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    Grant Rostig
    @grantrostig
    Calculus Revisted by Herb Gross MIT 1971. Much loved by many, I find it good so far. Here is link of the 1st of 3 courses: https://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/
    Grant Rostig
    @grantrostig
    Grant Rostig
    @grantrostig
    Grant Rostig
    @grantrostig
    Maybe vector calculus in not used in ML, but matrix calculus ( a different topic ) is. Also tensor calculus, if do believe?
    Grant Rostig
    @grantrostig
    Bishop on Bayesian inference: http://videolectures.net/mlss09uk_bishop_ibi/
    Grant Rostig
    @grantrostig
    Vapnik of the VC dimension takes on "Deep Learning" and GOD.... hint: DNN doesn't come out well in his books. The GOD stuff, I'm not sure what he is saying. :) @mindviews https://www.youtube.com/watch?v=STFcvzoxVw4
    Grant Rostig
    @grantrostig
    Also takes on what makes a good teacher, and how this relates to ML. Also what is intelligence in ML, he doesn't know.
    predicate: specially selected feature (or constructed/engineered feature).
    Grant Rostig
    @grantrostig
    Perhaps this lecture is similar to the MIT lecture that is reference above but is not yet present on Lex's youtube channel: https://www.youtube.com/watch?v=rNd7PDdhl4c
    Grant Rostig
    @grantrostig
    OK so Vacnik's new technique is called LUSI Learning Using Statistical Invariants
    another version of same lecture with clearer slides: https://www.youtube.com/watch?v=UQk76kdmx1c
    Luke Voss
    @mindviews
    @grantrostig :-) Good finds
    Translating Between Statistics and Machine Learning - a useful table comparing terms:
    https://insights.sei.cmu.edu/sei_blog/2018/11/translating-between-statistics-and-machine-learning.html
    Grant Rostig
    @grantrostig
    @mindviews , thanks for the link, worth knowing.
    Grant Rostig
    @grantrostig
    A book on Discrete Mathematics, free opensource - available in print too, not sure how good it is. https://www.amazon.com/Discrete-Mathematics-Introduction-Oscar-Levin/dp/1792901690/ref=cm_wl_huc_item
    Lucas Anesti
    @LucasAnesti_gitlab
    Nice that it is free. 300 pages seems small.
    Grant Rostig
    @grantrostig

    https://link.springer.com/article/10.1007/s10994-018-5742-0

    After listening to Lex's interview (on AI gitter) I have seen a video from NYU, but got lost in the math quickly.

    But principle looks interesting. Better than SVM he claims, (i think).

    Grant Rostig
    @grantrostig
    Math fun from 1965 https://www.youtube.com/watch?v=hgqUya0kGPA "The Dot and the Line: A Romance in Lower Mathematics"
    Grant Rostig
    @grantrostig
    Grant Rostig
    @grantrostig

    I'm studying limits in calculus, epsilon delta, and so on.

    But I ran into a problem with the proper definition of square root/taking the square root (and other possibly all even roots, and maybe also odd roots) where I was unsure of when +/- appears in equations.

    I have not found a good complete and insightful (semi-rigorous) reference within my books or online on the topic of rational exponents.

    Most websites get it wrong, but wolfram gets it totally correct:
    From a book that doesn't explain why in a helpful way:
    Question: simplify (x^12)^(1/4) where x is a real number (not just positive):
    Answer: |x|^3 where |.| is absolute value

    https://www.wolframalpha.com/input/?i=(x%5E12)%5E(1%2F4)

    Google gives an answer with imaginary 'i', which I'm not targeting right now, unless is elucidates my abs() problem.

    https://www.google.com/search?client=firefox-b-1-d&ei=jcE_Xb7VGMu7tgXYgKmgCA&q=(-3^12)^(1%2F4)

    Can you offer any insights?

    This is not very helpful but hints at what is needed:

    A technical point: When you are dealing with these exponents with variables, you might have to take account of the fact that you are sometimes taking even roots. Think about it: Suppose you start with the number –2. Then:
    (−2)2=4=2≠−2\large{\sqrt{(-2)^2} = \sqrt{4} = 2 \neq -2}(−2)2
    ​=4
    ​=2≠−2

    In other words, you put in a negative number, and got out a positive number! This is the official definition of absolute value:
    ∣x∣=x2\large{\lvert x \rvert = \sqrt{x^2}}∣x∣=x2

    Yeah, I know: they never told you this, but they expect you to know somehow, so I'm telling you now.

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    So if they give you, say, x3/6, then x had better not be negative, because x3 would still be negative, and you would be trying to take the sixth root of a negative number. If they give you x4/6, then a negative x becomes positive (because of the fourth power) and is then sixth-rooted, so it becomes | x |2/3 (by reducing the fractional power). On the other hand, if they give you something like x4/5, then you don't have to care whether x is positive or negative, because a fifth root doesn't have any problem with negatives. (By the way, these considerations are irrelevant if your book specifies that you should "assume all variables are non-negative".)

    Also apparently (x^(1/4))^12 != (x^12)^(1/4), but they both simplify down to x^3 when done naively.
    Grant Rostig
    @grantrostig
    so it looks like order does matter, need to worry in a similar way as to not dividing by 0 anywhere in a simplification.
    Grant Rostig
    @grantrostig
    now is the "formal" (I like that) definition of square root is := |a| = sqrt(a^2)
    then ((x^2)^6)^(1/4) may offer some clue.
    Grant Rostig
    @grantrostig
    Note: that the unhelpful snippet is apparently wrong anyway about x^(4/6) (according to my experiment on wolframalpha :
    Grant Rostig
    @grantrostig
    After much searching and wasting time on youtube I found this clue https://www.youtube.com/watch?v=dqek7EkXcYo
    Grant Rostig
    @grantrostig
    Hello Bill, are you there?
    Grant Rostig
    @grantrostig
    Hi Bill, here is a conversation starter: Solve |x+1| = x+1 where x is a Real number.
    bill dee
    @hufire_twitter
    x >= -1
    bill dee
    @hufire_twitter
    OK, I take it back: x.=0
    x>=0
    Grant Rostig
    @grantrostig
    I'll reply later. :)
    @hufire_twitter
    Grant Rostig
    @grantrostig
    Your answer has two equations, what is the relationship between them? IE. is it "and" or "or"?
    bill dee
    @hufire_twitter
    and
    I'll go back to x>=-1
    Grant Rostig
    @grantrostig
    Good move. ;)
    Lucas Anesti
    @LucasAnesti_gitlab
    Hey Grant, I was thinking about the roots and powers that we talked about yesterday, so I decided to go to Desmos and play with functions of the form x^(a/b) where a,b are integers. If you set up Desmos like the picture below, you can observe the behavior of the function as the root and exponent are changing. It is not at all what I imagined the function would look like in some instances. It is not the formal coverage that you would like but at least it does bring some insight. Ideally, one would make some observations then prove them using mathematical induction.
    Screenshot from 2019-08-15 10-44-01.png
    Grant Rostig
    @grantrostig
    I have found that desmos doesn't plot nearly as well as https://www.wolframalpha.com/input/?i=x%5E(1%2F4)
    Based on the difference I suspect that Desmos is actually wrong. This is not uncommon, however wolfram seems to be correct (always??)
    @LucasAnesti_gitlab thanks for posting.
    Grant Rostig
    @grantrostig
    Let's try another one: Solve for x: |x+1| > x where x is a Real number.
    @hufire_twitter