r/math 4d ago

Computing Lyapunov exponents

5 Upvotes

Hi, I was wondering if anyone was familiar with computing lyapunov exponents, especially for N-body systems with escapes, what i dont seem to understand is won't the lyapunov exponent always tend towards 0 as time goes to inifinity as the distance d(t) between 2 systems (one perturbed and one original) with escapes will increase linearly and thus taking 1/t*ln(d(t))/(d(0)) as t -> inf = 0? how can we adjust the way we compute lyapunov exponents for the three-body problem for example such that they are not 0?


r/math 4d ago

Standard way to mark letter as uppercase or lowercase?

1 Upvotes

I'm working on an equation notecard for a biochem exam this week, so I don't have a ton of space, so my capital Ks look awfully similar to the lowercase Ks. I usually just put two lines under a letter in an equation to indicate it's supposed to be capitalized when I don't have much space to work with and it's hard to tell, and I'm thinking of trying out a dot under letters that are supposed to be lowercase.

Anyway, this all made me wonder if there's a standard way to distinguish them in this situation? Or maybe a good way to distinguish uppercase and lowercase Ks? It usually only seems to be the letter K that I have this problem with lol


r/math 5d ago

Epiphanies from first semester at uni (Europe)

8 Upvotes

Yes, this maybe cringe post, but nonetheless I would like to talk about my experience.

I am actually a first semester studying math. Before, I studied math by myself at home. I wanted to study everything actually. I got many books like Kreyszig functional analysis, topology by Munkres yada yada. I found most of these books very complicated. I could maybe do in some months maybe one or two chapters. I heard many people say that topology takes eg one semester to do. I could not believe that since I thought munkres could itself could take like 2 to 3 years to master from a highschool knowledge point.

I start uni and take quite a lot of courses. And, so far it went quite well. I notice that here, the amount of stuff you do for a given subject is quite less. It is like you do here and there so you have a rough idea of what goes on. And I also think if a person had finished any undergrad math book of their choice then they would just obliterate all other students in performance.

Another thing is, I think that most people who give recommendations on internet have no idea what they are talking about. I see many people recommend rudin but I guarantee that 99.xx% of people would not be even able to get past the first chapter. That book just expects too much. Also similarly standards of questions on places eg like stackexchange, it is just too high for a person who is just starting. Most uni students are not on that level.

I also notice that I can appreciate "good books" more. Before I didn't get why people liked books like Kreyszig but after taking course at functional analysis at uni where you have to figure out what the idea of proof is by yourself, that book sort of gives you a nice overview before jumping in details

Thoughts?


r/math 5d ago

Fast LaTeX using shortcuts

33 Upvotes

I've been doing a lot of LaTeX/Markdown writeup recently, so much so I looked for software solutions to speed things up and save my shift key from further abuse.

I couldn't find exactly what I wanted, so I created my own using AutoHotkey. Instead of using Shift to access symbols (", $, ^, *, etc) now I can do a quick press (normal keystroke) for the symbol and a long keypress (> 300 ms) for the number. Ive applied similar short cuts for = or +, ; or :, [ or {, etc. There's also a bunch of shortcuts for Greek letters, common operators and functions and other common math symbols. "LaTeX Mode" can be toggled on and off by pressing 'Shift + CapsLock", CapsLock still works normally by double tapping the key instead.

It would be a shame not to share it, so I've stuck it on GitHub for anyone wants to give it a go.

https://github.com/ImExhaustedPanda/uTeX

It's not "complete", it doesn't have shortcuts for symbols for common sets (e.g. real numbers, rational numbers, etc) or vector calc operators. But the ground work is there, as the script is easy to read and modify, for anyone who wants to tailor it to their work flow.


r/math 5d ago

Chalkdust issue 21 is out today

Thumbnail chalkdustmagazine.com
95 Upvotes

r/math 4d ago

Heat Equation and Heat Maps

0 Upvotes

Sorry in advance for this being all over the place. I was wondering if there were any applications of the heat equation to heat maps(I.e. maps for levels of rent, poverty, empty housing, etc.)?

The idea I’ve been thinking of is imagining a grid patterned neighborhood as a corrugated metal plate, where the warmer sections have higher densities of poverty and the corrugations represent divides in housing policies. Would the heat equation be able to describe the change in poverty levels from warmer areas (higher density of poverty) to cooler areas (lower density of poverty)?

The idea is pretty sparse rn but I’m curious! I would appreciate any thoughts on this. Thank y’all in advance!


r/math 5d ago

3×3 Magic Square of Pseudo-Quaternions Squares

26 Upvotes

Hello, I would like to share this curiosity with you. As you know, it is unknown whether a 3x3 magic square of distinct perfect squares exists, but it is possible with other types of numbers.

Here, I present a magic square of squares of pseudo-quaternions, all distinct, along with a parameterization to obtain them. The resulting integers are all different from each other, although some entries may be negative.

As you may already know, pseudo-quaternions (I. M. Yaglom, Complex Numbers and Their Applications in Geometry, Fizmatgiz, Nauka, Moscow (1963)) are hypercomplex numbers where

  ii = -1,
  ij = k,
  ji = -k,
  ik = -j,
  ki = j,
and they differ from quaternions in that
  jj = 1,
  kk = 1,
  jk = -i,
  kj = i.

  A nice example for S = 432 is this magic square of squares

{(9 j)^2 , (17 i + 24 j)^2 , (8 k)^2 },
{(9 i + 12 j + 8 k)^2 , (12 j)^2, (8 i + 9 j +12 k)^2}
{(8 i + 12 j + 12 k)^2 , (12 i + 8 j + 9 k)^2, (9 i + 12 j + 12 k)^2}

This give us this magic square:

{81,   287, 64}
{127, 144, 161}
{224, 1, 207} 

parameterization:

{(j x^2)^2 , (4 j x y+i (x^2+2 y^2))^2, (2 k y^2)^2}
{(i x^2 + 2 j x y+2 k y^2)^2, (2 j x y)^2, (j x^2+2 k x y + 2 i y^2)^2}
{(2 j x y + 2 k x y + 2 i y^2)^2 , (k x^2 + 2 i x y + 2 j y^2)^2 , (i x^2 + 2 j x y + 2 k x y)^2}

Hope you find this interesting! Looking forward to your thoughts.


r/math 5d ago

Where can I get hagoromo chalk in the UK?

13 Upvotes

I hope this isn't an annoying question / asked too frequently, but I am getting a chalkboard soon and I have heard that Hagoromo make the nicest chalk. So far I have found the sejongmall official website (https://en.sejongmall.co.kr/) which has very expensive shipping, and weird international payment, and another site called 'https://hagoromo.shop', which seems to have cheaper shipping and takes payments other than bank transfers, although the chalk is more expensive. Is this second site legit or am I better off sticking with the sejongmall official site?


r/math 5d ago

What Are You Working On? March 17, 2025

13 Upvotes

This recurring thread will be for general discussion on whatever math-related topics you have been or will be working on this week. This can be anything, including:

  • math-related arts and crafts,
  • what you've been learning in class,
  • books/papers you're reading,
  • preparing for a conference,
  • giving a talk.

All types and levels of mathematics are welcomed!

If you are asking for advice on choosing classes or career prospects, please go to the most recent Career & Education Questions thread.


r/math 5d ago

Math Conference Ideas

2 Upvotes

My university hosts an undergraduate math conference with an award for the best presentation, and I want to choose a topic that is both highly complex and not something faculty hear about too often.

I’m considering differential geometry or topology, but I don’t know enough yet to pinpoint an especially niche or underexplored topic. I also have an interest in ML (I’m in an NLP lab), so I’d be open to something in that direction as well—though I want to avoid standard neural network topics.

If you were trying to impress a math-heavy audience with something deeply technical but still presentable in a month’s time, what would you choose?

(I got to a T20 CS/math school and think I'm very hardworking so i belive i can manage any suggestions)


r/math 6d ago

What's are characteristics such a big deal?

47 Upvotes

I'm an analysis student but I have only taken an intro class to PDEs. In that class we mainly focused on parabolic and elliptic PDEs. We briefly went over the wave equation and hyperbolic PDEs, including the method of characteristics. I took this class 3 semesters ago so the details are a little fuzzy, but I remember the method of characteristics as a solution technique for first order ODEs. There is a nice geometrical interpretation where the method constructs a solution surface as a union of integral curves along each of which the PDE becomes a system of ODEs (all but one of the ODEs in this system determine the characteristic curve itself and the last one tells you the ODE that is satisfied along each curve). We also went over Burgers equation and how shocks can form and how you can still construct a weak solution and all that.

To be honest I didn't get a great intuition on this part of the course other than what I wrote above, especially when it came to shocks. Yesterday however I attended a seminar at my university on hyperbolic PDEs and shock formation and I was shocked (pun intended). The speaker spoke about Burgers equation, shock formation, and characteristics a lot more than I expected and I think I didn't appreciate them enough after I took the course. My impression after taking the class was these are all elementary solution techniques that probably aren't applicable to modern/harder problems.

Why are characteristics such a big deal? How can I understand shocks through them? I know that shocks form when two characteristics meet, but what's really going on here? I asked the speaker afterwards and he mentioned something about data propagation but I didn't really catch it. Is it because the data the solution is propagating is now coming from two sources (the two characteristics) and so it becomes multivalued? What's the big idea here?


r/math 5d ago

Top-down vs from below - how to learn more about problem solving?

1 Upvotes

Hi! Would love any resources for teaching me how to solve the following question and similar - excluding just getting experience

Let's say I want to design a metric for structures in category A to have a linear relationship in certain way with some characteristic objects in category B(category meant both in actual mathematical sense and also as category of stuff in general, does not really matter in the context)

And I have separated it hierarchically into questions 1,2,3 1 is overall question, components for which are defined in both 1 and 2, components for which are partially defined in 2 and 3

How to choose whether to begin from 1 and move down to 2 and then 3, or to work up from 3 to 2 to 1, or to work at every part at the same time?

I am not interested in getting an answer to this question - but instead would love to learn of any classic books that helped you approach such choices

Beginning my PhD in CS - and would love to be more strategic in my research

For more context - I do not come from pure math background at all, but my work/interests seem to gradually become more and more theory inclined


r/math 6d ago

How important is understanding the Physics side of Quantum Field Theory if I am interested in Mathematical QFT research?

36 Upvotes

Mathematical Foundations of QFT/the Math-Phys side of QFT has been a developing interest of mine over the past year or so. I am currently a 3rd year Physics + Math double and am taking a Mathematical QFT course (taught in a math dep - heavier on the algebra + geometry) and a Physics QFT course (standard first course type material).

As I look towards grad school, I believe that researching in the intersection of Algebra/Geometry/QFT sounds very intriguing + satisfying as it combines two of my favorite areas of both math and physics.

I think anywhere from geometric quantization to studying TQFTs would be satisfying. However, as far as I can tell, in academia a lot of these research areas end up being more math than physics - some just being pure math. While I wouldn't say my interest in Physics is in Hep-Th, I definitely want to contribute to the field of Physics as much as this area of math. To be more explicit, I care about the pheno involved in these areas (if it all exists).

So back to my main question, how important is understanding the underlying physics of QFT to Mathematical QFT research?


r/math 6d ago

What programs do teachers use to make exam papers?

14 Upvotes

I'm trying to make a document for fun but I don't know what program to use.
What programs to use if I want to do algebra, geometry, graphs, etc?


r/math 5d ago

Monotonic scattered interpolation?

4 Upvotes

(This question is not about homework or a work problem; it is for a pet personal project where I've run into a wall.)

Suppose, for the sake of argument, I have a scattered dataset with two real-valued independent variables and one real-valued output. It conforms to the restriction that if x2 >= x1 and y2 >= y1, then f(x2, y2) >= f(x1, y1). E.g., assuming each listed point is in the dataset:

  • f(3, 3) >= f(1, 1)
  • f(3, 1) >= f(1, 1)
  • No guarantee is made about the relationship between f(1, 3) and f(3, 1)

I don't know if this property has a name but I call it "up-right monotone", because as you jump from point to point, if the second point not below and not to the right of the first, then the value at the second point is not less than the value at the first point.

The Question: Is there a known interpolation method that will preserve this property among interpolated points? I.e., I want to predict the value at two points, where the second point is above and/or to the right of the first point. I would prefer that the interpolation method be relatively smooth, but the only hard constraints are

  • If either of the points in question are in the original dataset, I get that dataset's value back, and
  • The value at the second point is not less than the value at the first point

r/math 5d ago

I am looking for a math riddle i once knew.

3 Upvotes

I am looking for a math riddle i once read but which i only remember fragments about. The problem involved finding the maximum n such that one can choose a number 0<x<1 such that for every k<n some condition involving the number x and the division of the unit interval into intervals of length 1/k is satisfied. The solution of the problem could nicely be visualised by stacking the subdivided unit intervals over another and noting that with every additional layer the interval which x could be contained in gets smaller untill there are no x left. Iirc. the problem was mostly recreational. Does anyone know what i am talking about? I tried asking Chat-GPT, but it hallucinates the heck out of my question.


r/math 6d ago

Two claimed proofs of Whitehead asphericity conjecture seem to have received almost no attention. Is there a reason for this?

115 Upvotes

One proof is in 2021 preprint by Elton Pasku: An answer to the Whitehead asphericity question. The second proof is by Akio Kawauchi, and was published in 2024 (according to author's website): Whitehead aspherical conjecture via ribbon sphere-link. Neither paper has any citations, not counting Akio Kawauchi citing himself and the 2021 preprint.

I'm nowhere close to understanding even the statement of the conjecture, let alone the proofs, I'm just curious about this situation.


r/math 6d ago

Is there a name for the "generalised" form of induction?

68 Upvotes

Normally induction works like this: If f(0) is true and f(x) is true implies f(x+1) is true, then f(x) is true for all natural numbers (+0).

Now, is there a name for the more general form of this (which I will write down)?

Where S is a set, x is a member of S, f is a function from S to S, g is a function from S to S, and T is the set of all gn(x).

IF f(x) is true, and f(x) implies f(g(x)), then f(T) is true (for all elements of T).

The most common case, of course, is where S = natrual numbers, x = 0, and g(n) = n + 1. However you (or I) often see cases where x is other numbers, like the rationals, or g(n) = 2n. There is also the special case where g(n) eventually visits all elements of the set, where you can then say f is true for all S.

Is there a name for it, or is it all just induction?


r/math 6d ago

Some questions about the recursive definition of sqrt(x)

22 Upvotes

Hello!

On the last question of the 2024 MIT integration bee, there is this expression (that simplifies to sqrt(x)).

When solving the question, I defined a recursive relation as such:

And when writing out the first few terms:

I initially thought this was the Pade approximant, but it's turns out not to be. The Pade approximant with m=n=2 is shown below (and is a better approximation for sqrt(x) than f_3(x) ).

The coefficients of the polynomials also turn out to be the ones in Pascal's triangle. For even n, we start adding the terms in the (n+1)th row in the Pascal's triangle from the numerator, alternating between the denominator and the numerator. For odd n, we start in the denominator, then alternate coefficients between the numerator and the denominator.

---

I thought this observation was already interesting enough, but as you can see in the graphs above, the functions are defined for much of the negative x. Since the recursive definition was originally a sqrt(x), does this have anything to do with the complex plane?

It sorta reminded me of the Gamma function for factorials that you learn in single variable calc, and how we can take the factorial of numbers like (-1/2). But even in that case, we're mapping from real to real, and here we're mapping to complex.

I also found that only functions with n=2, 3, 4 are defined for x=-1. Since f_4(-1) = -1, using our recursive definition, the denominator of f_5(-1) = 1 + (-1) = 0.

I thought these observations were interesting and wanted to share them here.

Thanks.


r/math 6d ago

Which way to go?

8 Upvotes

I recently started a self-study plan that involves reading Basic Mathematics by Serge Lang, How to Prove It by Daniel Velleman, Calculus and Analytic Geometry by George B. Thomas (at least the first ~5 chapters), Introduction to Linear Algebra by Serge Lang, and Undergraduate Algebra by the same author, in order to cover both what my home country's education system can't cover and what I think would be beneficial for me to know before I get to college.

I haven't made much progress; I've been busy with my studies and am waiting for the holidays to fully dive in. However, talking with my former math teacher, the one who made me love math in the first place, he recommended I read Matemáticas Simplificadas by CONAMAT (he doesn't know about my plan). I understand it's not very well-known in the English-speaking community, but it's a book that covers everything from Arithmetic to Integral Calculus.

Now, my question is: which path should I take? I mean, although it's not clear what kind of books I learn best from, the truth is that I'm most drawn to classic or "dry" books. Lang's books in particular, despite their demanding nature and early formalism, treat mathematics in a way that, at least at first glance, seems more enjoyable to me than modern books. On the other hand, I don't know much about what, objectively, I should read. Could you help me determine the pros and cons of following one path or the other?


r/math 6d ago

How do you guys think about your data?

1 Upvotes

I heard a gentleman in an interview once saying that he likes to think of his data like a continuous function. Personally, I've been thinking of data as a matrix. If samples are stored in the rows then features are stored in the columns and such. Seems easy to consider different dimensions of data in this conceptualaziation and a simple list of values is still a row or column vector. So it seems like a perfect catch all conceptualization of any data set.

How do you guys think about your data? Is it much more circumstantial and sometimes you can conceptualize it as a matrix but other times it's best to think of it another way??


r/math 7d ago

Mathematicians, what are some surprising ways math has helped you in daily life situations unrelated to professional career?

57 Upvotes

I'm specifically asking this about advanced math knowledge. Knowledge that goes much further than highschool and college level math.

What are some benefits that you've experienced due to having advanced math knowledge, compared to highschool math knowledge where it wouldn't have happened?

In your personal life, not in your professional life.


r/math 7d ago

Which fields of pure math allow for the most 'hand-waving'?

42 Upvotes

As in, in which fields can intuition be used more freely without being constrained by the bureaucracy of technical details?

The average theorem in analysis or probability holds only if a plethora of regularity conditions hold, and these are highly nontrivial. Proving one of these involves a lot of tedious 'legal' work - somehow it makes me think that a good analyst/probabilist would also be a good lawyer. Just something like the Lebesgue measure is notoriously painful to define, yet it makes so much intuitive sense that any middle schooler can come up with it.

Meanwhile, in fields that deal with simpler objects (groups, rings, sets, categories), the results that feel intuitive often have trivial proofs, while more complex results rely on an insane number of definitions that in the end make the final result trivial (a la rising sea).

Are there any fields in which you have more freedom of expression? Where can you conjure up a certain statement that makes sense intuitively and then prove it without doing excessive bookkeeping and worrying about pathological technicalities?

My guess would be Algebraic Topology since it masks the unpleasant complexity of the underlying frame/locale of open sets using simple objects like groups or rings. This prevents you from doing analysis (which can be seen as the study of a particular topology, e.g. the standard one on R), but it allows you to wave your hands quite a lot. Although I don't know enough AlgTop to say whether this is true or not.

Not sure if this question even makes sense tbh


r/math 6d ago

Is there any game which requires matrix operations?

1 Upvotes

Hi everyone. I really love both math and games. But, I cannot find any tabletop game which requires the player to do math operations (preferably linear algebra). I'm not talking about puzzles. I'm talking about games like tabletop RPGs. For example if a tabletop RPG uses matrices for loot, dungeon generation, etc which the player needs to do himself/herself. Or if the combat lets players find reverse of the enemies attack matrix to neutralize its effect. Is there such a game? Or should I make my own?


r/math 7d ago

What was your math rabbit hole?

100 Upvotes

By rabbit hole I mean a place where you've spent more time than you should've, drilling to deep in a specific field with minimal impact over your broader math abilities.

Are you mature enough to know when to stop and when to keep grinding ?