This is already supported via listChanged. The problem is that >90% of clients currently don’t implement this - including Anthropic’s, https://modelcontextprotocol.io/clients
The model in question is "convince small and medium businesses that they need to buy my software in order to do things the same way as large companies X and Y and have a hope of remaining competitive". For Oracle X and Y were banks, retail and logistics companies, for the new generation of "big data" vendors it is Google and Facebook.
I wonder what proportion of "pure" CS algorithms can be conceptualized as an application of one of the fixed point theorems and/or properties of monotone operators. There has got to be _something_ useful about the functional analysis perspective and people doing serious work in algorithms are certainly familiar with it as a group.
Have you checked the "Articles" section on betterexplained.com? Clearly the author of the article is trying to put his ideas into practice - not perfect but rather helpful in fostering something like actual understanding of topics that are all too often presented as a sequence of rote manipulations (more or less all of K12 and many "service" university courses follow this).
Some really nice suggestions in the article that for whatever reason are not often brought up while discussing maths education.
A good way to bootstrap the "math avengers" website would be to get people to write up running commentary to some classic maths texts, e.g. Silvanus Thompson (out of copyright), Halmos, Rudin etc.
Essentially all high school maths programs are less than great to put it politely and often created by people with rather limited appreciation of the subject. Better university textbooks are not readily accessible without an instructor. Running commentary from several authors giveing additional motivation, examples, clarifications or alternative derivations can be of great help to students and wikipedia style platform can be great for organising such a project.
Sites like wikipedia and mathoverflow / stackexchange are great for specific questions but lack structure - centering the efforts around certain "canonical" texts can help to organise the material which otherwise would be overwhelming.
As pointed out in the comments on blogspot, CS is hardly the degree with biggest focus on optimization. Try operations research, systems & control, economics or even the MBA!
If you don't already understand them, probably a good idea to skip the detailed derivations and look for the big picture. The course is really quite hard to follow closely if it's your first exposure to the material.
Find a semi recent advanced textbook (preferably one that is used in at least one of the better schools) and use google scholar from there (both papers cited in the text and those citing it).
The formal bibliometric tools such as scopus, reuter-thompson etc are hugely misleading to say the least with the ever growing avalanche of publications over the last decade (increasing number of people are being paid bonuses for each publication in an "international" venue). See this character who according to reuter-thompson is a "rising star" of computer science [1] and also happens to be a collaborator of El-Naschie [2].
These "best paper" lists are almost comical and a very poor way to find important papers. Have a look at citation statistics for the older "winners", they are only marginally better than the average for the venue - essentially nobody still reads them today and they've had hardly any impact all.
To find _important_ papers you want at least 5-10 years of hindsight - look for those that are still being cited a lot correcting for citation rings, dubious journals/conferences etc. As a side benefit, these can almost always be found online on some course website without requiring IEEE / ACM subscriptions.
There is a number of really quite good applied maths courses on youtube (roughly in this order from each group):
MIT 18.06, 18.085, 18.086, 6.262, 6.450
Stanford EE263, EE364A, EE261
Profs Strang, Boyd and Gallager are quite a bit better with maths than the typical engineering lecturer, even though their courses are not exactly at the level of Rudin, Breiman et al.
Thanks for the reply. If you are already running these private competitions it might be useful to advertise them a bit more openly (then you will need some formal criteria for joining to avoid user resentment, e.g. those in top 100). You are right that the system as is can help to find people who have some combination of persistence, general intuition for dealing with data and a modicum of modelling skills - "the world's best data scientists" is doubtful but certainly beats interviewing.
Not surprising at all - kaggle (as currently implemented) is a fundamentally broken model. On top of the rather unpleasant "everybody pays auction" or "winner take all" system, they have a severe problem with metrics - the majority of the datasets are not anywhere near large enough to give stable out of sample error estimates, which means that in many cases the "winners" are barely better than random.
Perhaps they might be onto something with "kaggle prospect", but unless they pivot in some creative new direction, it's hard to see the service being very useful.
All true, but the idea that a good fraction of combinatorial algorithms that undergrads see can be replaced (albeit less efficiently) by linear programming is important. Not clear how classical CS curriculum helps to appreciate this either.
And after all, LP used to be considered an almost elementary topic before it mysteriously dropped out the curriculum (perhaps something to do with linear algebra no longer being compulsory).
Just for fun - "stochastic optimization" as in here:
www2.isye.gatech.edu/~ashapiro/download.php?Down=book
is in fact identical to "empirical risk minimization" in Vapnik's statistical learning theory. As soon as you are not 100% sure about any of the numbers in your routing model, you find yourself in the same setting as that studied in "machine learning"!
I think now it is fairly generally appreciated that interior point methods constitute perhaps the most powerful class of tractable algorithms there is, yet remarkably they are hardly ever mentioned in any of the undergrad CS algorithms classes. Usually there is a passing mention of linear programming to establish an auxiliary result like max flow / min cut duality but that's it.
OR/CS is not the ultimate combination. If you want to do interesting work in this space you ideally need a background in all of optimization (ILP, convex NLP, stochastic optimization),control theory, certain areas of economics (general equilibrium, game theory, mechanism design, concepts behind applied finance), statistics/econometrics (out of sample performance, hypothesis testing, causality, dealing with non random samples) and probability (mainly stochastic processes).
OR itself contains a large number of applications that combine many of the above, e.g. network revenue management, but someone who has taken grad courses from the OR department alone would genuinely struggle to do anything significantly new or interesting.
People from computer science departments have also been gradually moving into these areas, witness growth in machine learning, algorithmic game theory etc.
Do you know a reference that presents state estimation from this point of view? I have painstakingly arrived to this myself, following somewhat sketchy remarks in Gilbert Strang's "Computational Science and Engineering".
The classical exposition is a perfect example of confounding the model and the algorithm but it just refuses to die.
All good advice - operator theory in various guises is ubiquitous in applications but certainly not something many discern even through grad school in CS.
Probably not much point trying to convince people on HN though - having perhaps suffered through an abysmal 'calculus' sequence they are not very receptive to the message that we have barely tapped practical consequences 50 year old mathematics.
You should perhaps do a stand alone blog - even on google plus!
If you are interested in learning this topic, do not go directly to Koller/Friedman book - it sure contains a lot of material but its presentation is not well integrated (just look at the topic dependency graph at the beginning).
A much more cohesive introduction would be Michael Jordan's book draft that has been floating around for nearly a decade now. You can find some of the older versions online, e.g. http://www.cs.cmu.edu/~lebanon/pub/book
Go directly to chapter 5 to see how the language of PGMs can help to clarify a lot of standard material in stats and ML.