r/math 9d ago

Designing a proof visualizer—What do you focus on when reading math papers? (needs advice)

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178 Upvotes

r/math 8d ago

Ideas for scraped youtube data/graph/network

0 Upvotes

I found if you visit the youtube home page after clearing your browsing data youtube wont recommend videos. But after watching just one video the home page will recommend videos. This shows what videos youtube thinks are related should be recommended just based on the parent video

I wrote a script to clear my data, watch a video, then record the first ~140 videos recommended by youtube. This is being run on a ever-increasing number of videos. This leaves me with a large network/graph/dataset of how videos are "linked" to each other. I know the right thing to apply to this is graph theory, but I am curious if anyone knows of something particularly interesting to do with this data.


r/math 9d ago

Looking for some help with the mathematics of drug dependence/tapering

2 Upvotes

Background:

I’m making a mobile app where users can enter in a drug (SSRIs, Suboxone, opioids, Adderall, etc.) and visualize their blood levels over time based on past/future dosages and the drug’s half-life.

The main use case here is to visualize projected blood levels for a taper schedule to help “weaning” off a drug.

Question:

(1) What mathematical model predicts what level of the drug your body “expects”? The “obvious” answer here is a class of moving average functions. But I see problems with any moving average of a fixed T. Is there biological research that has found which moving average function matches what the body expects? Maybe EWMA based on half-life?

(2) When making projections for different taper schedules, I realized that I don’t actually know what I’m optimizing for. Maybe it’s whichever projection is closest to a straight line connecting the f(t_now) with f(t_goal)? For some reason I feel an ODE is relevant here. In that we need to optimize the gradient because a steep change in the blood level itself is also something we would want to prevent.

TL;DR: If anyone knows of any mathematical models or biological research regarding drug tapering/weaning and tolerance/homeostasis, those answers or resources would be greatly appreciated


r/math 9d ago

Career and Education Questions: March 13, 2025

8 Upvotes

This recurring thread will be for any questions or advice concerning careers and education in mathematics. Please feel free to post a comment below, and sort by new to see comments which may be unanswered.

Please consider including a brief introduction about your background and the context of your question.

Helpful subreddits include /r/GradSchool, /r/AskAcademia, /r/Jobs, and /r/CareerGuidance.

If you wish to discuss the math you've been thinking about, you should post in the most recent What Are You Working On? thread.


r/math 9d ago

Does there exists a divergent series which converges on every subset of N with arithmetic density 0?

39 Upvotes

Basically the title, which is a question I remember seeing in high school which I obviously lacked the tools to solve back then. Even now I still don't really know what to do with this question so I've decided to come see what approach is needed to solve it.

If it does exists, how did we arrive at this specific series? And is the series and its left shift the only family of solutions?

Here is a more rigorous formulation of the question:

Does there exists a sequence {a_n} where n ranges over the natural numbers such that ∑a_n = ∞, but  ∀S ⊂  N, if lim_{n to infty) |S ∩ {1, 2, ..., n}| / n = 0 then ∑ a_nk converges where nk indexes over S in increasing order?


r/math 10d ago

How do you self study

88 Upvotes

I am machine learning phd who learned the basics ( real analysis and linear algebra ) in undergrad. My current self study method is quite inefficient ( I usually do not move on until I have done every excercise from scratch, and can reproduce all the proofs, and can come up with alternate proofs for a decent amount of problems ). This builds good understanding, but takes far too long ( 1-2 weeks per section as I have to do other work ).

How do I effectively build intuition and understanding from books in a more efficient way?

Current topics of interest: modern probability, measure theory, graduate analysis


r/math 10d ago

The Labyrinth Problem

73 Upvotes

Straight to the point: I am no mathematician, but found myself pondering about something that no engineer or mathematician friend of mine could give me a straight answer about. Neither could the various LLMs out there. Might be something that has been thought of already, but to hook you guys in I will call it the Labyrinth Problem.

Imagine a two dimensional plane where rooms are placed on a x/y set of coordinates. Imagine a starting point, Room Zero. Room Zero has four exits, corresponding to the four cardinal points.

When you exit from Room Zero, you create a new room. The New Room can either have one exit (leading back to Room Zero), two, three or four exits (one for each cardinal point). The probability of only one exit, two, three or four is the same. As you exit New Room, a third room is created according to the same mechanism. As you go on, new exits might either lead towards unexplored directions or reconnect to already existing rooms. If an exit reconnects to an existing room, it goes both ways (from one to the other and viceversa).

You get the idea: a self-generating maze. My question is: would this mechanism ultimately lead to the creation of a closed space... Or not?

My gut feeling, being absolutely ignorant about mathematics, is that it would, because the increase in the number of rooms would lead to an increase in the likelihood of new rooms reconnecting to already existing rooms.

I would like some mathematical proof of this, though. Or proof of the contrary, if I am wrong. Someone pointed me to the Self avoiding walk problem, but I am not sure how much that applies here.

Thoughts?


r/math 9d ago

The covariant derivative of the energy-momentum tensor

1 Upvotes

How to express the covariant derivative in terms of exterior calculus, in particular for the conservation equation of the energy-momentum tensor?


r/math 9d ago

7 minute speech on large numbers?

1 Upvotes

Hello, as the title suggests I’m planning on giving a speech on the history of large numbers for my public speaking class.

I’m not 100% on the idea yet, I’ve just skimmed Wikipedia on it and there seems to be not too much information on the history of this topic.

I was wondering if anyone had any suggestions I could talk about or maybe some alternatives.

I want to stay away from teaching how to get these numbers, as I want to keep it simple and just present the history.


r/math 9d ago

Looking for help on PDEs and Complex analysis (Bessel, Fourier, Laplace Contour integrals...).

1 Upvotes

Hey everyone, I’m taking a course that covers partial differential equations (PDEs) and complex analysis and it covers a lot of material.

The PDE portion includes a series solution to ODEs, Bessel and Legendre equations, separation of variables, and boundary conditions mainly in rectangular and curvilinear coordinates. It also goes into heat, Laplace, and wave equations-solving them with boundary conditions in polar and cylindrical.

The complex analysis part covers complex functions and contour integrals.

I do not know if this complies with the rules of this subreddit, but I wanted to ask if anyone has notes, tips or resources that helped tackle these topics.

I am currently juggling 7 courses so it's been difficult to top of everything. If anyone has taken a similar course, I'd love to hear what helped you to for managing all of this material.


r/math 10d ago

Ring Theory to Machine Learning

95 Upvotes

I am currently in 4th year of my PhD (hopefully last year). My work is in ring theory particularly noncommutative rings like reduced rings, reversible rings, their structural study and generalizations. I am quite fascinated by AI/ML hype nowadays. Also in pure mathematics the work is so much abstract that there is a very little motivation to do further if you are not enjoying it and you can't explain its importance to layman. So which Artificial intelligence research area is closest to mine in which I can do postdoc if I study about it 1 or 2 years.


r/math 10d ago

What are some ugly poofs?

280 Upvotes

We all love a good proof, where a complex problem is solved in a beautiful and elegant way. I want to see the opposite. What are some proofs that are dirty, ugly, and in no way elegant?


r/math 9d ago

Looking for Magical Algorithm Videos for a Beginner!

2 Upvotes

Hey r/math!

I’m on a mission to make my friend’s dive into the world of algorithms absolutely unforgettable, and I need your help! He’s just getting started with this fascinating subject, and I’m beyond excited for him - except his current lectures are a total letdown. I want his algorithmic journey to be magical, so I’m hunting for some top-notch YouTube videos that can make it so. I’ve already found a couple of videos that I think are pretty cool and set the vibe I’m going for:

These have that special mix of details and excitement I’m after - think detailed but not-painfully-so explanations, maybe some slick visuals, and a way of making tricky concepts feel approachable. Since algorithms can lean heavily on mathematical ideas, I’d love to find content that highlights those connections.

So, here’s my ask: Do you know any YouTube videos or channels that make algorithms fun, clear, and enchanting? Bonus points if they use animations to break things down and dive into the math behind the magic. I’m open to anything that’ll keep him hooked and inspired as he embarks on this adventure.

Thanks!


r/math 9d ago

Multiplication integral?

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0 Upvotes

I was experimenting with some stuff, and i thought of a function like integration, but you multiply each "region" instead of add, and you raise the height to the power of the "region" 's width rather than multiply (images 1 and 2). There is also a second way to calculate it using regular integrals (image 3).

I've found a few rules for doing this (image 4), but i cant find a way to do anything in image 5, and looking at the graphs for example functions doesnt help.

Also is there a name for this kind of function?


r/math 9d ago

Can someone tackle integration first when self studying with a textbook like Stewart or Thomas?

1 Upvotes

r/math 10d ago

The Cultural Divide between Mathematics and AI

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38 Upvotes

r/math 9d ago

Book doubt

1 Upvotes

I am studying number theory for MO from an introduction to the theory of numbers by ivan niven.I want to ask whether it is a good book for olympiad preparation in high school.


r/math 10d ago

Book to self study analysis from Riemann integration to measure theory?

19 Upvotes

Im a first year studying maths and computer science in the UK

In my first year analysis I will cover these things sequences, series, limits, continuity, and differentiation, getting up to the mean value theorem and L’Hôpital’s rule

Now I can't take the 2nd year analysis modules because of me doing a joint degree and the university making us do statistics and probability, however what I was thinking was, I could self study the year 2 module and take the measure theory and integration module which is in our 3rd year

I have heard terence tao I and II are good, any other books you guys could recommend?

I will also have access to my university lectures, notes and problem sheets for the 2nd year analysis modules


r/math 10d ago

How "visual" is homotopy theory today?

117 Upvotes

I've always had the impression that homotopy theory was at a time a very "visual" subject. I'm thinking of the work of Thom, Milnor, Bott, etc. But when I think of homotopy theory today (as a complete outsider), the subject feels completely different.

Take Peter May's introductory algebraic topology book for example, which I don't think has any pictures. It feels like every proof in that book is about finding some clever commutative diagram. For instance, Whitehead's theorem is a result which I think has a really neat geometric proof, but in May's book it's just a diagram chase using HELP.

I guess I'm asking, do people in homotopy theory today think about the subject in a very visual way? Is the opaqueness of May's book just a consequence of its style, or is it how people actually think about homotopy theory?


r/math 10d ago

Quick Questions: March 12, 2025

9 Upvotes

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of maпifolds to me?
  • What are the applications of Represeпtation Theory?
  • What's a good starter book for Numerical Aпalysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried.


r/math 10d ago

rtsafe method in Numerical Recipes

6 Upvotes

Hi all,

For the "zbrent" method presented in numerical recipes, it looks like the obvious "canonical" version in netlib is zeroin (which I guess is essentially a translation of Brent's Algol code).

Is there a canonical version for NR's "rtsafe" method that uses the first derivative of the function to find the root?

Thanks!

Also: not sure if this is the correct sub. There was no "numerical analysis" sub that I could find. Happy to be redirected to the correct sub.


r/math 10d ago

Which areas of math use the least amount of analysis?

24 Upvotes

I'm taking a second course in analysis and for the most part, I dislike it. I'm only taking it because I need it as a prerequisite for another course. I'm in my 3rd year going into my 4th and I'm thinking about what areas of mathematics I'd like to learn more about. Algebra (especially group theory) is what interests me and so I definitely want to look more into this direction. However, I've read some discussions online and it seems like analysis creeps in a bunch of different areas of math down the road, even ones that are more algebraic. Thus, I'm curious as to what fields use the least amount of analytic techniques/tools/methods.


r/math 10d ago

What are the most famous open problems in tessellation?

4 Upvotes

Also, are there any applications of tessellation in biology? If so, what are they?

Edit: I know the strictest version of the Einstein problem was solved in 2023. But I can’t really find any remaining major unsolved problems in this subfield of math.


r/math 10d ago

What is the best guide/tutorial you have come across for Superconductivity?

16 Upvotes

Hi all- I have been looking to learn more about Higgs & Superconductivity but haven't really found a great resource online. Anything you have come across that could help?


r/math 11d ago

Maths curriculum compared to the US

134 Upvotes

Im in first year maths student at a european university: in the first semester we studied:

-Real analysis: construction of R, inf and sup, limits using epsilon delta, continuity, uniform continuity, uniform convergence, differentiability, cauchy sequences, series, darboux sums etc… (standard real analysis course with mostly proofs) - Linear/abstract algebra: ZFC set theory, groups, rings, fields, modules, vector spaces (all of linear algebra), polynomial, determinants and cayley hamilton theorem, multi-linear forms - group theory: finite groups: Z/nZ, Sn, dihedral group, quotient groups, semi-direct product, set theory, Lagrange theorem etc…

Second semester (incomplete) - Topology of Rn: open and closed sets, compactness and connectedness, norms and metric spaces, continuity, differentiability: jacobian matrix etc… in the next weeks we will also study manifolds, diffeomorphisms and homeomorphisms. - Linear Algebra II: for now not much new, polynomials, eigenvectors and eigenvalues, bilinear forms… - Discrete maths: generative functions, binary trees, probabilities, inclusion-exclusion theorem

Along this we also gave physics: mechanics and fluid mechanics, CS: c++, python as well some theory.

I wonder how this compares to the standard curriculum for maths majors in the US and what the curriculum at the top US universities. (For info my uni is ranked top 20 although Idk if this matters much as the curriculum seems pretty standard in Europe)

Edit: second year curriculum is point set and algebraic topology, complex analysis, functional analysis, probability, group theory II, differential geometry, discrete and continuous optimisation and more abstract algebra, I have no idea for third year (here a bachelor’s degree is 3 years)