Mathematical Modeling and Applied Calculus

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1. LAIFscratchNov 2021
   The best book if you have any programming background is 'Mathematical Modeling and Applied Calculus' by Joel Kilty and Alex M. McAllister reviewed here: https://www.maa.org/press/maa-reviews/mathematical-modeling-...

   There's a small workshop for it here: https://learnaifromscratch.github.io/calculus.html throwing in some youtube tutorials. The book presents everything as functions and their parameters, like linear functions, trig, sigmoidal, e and logarithms, you learn all the parameters to these functions and can type into desmos online graph to see what they're doing visually. You don't have to do the whole thing just use it for background material when an algorithm text uses calculus methods like L'Hopital's rule.

   Poh-Shen Loh has a discrete math course open on his youtube channel https://www.youtube.com/c/DailyChallengewithPoShenLoh/search... you can use the book he recommends to look up anything that is assumed knowledge in lectures. Discrete Mathematics, by L. Lovász, J. Pelikán, and K. Vesztergombi. A book called Asymptopia by Spencer is well done too, good chapters for learning everything you want about big-O/omega/theta some topics are advanced and some anyone can do.

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2. Evgenii1Oct 2021
   I self study machine learning here https://learnaifromscratch.github.io/ai.html it's an early and shitty draft and proof of concept that you can do self-directed learning for these topics while looking up the background you need to know, which for me is much more interesting than taking a generalized math curriculum of absolutely everything. The courses so far we haven't escaped the content of Wasserman's 'All of Statistics' book yet on classification or probabilistic graphs, so you could if you wanted watch the lectures and only do Wasserman's book.

   If you want to try the OCW linear route of taking everything for whatever reasons, you will have to get up to MIT student levels trying to unravel the algebra done in the early calculus courses and later where they just assume you possess this background. One way to do that is those problem solving books like this one which 'bridges the gap between highschool math and university' https://bookstore.ams.org/mcl-25 at least you then get worked out solutions. Another way is Poh-Shen Loh's Discrete Math course he opened up on YouTube which is done the same way he holds the CMU Putnam seminar, working through a bunch of combinatorics and algebra will more than prepare you to understand those continuous math OCW courses https://youtu.be/0K540qqyJJU

   Like everybody else there is of course the issue of: who is going to check my work. For me I went with the time tested tradition of hiring a tutor, a local grad student and paid them once a week to go on chat/zoom or meet at a coffee shop before the pandemic and spend a few minutes going over everything I'm doing wrong. In the early days however I used constructive logic ie: 'proof theory', to audit my own work: https://symbolaris.com/course/constlog-schedule.html and read a huge amount of Per-Martin Lof papers on the justifications of logical operators like implies, disjunction, conjunction, etc. Of all the math I've ever taken I would say that proof theory was the most useful for somebody by themselves who isn't sure of what they are doing (I'm still not 100% sure.. hence why I hire people now).

   If you want a great Calculus text that explains those nasty looking Euler's e nested statistics distributions try Mathematical Modeling and Applied Calculus by Joel Kilty everything from partial derivatives, gradients, x^n, e^x, trig, integrals, limits is explained in terms of parameters to modeling functions, if you write software it will be easy to understand. I haven't posted it yet but I tried going through Allan Gut's probability book using only that math modeling calc text and have not run into anything applied, as in concepts about limits or integrals, that wasn't already covered. Of course the concepts are much more abstract measuring a bunch of intervals and a different method of integration and I don't pretend I'll be making any advances in this area beyond applied usage but it can be done, jump in and pick up the background as you go as opposed to doing all the background at once, losing interest and giving up.

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3. mrobotOct 2021
   I am kinda disappointed the "math foundations" (first part) does not have the word "logarithm" anywhere on the page, as this is for cs / AI.

   The CS part of this thing (different page) does talk briefly about logarithms, but just a little. In one part it says "A (base-10) logarithm of a number is essentially how many digits a number has."

   The final (AI) part then ends up needing exponential functions and logarithmic functions. It references a book

   "Obtain the book Mathematical Modeling and Applied Calculus listed in the beginning of this page via library genesis or other means, and skip to chapter 1.4 Exponential Functions. There is a short demonstration here that assumes you have a basic idea what a derivative is from the other above videos. Read chapter 1.5 on inverses, then 1.6 Logarithmic Functions. By read I mean leisurely skim through the material knowing when to go practice or read more in depth later if needed."

   I skimmed the three chapters of the book to see how they teach it, and i really kinda didn't like the way they approached it and what they leave out. I think even if you understood everything there, you wouldn't really have a good understanding of log and exponent, what e actually is, how logs relate to each other, how they relate to polynomials, how exponential funcs relate to doubly exponential ones and so on... just like good roots to be able to understand complexity really well. I dunno.

   It's a draft right? Maybe they will fix that up and make it more self-contained. I don't think i would really want to do it like this from scratch. Math is too often taught in such a mechanical way without really explaining how everything relates. I want people to actually really have good intuition about the things i teach them before i use them as requisite to teach them something that requires them.

   Is AI really a good place to start? Why even do it this way?

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