Mathematical Foundations of Computer Networking (2012) | Hacker News Reader

Mathematical Foundations of Computer Networking (2012)

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88 pointsteleforce11 comments

Great recommendation. Expensive, but bought it anyway because it's the first time I have seen it, and the table of contents listed all the mathematical techniques I recognize as "oh, that's an X domain problem," like queueing, information theory, conditional probability, fourier transforms, but didn't have the depth to implement models with them in a practical amount of time.

I noticed there wasn't a graph theory chapter, which perhaps if they sell out of these they can add one in the next edition. A breadth first intuition for things like power laws, complexity, combinatoric explosion, and related ideas has shortened a lot of meetings.

Even if it's impenetrable, worst case I will still be able to recognize problems as likely having solutions in those domains and speak to enough of the concepts to find someone with the depth to solve them.

Pdf of the book is available at : https://www.cl.cam.ac.uk/teaching/1213/PrincComm/mfcn.pdf

The author has another book An Engineering Approach to Computer Networking: ATM Networks, the Internet, and the Telephone Network which is also excellent and worth studying.

Author's web page for more resources : https://svr-sk818-web.cl.cam.ac.uk/keshav/wiki/index.php/Mai...

This is cool! He's the same professor who wrote 'How To Read A Paper' (https://dl.acm.org/doi/10.1145/1273445.1273458).

Prof. Keshav was the original author of the REAL network simulator, the precursor to the popular ns-3 network simulator:

https://en.m.wikipedia.org/wiki/Ns_(simulator)

Looking at the table of contents, it sounds quite interesting, but I find some bits missing. (Maybe due to 2012 date?)

DC networks generally follow a spine-leaf design, have ToR switches. They are DAGs and trees.

These are effectively ultrametric spaces, which have a lot of nice properties that can be exploited for optimization and ML (e.g. these are generally bipartite graphs, so belief revision is guaranteed to terminate).

In the same vein, basic abstract algebra and group theory (i.e. symmetries) could be quite useful as well.

I'll have to check this book out.

I was learning J 12 years ago, and I happened upon this book, "Network Performance Analysis Using the J Programming Language" from 2008.[1]

J is very mathy, and this was a great way to learn J for a useful application.

[1] https://link.springer.com/book/10.1007/978-1-84628-823-4

This is a coincidence! I just bought this book last week. It is slim but seems non-trivial. Mathematical Foundations of Computer Networking is definitely needed if one is to understand this book.

My interest is to study the J language in an application setting but could only find this book in paper copy form. I am quite surprised as to why the AI/ML community has not discovered the J language since at first glance it seems it would be a good fit.

Check out APL and Futhark. There are some nice examples of ANNs implemented in J and APL[1]. I am currently studying hardware efforts for neuromorhic systems. The array model is great, but when running on von Neumann architectures you lose execution potential. J was an inspiration for Pandas written by Wes McKinney. It is column-based vs. Numpy's row-based model.

[1] https://aplwiki.com/wiki/Neural_networks

Thanks for the pointers, will definitely look into it.

>The array model is great, but when running on von Neumann architectures you lose execution potential

I expected that the array model would be best for SIMD and GPU parallel processing and as such a good fit for ML.

See Also: Array Languages Make Neural Networks Fast - https://arxiv.org/pdf/1912.05234

Some videos on youtube

https://www.youtube.com/playlist?list=PLFB088DB91845CA34

Wow this is an awesome recommendation! Seems like a good level for me and goes over topics I've always wanted to learn more about.

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