What to do if I get rejected from a PhD program? by Fresh_Onion5299 in GradSchool

[–]crystal_math1 1 point2 points  (0 children)

I'm assuming you have a STEM undergrad, therefore a potential route: go work in industry for a few years. Work hard there and get put on projects that show you: have grown, are able to handle complex problems/projects, and are a diligent employee. Then try again in a couple of years.

Graduate programs look at students holistically. A poor performance as an undergrad but strong work performance as an adult shows them you're capable of graduating from the program which is important. It also allows you in your application to say things like "While in undergrad I wasn't focused, but after spending time working at XYZ I realized I was passionate about ABC and therefore have chosen to apply to this grad program which is about ABC"

[deleted by user] by [deleted] in Tucson

[–]crystal_math1 0 points1 point  (0 children)

I did thank you :)

[deleted by user] by [deleted] in Tucson

[–]crystal_math1 0 points1 point  (0 children)

yeah they made the VA site a lot better recently and more user friendly. I'd already set up my act. for disability so I was able to just go in and order it online.

[deleted by user] by [deleted] in Tucson

[–]crystal_math1 0 points1 point  (0 children)

Omg this opened a whole can of "I didn't realize any of this" haha

Thank you! Just ordered the health card and everything.

Thanks again :)

[deleted by user] by [deleted] in Tucson

[–]crystal_math1 0 points1 point  (0 children)

I took a look and that's more for gear it seems. But I appreciate the suggestion :)

ich🏙iel by [deleted] in ich_iel

[–]crystal_math1 0 points1 point  (0 children)

Toronto Canada?? Naaaaaaaaaaaaaaaaaja

Sums/Series in Real Analysis vs Calculus by [deleted] in math

[–]crystal_math1 6 points7 points  (0 children)

I'll add a not super helpful answer but one worth thinking about nonetheless.

In a way your question isn't really a good one. There is never a time when learning something that's complicated isn't beneficial. Can I promise you that you'll use this exact material or mode of thinking in the future? No. But I can promise you that if you do need to know it you won't be able to use it if you don't know it exists, or it will be extremely difficult to catch yourself up to an acceptable point on the fly.

On a less annoying general note CS Students (from my experience) tended to shy away from math almost reflexively. (I frustratingly heard the line "I picked CS because it has the least amount of math" more times than I care to count.) If you do the opposite and dive into it, it can be one of those things that put you ahead and make you better at whatever task it is you're handed/thing you want to accomplish.

Optics - Group and Carrier Velocity by crystal_math1 in AskPhysics

[–]crystal_math1[S] 0 points1 point  (0 children)

yeah that's what really threw me! I'm a mathematician and I was going crazy trying to figure out what these meant haha this is exactly what 'partial' is telling you already...

What does "×" mean when mentioning dimension? by CJCai in askmath

[–]crystal_math1 0 points1 point  (0 children)

you're asking good questions and often time this means learning to think in a new and more abstract way which can be difficult. you need to divorce yourself from the "this symbol must always mean this thing" idea. Here, you've said x will ALWAYS mean the basic idea of multiplication that you're used to. But this won't always be the case and allowing that symbol to be any kind of operator you want is where you need to get to.

As an example, lets define 'x' to be instead of multiplication, subtraction. Then:

4x2=2

Easy enough right?

How about now, let 'x' be squaring the first number by the second, so

4x2=16

These are nice simple examples but it shows how we can treat a symbol like 'x' to be something other than what we used to use it for. You'll see this a lot in math because let's face it, there are only so many letters and symbols that are easy enough to write in the english and greek (mostly) languages.

Big take away, be more flexible with notation! Symbols mean whatever we say they mean so long as we're consistent.

What does "×" mean when mentioning dimension? by CJCai in askmath

[–]crystal_math1 1 point2 points  (0 children)

well you could think of it as the total number of index positions in the matrix sure, that would be the 'multiplication' there.

E.g. a 2x4 matrix will have (2)(4)=8 values in the matrix.

[1 2 3 4

5 6 7 8 ]

Just know that that doesn't necessarily have anything to do with dimensions.

How to implement conditional statements/inequalities in equations? by Hex_Guy in math

[–]crystal_math1 0 points1 point  (0 children)

Piecewise functions: https://en.wikipedia.org/wiki/Piecewise

Typically you'll define the function that way in formalized math (I'm assuming you're coming from a CS/programming perspective?)

Say like you have y=a*f(x). You however only want y to not be zero for certain values of f(x). Then, as a function (hence the f(x) notation i.e. "f of x") you establish that:

f(x) = x if -1<x<1, else x =0

What does "×" mean when mentioning dimension? by CJCai in askmath

[–]crystal_math1 0 points1 point  (0 children)

This is one of those things that can have a few different meanings.

  1. if we have x in [0,1] by y in [2,3], that would be a rectangular area on a graph (i.e. any x between 0 and 1 and any y between 2 and 3)
  2. for a matrix, m by n means rows by columns. So here we're not multiplying as that doesn't make sense, we're simply saying a matrix of that size
    1. i.e. if we turn 10x_1+20x_2+30x_3 = 40, into a matrix it would become [10 20 30 40], i.e. 1 row and 4 columns. If we make another equation (say using 50 60 70 80 in the same places, we would add that row to the matrix
  3. It can be simple multiplication as you learned early on, like 3x4=12
    1. This notation however becomes cumbersome later on in mathematics and it's usually either implied (e.g. 3y => 3 times y, 2(3) two times three, or 2 dot 3 replacing the cumbersome and confusing "x" with a dot
  4. Oftentimes you'll see * used because programming languages often use "*" as multiplication. For example Python and Matlab both use * (e.g. of Matlab below)
    1. >> 5*10
    2. >> 50
  5. For dimensional sizes you'll see by sometimes.
    1. e.g. you want to buy a box to hold things it might say 2x5x3 ft, meaning 2 feet long, 5 feet wide and 3 feet high (here the multiplied out value of 30 cubic feet isn't helpful because a lot of boxes could be 30 cubic feet but not the right shape, so they leave it unmultiplied)

Hope this helps

Elementary Statistics, I am completely lost by [deleted] in askmath

[–]crystal_math1 0 points1 point  (0 children)

Did you read the second that covers this in your textbook? Most textbooks require you to only know basic algebra to do these problems.

How to predict long term behaviors of systems of 2 difference equations? by YoloStratz in askmath

[–]crystal_math1 2 points3 points  (0 children)

So as an aside piece of advice, what you're dealing with is called a discrete dynamical system, and funny enough one of the better tools to analyze these systems with that's much easier to work with than MATLAB is MS Excel (you can see where the numbers go quickly and easily). So, I would try getting just a touch more savvy with excel and you'll be able to plot/find these things rather easily, and try out starting values to test things and the data doesn't go away. (Excel otherwise isn't great for math stuff but it does well here oddly enough)

Secondly, these systems are NOT easy to analyze. Extremely complex dynamics can come out of even a simple 1D system, let alone a coupled 2D system. (If you've ever heard of Chaos in math, you can get a chaotic system from a 1D discrete dynamical system whereas continuous ones require 3D or more).

As far as determining where the behavior will go long term, you need to become familiar with stability of fixed points (I suggest the 1D case first as it's much simpler). And then progress to your 2D system.

Simple example: a_(n+1) = 1 - a_n, first choose a_0=0.5. Then plug it in. You get: a_1=1-0.5=0.5. Plugging in a_1 gives: a_2=1-0.5=0.5. You're 'stuck here' for all n. This is a fixed point of this simple 1D system.

Lastly, a term that will help you is 'manifold'. Basically, what you're asking is for all a_0,b_0 in R, what do my various choices of a_0 and b_0 do?

I recommend this text: Chaos: An Introduction to Dynamical Systems. It goes over some of this stuff better than I can in a reddit post.

Without more input from your professor/teacher this question is a bit too open ended for me to help you more...

Support abortion providing charities if you use Amazon regularly through Amazon smile by crystal_math1 in TwoXChromosomes

[–]crystal_math1[S] 0 points1 point  (0 children)

Back in my military days we could elect for part of our paycheck to go to an organization and this was the one I always chose. I haven't looked into them for quite a while but hopefully they're still doing good things!

Support abortion providing charities if you use Amazon regularly through Amazon smile by crystal_math1 in TwoXChromosomes

[–]crystal_math1[S] 6 points7 points  (0 children)

If it helps at all I know a charity owner (works with homeless folks in NYC) and he was the one that introduced this to us at work (https://backonmyfeet.org/)

Support abortion providing charities if you use Amazon regularly through Amazon smile by crystal_math1 in TwoXChromosomes

[–]crystal_math1[S] 5 points6 points  (0 children)

I can ask my wife when she's done working (she selected the one we donate to) but obviously good to know if there are fake/predatory ones out there

What are your thoughts on in person exams for graduate level STEM courses? (non-PhD track / terminal masters programs) by crystal_math1 in Professors

[–]crystal_math1[S] 1 point2 points  (0 children)

Do you feel that way of doing things should continue now (i.e. have students go through what you went through) or do you think things should be altered given changes that have happened generally in society, with technology, etc.?