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xda xiaomi redmi2 :: xiaomi community :: more flashboot commands :: reddit post (self-teach calc) :: Ranking engineering degrees by difficulty (15:07), 2023
Math is difficult, because the explanations come too late in the game. You have to get to Linear Algebra to explain basics, which most people can't accomplish
spreadsheets, Python, R, SPSS
Most people cannot afford SPSS, ergo PSPP is a a good option. If using Linux, most repo's have it. In Arch, it's in the AUR. There's plenty of PSPP videos on YT, as well as SPSS videos that a person can adapt.
Python, Numpy, Plotly (1:10:57) Derek Banas, 2022. Uses Jupyter on Anaconda but a couple tweaks will do it in Google Cloud. 16:00 explains Numpy, 17:00 read CSV, scraping 21:00, Plotly 45:00
Pandas Merge (Excel) (9:08) Alan Hettinger, 2022. Similar to a SQL join. When we want to put things together from various tables into a combined output. Can dapt Jupyter to Google Colab with Google Sheets as-is, or download them as CSV's first and then merge.
Pandas Merge (Sheets) (10:48) Tobias Willman, 2020. Adapt the Jupyter above using this guy's vid.
Self-study generally
self-study feynman's books (27:33) Math Sorcerer, 2023. Mathematics for self-study series of books, espec trig and calculus.
V600 scanning tips (5:53) erwnalejo, 2021. Somewhere in Western Kansas. Lomo digitaliza, blue tack to adjust height. Links in comments to products. Lomo is an extra $50.
epson scanning tips (28:11) Nick Carver, 2019. Paper masks some of the holder. 5:40 uses a squeeze ball. 2400 dpi is fine for any normal use including 8.5 x 11 blowups, etc.
V600 overview (52:17) Film Friends,
PreCalc
Two best books I know are Larson and Sullivan's. I found a 9th edition Sullivan and a
Polar coordinates
Difficult because we move back and forth between analytic trig and graphic trig, then introduce time changes in the angles
Series
Infinite series means infinite terms, not that the sum diverges to infinity. Also the best way to learn them is M1 in MVP math.
Harmonic Series (sum of sums) (46:34) Mathologer, 2020. Infinite sum of 1/(n+1) Gamma explained at 24:21.
Buying land (32:06) Brantley Blended, 2018. listing, PLAT recency, survey recency (due diligence period), boundaries,
Matrices
My road to matrices has been difficult, b/c for years it was one of those categories where 1) I simply had to remember formulas and 2) Math teachers acted like matrices were easy, like I was an idiot, because the problems were easy. Nearly always in Math, my intuition is right when something doesn't quite seem that easy. So lets call matrices what they are: representations of vectors with several degrees of freedom, not just 'simple arrays'. Although the latter is correct, it's like saying cars are easy to make b/c they fit in a garage.
The real way to look at it is via transformations, rotations, and vectors, as well as ways to write functions (remember we can also write functions with limits). That is to say, linear algebra. M
1. Berkeley HS Math 1, Module 6 (webpage). This has some good videos on different transformations: reflections, rotations, and translations. The shortcoming is that the they move the points, instead of changing the underlying grid (as we do with matrix scalars).
2. Linear transformations (10:58) 3 Blue 1 Brown, 2016. The real value of what matrices actually are, and also acknowledged by the host. They know how important this is. Connecting matrices and vectors. 3:52 i-hat (x), j-hat (y).
3. Why can't we multiply vectors (51:15) Freya Holmer. A good review, awkwardly stated, of basic maths up to matrices/vectors. Multiplying R3 vectors gives quaternions, multiplying R2 vectors gives us complex numbers.
A tour of differential equations(27:16) 3 Blue, 1 Brown, 2017. How we work backwards with diff equations
4. interesting vector usage (14:40) Kieran Borovic, 2023. an interesting way to convert categories of nature into a 7 row vector.
Integral tricks
Most difficult are problems that combine U-sub (reverse chain) and IBP, integration by parts, but also must know d/dx, dx/dy, Dx
Integral conceptualization (10:54) Math The World, 2024. *does not* use the best Cherkassky/Russian way of series, however gets much nearer than most and points out the problem of focusing too much on area under curve.
Why dx at end of integral (4:36) Krista King, 2016. sometimes I forget why it's smashed onto the end of an integral or double integral and so this is a good reminder it's the dx(limit of distance,0), not the Dx (distance).
What is dx alone? (5:38) Jim Fowler, (2013). Just as important as the one above. A little deeper.
u-subs (11:02) The Organic Chemistry Tutor, 2018 . a few definite integrals from organic chemistry tutor.
Cheat sheet (PDF) Most of the tricks and common integrals.
Exponents/Logs
exponentiate (30:08) Mathemaniac, 2024.
Lesser used
I consider that these are like the irregular verbs of math. We have to know them typically by use, as they are difficult to remember how to derive. Trig identities, hyperbolic derivatives and integrals. Geometric Algebra -- nuclear physics.
Logic
Russell's paradox (28:27) Jeffrey Kaplan, 2022. Covers naive set theory inadvertently (as opposed to axiomatic set theory).
attach/remove ft lens (2:46) Caleb Ginsburg, 2021. Turn to f5.6, then turn speed selector to 400 ASA in alignment with 5.6, then push the release button. It sort of hinges from top to bottom.
Statistics
Old skool brandon foltz, are still some of the best videos out there.
the most important statistical skill (13:35) Very Normal, 2024. Monte carlo is about iterations
