how to develop algebraic intuition

this is a vague question but what’s a good way to develop algebraic intuition?

i have pretty good analysis intuition (dipped my toes into most grad analysis topics – measure theory, spectral theory, pdes, optimization, sdes, etc.) but for the life of me even undergrad algebra things are sometimes unintuitive to me (often when they intersect with number theory type things).

obviously i’m aware of the age old adage of just doing problems and i’ve tried – i have i think 4? algebra books ranging in difficulty from frayleigh to ashe – but i just can’t make substantial progress because i’m constantly stymied by seemingly trivial steps in proofs.

a little while ago i had the idea that maybe playing with the objects using something like magma would be useful but i can’t afford a magma subscription just for fun.

also i thought about approaching it from the other direction – cat theory through something practical like haskell. but the trouble there is (as everyone says) cat theory doesn’t make sense unless you have algebraic examples to translate to.

i’ll give an example that i should probably be embarrassed about but since i have no mathematical shame i’m not: i’ve read the definitions of group, ring, field, algebra, probably over 100 times each. i still for the life of me can never remember which ones have units and/or inverses for each of the operations (though i do know which ones have two operations) and which ones don’t. like there’s nothing about the word ring (i just now had to look it up) to me that leaps out as addition should be invertible but multiplication need not be.

it’s like i’m one of those people that immediately forgets your name after you introduce yourself to me (which is in fact true for me) but for algebraic definitions. note i do not have this problem in the least in analysis because i always have a picture of what’s going on. e.g. my last analysis class was ~10 years ago and i can define uniform and lipshitz continuity without skipping a beat (though i don’t remember absolute continuity i realize).

now i’ve gotten away with this because i’m not a math phd (CS) but still there are things i’m personally interested in (like de rham cohomology) that just demand facility with algebra.

anyway this isn’t a rant or a cry for help – i’m genuinely interested in ideas for other ways to approach this seemingly ludicrous learning … “disability”.

submitted by /u/ice109
[link] [comments]

[Q] Subsetting data into a new dataset based on into irregular column selection

Hey folks,

So I am trying to subset a Dataset that consist of 106 columns into a smaller set of variables. I tried to store the desired sub-selection of variables I am interested in in a list via the c( ) function and then tried to ransform it into a data, but it creates a dataset of 101253 variables which is bigger than my original data set. Any suggestion on how I can achieve what I desire?

test = as.data.frame(c(bnb[,23:24],bnb[,26],bnb[,32], bnb[,36:40],bnb[,42:48],bnb[,52:58], bnb[,64:66],bnb[,83:84],bnb[,87:93], bnb[,99], bnb[,106],bnb[,61])) 

submitted by /u/deniz_sen
[link] [comments]

[Q] Sample sizes for attribute data with multiple variables

R&D Engineer here, so my statistics knowledge isn’t what it used to be. Apologies if i’m using the wrong terms

I need to determine the minimum sample size for a test assessing whether a user can mechanically actuate two different interacting parts. Essentially I have 3 variables

X = the part I’ve designed Y = The part that my part needs to fit with (not controlled by me) Z = the user, who may or may not be able to use the components together depending on strength / dexterity etc.

X is a relatively expensive “single use” device. We don’t expect that reusing a single sample multiple times will influence the result. There will be part to part variation however.

Y is a relatively inexpensive single use device that X must fit inside. We can likely get as many of these as is required. This part will likely Wear relative to X (much softer) and may influence the results if its used more than 10-20 times. These are molded to a relatively tight tolerance with respect to X, but will still have variation

I work in a large office with a large cross section of people to draw from. The result for each run will be binary, whether the user could complete the action or not. Obviously a continuous variable would be preferable, but this particular interaction is not easy to set up on an instron.

How can i calculate the minimum sample size for X Y and Z at different powers? What would this type of analysis be called?

Thanks

submitted by /u/dieselmonkey
[link] [comments]

[Q] Help with SQL

Hello everyone. I recently gained access to a healthcare database of hospital stays and was hoping to do some analysis on it. Unfortunately, it has to be put into a SQL database and then linked to SAS (I don’t have SPSS). Does anyone have any tips on how to do this? I am tech-savvy but have little experience with programming or SQL.

submitted by /u/gandhiarnold
[link] [comments]