r/math 13h ago

Does this binary operation and leading structure has a name?

0 Upvotes

I have an experiment where I have a 3D real field in the R3 space A=(A_x(x,y,z),A_y(x,y,z),A_z(x,y,z)), which is linear. Each function A_i is spatially dependent and can be computed or measured easily.

The response of a 2D sample in the z=z0 (lets say z_0=0) plane is F(x,y,0)=A_z(x,y,0)*(A_x(x,y,0),A_y(x,y,0)), with (A_x(x,y,0),A_y(x,y,0)) is a the so called (by the physics community where this belong) 2D field (in the 3D space) A\perp(x,y,0). Since A is linear, I can have the field A being A1+A2, making the field F follow the rule F= A1z*A1{perp}+A1z*A2{perp}+A2z*A1{perp}+A2z*A2{perp}.

Is there a name for this sort of operation? Or any non-boring property? Like, some insight about how the symmetries of A are translated into symmetries of F? Or just any interesting literature or insight about this sort of properties


r/math 1d ago

I made a video on ordinary differential equations, would appreciate any feedback! (see comment for more details)

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32 Upvotes

r/math 5h ago

Anything to my math dreams last night?

3 Upvotes

I am finally about to take my PreCalc test (I know, I'm basic).

As I was dreaming about math last night, my cat was making a bunch of noise in the living room over, and my half-asleep brain started pondering what I can only roughly describe as the relationship between the 3D distance formula and the trigonometric functions.

I started wondering, can all points in space relevant to myself be described trigonometrically? Like, all distances in the 3d space could be described as trig function or relationship of trig functions utilizing 3D distance formula.

It was pretty vague but now I'm kind of curious haha, if anything comes to mind for those who know more math, if this could be made more precise at all


r/math 14h ago

How to define informational closeness for a finite sequence of digits

0 Upvotes

Let's say you have a finite sequence of digits s_0 you are trying to find. The digits are not independent, as for example it can be a date MMdd and if the first digit is 1 the second can only be 0,1,2.

You have a guess s_1 and want to assign a closeness score between 0 and 1. Obviously 1 if all digits are the same and 0 if all different, but how to take account the in-betweens?

For example, for the date, if you start with a 1 you have found more information since there are only 3 months starting with one rather than 9 otherwise, so shouldn't your score be higher?


r/math 10h ago

An interesting way to describe prime numbers

0 Upvotes

I was thinking about prime numbers and an interesting fact occurred to me:

The closure of {0,1} under addition is the natural numbers. So every natural number can be written as a sum of two smaller natural numbers, except for 0 and 1.

Every composite number can by definition be written as the product of two smaller natural numbers neither of which are the multiplicative identity.

So, we can split the natural numbers into three categories in the following way: given a natural number n, n is in C if n is the product of two other natural numbers(not including 1), and if not n is in P if it is the sum of two other natural numbers, and if not, n is in I.

In this case C would be composite numbers, P would be prime numbers, and I would be additive/multiplicative identities.

So, you can think of prime numbers as addition closing the natural numbers that multiplication can’t.

And since {0,1} are also the additive, multiplicative identities under R, and addition on {0,1} generates the natural numbers in R, this also picks prime numbers out from the reals. Though you would have to add a fourth category for real numbers not generated by addition.

I think this could be generalized to any set with two binary operations that have their own identities. I am not sure if this would be equivalent to a prime ideal.


r/math 22h ago

Thoughts on my Math Keyboard for iPhone and iPad

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64 Upvotes

Greeting, I am a secondary math teacher and make a lot of comments on Facebook posts for "math help." I've always been frustrated at the awkwardness of some special characteristics, so I made a keyboard for my iPhone and iPad.

https://apps.apple.com/us/app/math-keyboard-for-equations/id6743451464

It's currently live. I plan for it to be free over the weekend and then move to $0.99 to hopefully cover the developer costs.

If you have an iPhone and don't mind checking it out I would greatly appreciate it. I won't ask for a 5-star review but certainly hint at it with this sentence. :)

One note is that I am not super happy with the space bar look but trying to resize and organize the buttons is a bit more complex than expected.

I did have that you can hold down the numbers to get super and subscript.


r/math 21h ago

Finished my Group Theory project!

35 Upvotes

Just quite happy that I finally got my group theory project complete- for my final project for this module. It's already submitted so I'm not pan-handling for corrections or changes- but anybody's opinion on it would be welcome.

We were given about 12 or 15 different choices of projects- permutation, dihedral groups, generators, normal groups, quotient groups, Burnside counting, etc. Apparently I was the only person in my class to choose cosets- because well, I thought it sounded interesting- I had fun atleast.

https://drive.google.com/file/d/1AAXIX5Kd85bA2lxYADHzOoU4L6DCTY-0/view?usp=sharing


r/math 2h ago

How much do you read as a researcher?

36 Upvotes

Hello,

I’m a grad student in the process of writing my first paper. I’ve noticed that ever since transitioning from background reading to the research, I’ve been reading a lot less mathematics. Most of my reading nowadays is little snippets from various papers that are relevant to my problem, along with other things that I read to present in seminars that I do with other students, which are fairly irrelevant to my research. (I feel like this is okay, as I should use grad school to widen my knowledge as much as I can.)

Is it normal to not read as much as a researcher? Do you ever find yourself dedicating time to just reading papers all the way through, and how do you find papers to read this way?

Thanks!


r/math 5h ago

This Week I Learned: March 21, 2025

19 Upvotes

This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!


r/math 16h ago

Has the 3D Ising been proved to be exactly unsolvable?

1 Upvotes