to concentrate the content into larger "vertical threads."

Early on I tried creating a few spin-off threads but found quickly that it's difficult to keep track of the content. I have about 12 threads on ENSO (started in 2014 to 2016) but all are dead except for the main one.

Comment Source:David said: > .. which is to concentrate the content into larger "vertical threads." Early on I tried creating a few spin-off threads but found quickly that it's difficult to keep track of the content. I have about 12 threads on ENSO (started in 2014 to 2016) but all are dead except for the main one.