Looking for collaborators: Virgilio Project

Hi everyone, I’m the author of the Virgilio Project, an open source repository on GitHub that shows to beginners the way to learn Data Science for free in a structured and reliable way, on the Web. I’m planning with my collaborators to create some beginners guide to get started with the necessary math for Data Science (even without high school). and I’m here to ask if someone is interested in having a part in this writing and creation process.

This is the repo, is getting noticed fastly for the quality of the material organization (the guides).

https://github.com/clone95/Virgilio

If you’re interested, text me on Telegram – @Clone95

I think is a great opportunity to help others and show your ability to explain things to beginners (and not only!).

Thanks for your attention! 🙂

submitted by /u/clone290595
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Question on truth vs. provability

Recently I read about the lives of Russell and some other 20th century mathematicians, and their search for a/the foundation of mathematics. Somewhere in the story came along Gödel and his incompleteness theorems. Paraphrased, one of them states that “in a ‘good enough’ logical system, there will always be statements that are true, but unprovable”.

I was wondering how this could be. To me it seems that if a statement is unprovable in some system, then we can add either the statement or its negation as an axiom to the system, yielding in both cases an extended consistent system (i.e. it is not possible to reach a contradiction within either of them). But in that case, how could such a statement have been true in the initial system (given that it’s negation is true in some consistent extension)?

Also, I tried reading Russell’s/Whitehead’s ‘Principia Mathematica’ and Gödel’s ‘On formally undecidable propositions […]’. However, I find them quite hard to read, and I was wondering if there are some book with a modern treatment on this topic (preferably self-contained books)? Regarding the level of such books, I’m doing a master’s degree in math, but I’m not at all an expert on logic.

submitted by /u/_JesseV
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How should I go about teaching me Optimization techniques?

Background: Environmental Engineer who works with stochastic simulation and adjacent to optimization.

Hi, all

As you read from my background, I work with stochastic simulation. More specifically, I work with the generation of flow scenarios from autoregressive models. The result of the simulation process is fed into a chain of optimization models that use every from linear programming to stochastic dynamic programming to mixed-integer programming to find the optimal allocation of resources.

I aspire to get closer to optimization so I can expand the topics I can work with, but I lack the background for it. I’ve been asking colleagues about ways they think I should start exposing myself to the field and the answers varied. One said I should go with Linear Programming (LP) because “it’s the basis upon which you build more advanced knowledge”. Another said I should start with Non-linear Programming (NLP) because “LP is nothing but a particular case of NLP. Once you learn NLP, you know LP”. Yet a third one said I should start with neither, instead, I should go with a general introduction to optimization (OPT) like the class notes from R. T. Rockafeller you can see here.

I know myself around Linear Algebra (LA) and Statistics & Probably (S&P). Although, I admit, I do go looking for explanations on textbooks more often than I like. I wish I knew more, and I’m watching online courses to handle this situation. (In case anyone cares to know, for LA I’m watching the video lectures from Dr. Strang from MIT made available thru MIT OCW. For S&P, I’m going with Harvard’s Statistics 101 course.).

Now, my question(s): Have you done something similar? Have you gone into optimization even though your original field didn’t prepare you for this? If so, how did you go about it? Do you know of video lectures online that were helpful to you?

I am doing my M.Sc. now and I’m certainly going to do some stochastic simulation in it and the result, as expected, will feed optimization models. I will work for a year or two more (I already have worked 4 years at this job) and then I’ll try to apply to a Ph.D. in Operations Research. While some schools are very hands-on with their OP research, some like University of Washington, CMU, Cornell, or Northwestern University are very math-y. With that said, should I learn Analysis? I have found a series of online lectures and they have both “Introduction to Analysis” course and its sequence, “Real Analysis”.

In case you have gone to a school whose OP research was math-y, how much of Real Analysis did you use? Is it a reality that you have to go in knowing it, or you can learn it while you’re there? In this topic, which deviates from the original question about how to have a foray into OPT, I’m looking for insights from those who’ve gone to strong schools/departments and how you fared.

Thank you so very much for your time and input. Your answer is highly appreciated. =)

submitted by /u/MasonBo_90
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If you think you might be interested in helping the Metamath project add to its database of computer-verified proofs (> 30 000 so far!), here’s a recent thread on contributing to set.mm, the set of proofs built on ZFC

Question about number sets

I’d like to preface this by stating that I’m by no means competent in maths, but I do enjoy thinking about various math concepts/ideas sometimes.

Recently I saw a video of a certain well-known youtube math teacher introducing number sets, like naturals, integers, etc. When it came to complex numbers he said that the set is closed under all complex numbers and operations, which wasn’t the case for every previous set. At this point I thought, what about division by zero? Isn’t it undefined/meaningless EXACTLY in the same way that sqrt(-1) was thought to be meaningless? As well as sqrt(2) before that? In fact isn’t that a sure sign that C isn’t closed under the simple operation of division?

Quick research and I learn about Riemann sphere which extends complex numbers to add a point at infinity. In this way -∞ = ∞ and division by zero is allowed.

Question 1: Is extended complex plane (Riemann sphere) a natural continuation of the sequence Natural-Integer-Rational-Real-Complex?

Question 2: I also learned that for extended complex plane certain other operations are left undefined, like ∞ – ∞ or 0 × ∞. And noticing how we came from number line to number plane to number plane curved in extra dimension, couldn’t this mean that the next steps (to make sense of operations that remain undefined) would be to consider the volume of a Riemann sphere and even higher dimensions (“3d” object curved in 1+ dimension)?

submitted by /u/ThrowawayAccount0793
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