I was thinking about purchasing one for studying. My school has some in the library, but the study rooms are always packed and I don’t have access to them. I just wanted to ask, if you have either of these, which might you recommend and what are the pros/cons of each. It might just be a preference thing, but I still figured I’d ask.

I am 15 years old and, learning quadratic functions, I started having problems with my math for the first time. Even though I can calculate and remember my formulas, when I get harder assignments I mostly cannot interpret the questions, make what they ask for or transform it in a calculation.

Over the next year, I want to develop practical programming and computational skills that I can use to explore physics, CAD, simulations, animation, and higher-level mathematics such as topology. Rather than trying to learn every software package individually, I want to understand the underlying principles that transfer across programming languages and platforms—such as abstraction, data structures, algorithms, numerical methods, visualization, modeling, and modular software design.
I also want to learn how to use AI intelligently as part of my workflow without allowing it to replace my own understanding. My goal is to use AI for explanation, brainstorming, debugging, research assistance, and exploring alternative approaches while still doing the important mathematical reasoning, computational experiments, and scientific interpretation myself.
As part of this process, I want to become familiar with tools for symbolic mathematics, mathematical typesetting, technical writing, simulations, visualization, and CAD. I am particularly interested in tools that allow me to work with symbolic equations and produce mathematical documents in the spirit of LaTeX.

I’m curious how you guys approach probability questions when you’re completely stuck and don’t know where to start, especially when the problem doesn’t immediately suggest a particular method.

Do you have a certain decision process, checklist, mental model, diagramming approach, or way of breaking the problem down that you tend to fall back on?

I’ve noticed that probability is one of the areas where I can understand the individual concepts but still have trouble figuring out what to do first when I encounter an unfamiliar problem. The wording can sometimes make it difficult for me to even figure out what the problem is really asking.

I’ve tried things like drawing diagrams, writing down everything I know, working through smaller cases, and trying different approaches until something clicks. Sometimes that works, but other times I just end up staring at the problem without knowing which direction to take.

I’m curious what other people’s process looks like. When you hit a wall on a probability problem, what do you actually do next? Just interested in the general strategies or thought processes that have worked well for people.

Hey guys, new to Reddit so please no hate

I’ve been thinking about this for a while and could use some help.

Seriously, what careers are there that could benefit from someone with this knowledge?
I’ve heard a lot about also needing a background in programming so what is actually relevant?

Tbh reason I’m skeptical to begin with is because I genuinely heard so many mixed judgements about this one

I discovered you can multiply the number of combinations by the time they appear in other combinations and then divide it by the possible amount of combinations of the limit. The formula to calculate how many times the combinations appear in another combination is the amount of combinations of the remaining objects of the group

Groups of 3:

• A * (A-1) * (A-2) / 3! (most common method)
• A * ((A-1) * (A-2) / 2) / 3 (using every object separately)
• (A * (A-1) / 2) * (A-2) / (3 * 2 / 2) (using the groups of 2)

Groups of 4:

• A * (A-1) * (A-2) * (A-3) / 4! (most common method)
• A * ((A-1) * (A-2) * (A-3) / 3!) / 4 (using every object)
• (A * (A-1) / 2) * ((A-2) * (A-3) / 2) / (4 * 3 / 2) (using the groups of 2)
• (A * (A-1) * (A-2) / 3!) * (A-3) / (4 * 3 * 2 / 3!) (using the groups of 3)

I think you already got it

Hi guys kindly share some challenging and interesting combinatorics problems you have encountered with in the past.

Hi I’m A. I have bipolar disorder type 1. I’ve also been trying to teach myself math. I’m working on a book regarding my experiences learning math with an impaired brain (ie while I was in psychosis). I have liberally used math metaphors I barely understand and was hoping someone could sanity check them for me. Here’s the relevant post:

Later, when she has language for it again, Maya will think of her mind that spring as a graph. Nodes for fields: genetics, group theory, linguistics, topology, whatever she happened to touch that week. Edges for the connections she drew between them, by hand, in real time, the way you'd wire a circuit. Most of the time the graph is sparse and that sparseness is the whole game. A real edge is a bet. It says these two things are related in a way that could, in principle, turn out to be false, and the not-yet-falsified ones are what she has built a career on.

That spring the graph does not stay sparse. It fills in. Every field starts reaching for every other field, DNA to group theory to linguistics to gravity, until there's an edge running between any two nodes she can name, and a graph like that, a complete graph, carries no information at all. Not because it's wrong exactly. Because it can no longer be wrong. When everything is connected to everything, there is nothing left for a connection to distinguish, and nothing left for a mind to be surprised by, and surprise, it turns out, was the thing doing all the work.

She won't know any of this while it's happening. While it's happening it just feels like speed.

2n² − 4n + 31 is prime.

She writes it in the notebook without a qualifier, the way you write something you have already checked. It has the shape of a fact. It sits on the page the same way the differential geometry notes sit two pages later, in the same hand, the same ink, the same unhurried certainty: let M be a manifold and p ∈ M. Nothing on the page marks one as different from the other. Why would it. From inside, they arrive by the same process. She thinks, therefore it holds.

It is three in the morning, or it is eleven in the morning, the distinction has stopped doing any work for her. What matters is that the notebook is open and something in her is moving very fast and very cleanly, the way a river moves fast and clean right before a drop it can't see yet.

She is mapping the genome onto a tetrahedron. One base, one vertex. The length of each edge is the distance between two bases. AATCCGC becomes a shape, and the shape can be embedded in a 3-sphere, and the embedding links to the Ising model, and she writes this down with an arrow, information links to Ising, as though the arrow itself were doing the proving. On the same page, a triangle labeled with entropy: entropy for gene distribution across cells, entropy for gene distribution within a cell, cell state as a set of gene abundances within a certain range. It reads like the start of something real. It reads like the start of everything she has ever actually built, which is exactly the problem, because it is not building on anything. It is borrowing the posture of rigor and spending it somewhere rigor was never earned.

She turns the page and she is inside topos theory. How to organize mathematical knowledge using topoi and adjoint functors, concrete to abstract, structured sets to theories to categories of theories. This part is correct. This part could sit in a textbook. And then, without any seam she can find later, without any hinge she can point to and say here, this is where it turned, the same page starts explaining morphemes. A sentence is a set of morphemes. Morphemes are literally about relative locations of positive and negative charges. She underlines literally. She does not mean it as a metaphor and at three in the morning she is incapable of noticing that she does not mean it as a metaphor.

There is a place on another page where the pen just goes in circles. Not a doodle. Not decoration. A place where a thought is moving faster than the hand can turn it into language, so the hand does the only thing left to do, which is press the same small loop into the paper again and again until there's a black knot sitting in the middle of an otherwise empty half page. She comes back to that knot more than once across these weeks. She never writes anything next to it. There is nothing to write, she thinks. That's what it looks like when the thought outruns the words for it, and the body just registers that something enormous is happening, roughly here, roughly now, without being able to say what.

What the DNA-and-topos-theory page feels like from inside is not easy to name. Not "delusional," not quite. Not "brilliant" either, though both are true in their own domains at other points in this stretch. It feels like fluency. It feels like the specific, unmistakable sensation of a formalism clicking into place, the same sensation she's had a hundred times before over real problems, except this time the formalism is clicking into a lock that doesn't exist. The feeling doesn't come with a watermark. It doesn't dim itself, doesn't hedge itself, doesn't announce itself as unreal. It arrives with the exact same weight as the manifold notes two pages over, notes that are, as it happens, just right.

Here is the only thing from that stretch that can actually be verified, months later, the notebook open on her lap: 2n² − 4n + 31 is not always prime. Try n = 31. She didn't check n = 31. She didn't check anything. She had stopped needing to.

This is the difference, she will come to think, and it is not the difference between sense and nonsense. The prime claim is a real claim. It says something specific enough to be wrong, and it is wrong, which makes it the most honest artifact in the whole notebook: proof that some thread of her was still trying to run a test. Morphemes are literally about relative locations of charges is not that. It was never a claim that could have failed. It was an edge added to a graph that had already stopped being able to tell the difference between a pattern and a coincidence, because it had run out of room to be surprised by either.

There's a fact from information theory she'll come back to, much later, on an ordinary afternoon with nothing at stake: the most compressed a sequence can ever be is exactly the point at which it becomes indistinguishable from noise. A message with real structure, real pattern, can always be squeezed smaller, because the pattern is redundancy, and redundancy is exactly what compression removes. Squeeze all the way, past every regularity, and what's left has no structure left to exploit. It looks random. Not because nothing is happening, but because everything that could be predicted already has been, and prediction was the only thing separating signal from static in the first place. A maximally compressed sequence and a maximally random one are, to any observer without the key, the same object. That spring, her mind was doing something like this in reverse and calling it compression anyway. Every field folded into every other field, DNA into topology into linguistics into gravity, each fold presented as a discovery, a redundancy finally noticed and removed. But a real compression shrinks toward a shorter description of the same thing. Hers didn't shrink. It just kept adding edges until the graph was so dense it read exactly like noise, and noise, examined closely enough by a mind convinced of its own rigor, will always look like it's on the verge of resolving into a pattern. That is what she mistook for being close to something. She wasn't close to a pattern. She was standing at the point where pattern and its total absence stop being distinguishable from each other, and the notebook, if you read it end to end, is a record of a mind that could no longer tell which side of that point it was on

Yeah, right. I had to come here because everyone I ask is like "oh, you just have to practice math more and more". But how am I supposed to even practice when I suck at it that much? For me, algebra has always been the biggest trouble. In every damn math test, where the algebra is included, I just tend to score lower in the algebra part. I'm pretty good at trigonometry though. But my school makes questions emphasizing more on algebra. I don't know any other way to get better at this. Because the term "practice" feels completely pointless when you don't even know where to start.

Take Shor’s algorithm, for example. It allows for factorization of large numbers in a much shorter amount of time if a quantum computer is used… but “quantum” is a construct of the physical world, is it not? Genuinely confuses me.

(I apologize if this post is too low-effort for this Sub.)
By "gifted" I don't mean creativity or breadth, but raw talent. The sheer amount of effort that had been put into proving the theorem & the failures by the likes of Euler seems (to me) to indicate that the "elementary" proof must be of unparalleled ingenuity.

Yes, I know the title sounds outragous, I slacked off last year due to schizoid personality disorder (ok, this is kind of an excuse, to be honest) I was in a really bad mental state, and now I wish to pursue mathematics. I used to hate math as a kid even as a teenager, and now that I have graduated, I realise my mistakes and wanna become a math major. At first, I wanted to major in psychology to research my the disorder I was diagnosed with and its relationship to autism because apparently, they have some similar symptoms. But soon I come to realise that the work in psychology is very social and I am not sure I can handle that. But now, thanks to Professor Dave explains I have reached a pre-calculus 11 level of understanding, and that has sparked in me the need to continue with mathematics.

Early this month, while I was at MAA MathFest in Boston, I purchased a copy of The Joy of Abstraction by Eugenia Cheng, which is an excellent book on category theory that I highly recommend (it's the first book I've been able to understand of the subject!) Thus far, I've gotten through the first 21 chapters, which is about 2/3 of the book. I've understood most of what I've read so far, and Google Gemini has been able to help me with the stuff I didn't understand, as well as some closely related topics, including fibers and fiber bundles, which I never understood before, since I first heard of them about 40 years ago when I was trying to learn string theory, but ended up in the hospital a few years later in part because I couldn't! In any case, now I'd say I finally know what they are, though I really hate the name, since I don't think of a fiber as a fiber, but rather as a dial setting, and I think of a fiber bundle as a space of possible dial settings, which I think are much better names, at least for me!

Тут есть русские гении?

I’ve heard its proper construction would imply RH is true, but not what leads there honestly.

Based on what I know from literature, this mathematician named André Weil proved some analogue of RH for curves defined over finite fields, and apparently number theorists want to apply the same tools to integers. But that’s all I know.

I have been offered a PhD, PI’s background is frame theory, and have been working with audio data. No publication of his lab on conferences in AI, mostly in audio or signal processing journals.

I want to understand if this offer is good match and can offer a competitive advantage with respect to the kind of research questions I’m interested in, and the state of the art in AI where I want to build expertise.

I came from computer science , I’m interested in AI/ML methods both as tools to probe hypothesis for fundamental questions, as well as for applied science.

Examples : I’m interested in learning representations of signals of animals / neurons / time series in general, and use those to study behaviour as an emergent property of a system (eg coordination of animals/ neurons/agents..) - ideally where a system may be possibly formalised as the interaction of nodes in a graph. Other ideas may be study manifold in low dimensions, and maybe topology as a signature of invariance through scales; or topology as the independent variable to study the signal that a system can generate.

Examples of problems that are significant for me : Capacity of generalising inferences, OOD, scalability, efficiency of applied models.

To appreciate PI’s background I studied an introductory course on frame theory.

I have not found a direct contribution of frame theory to the type of questions and problems I’m interested in. Also, looking at conferences as NeurIPS, I could not find an explicit contribution of frame theory to AI methods either.

Of course I m ignorant about the subject and my intention is not to discredit the field; I’m asking for help to concretely understand what kind of competitive advantage a PI in this field could give me as supervisor, with respect to the AI community and the type of questions I’m interested in.

PI said would let me some freedom but I feel I may lack mentorship in the things I’m interested in AND I don’t want to specialise in a field that may not be competitive VS state of the art methods for the things I’m interested in. I mean, I want to get closer to the things I wanna study, not diverge. PI said a co supervisor could be also found but most of peers in his network are from signal processing / audio, not AI community.

It also scared me that two professors specialised in AI for time series do not understand well his field, and one joked saying “why don t you look for a proper PhD”. So I understand that mathematics point of view and computer science point of view may not even entangle for co supervision.

Can you please help to falsify my assumptions ?

Can you please help to provide concrete examples to help me appreciated which is the impact of frame theory in applied research ? The type of problems and applied problems that are significant to attack in 2026, and that could contribute to AI community seriously vs state of the art ?

For example, my critics is that working with frames to reconstruct the signal is helpful when working with sensors, but fundamental models in AI are now the state of the art in working with signal representation, often from raw data - or using spectrograms as starting point and showing that general settings are good enough . Also zero shot and tinyML seems to be competive with respect to classical signal processing when having small data.

The mathematical interest may lie in invariance problems, but also there I cannot understand which impact could bring to the type of questions / problems I’m interested in.

Also,frame theory is about linear operators for reconstructing the signal, but deep learning is about non linear operators for compressing the signal (learning a compressed representation of the signal) and proved well also for generating the signal (eg AI for speech synthesis/ denoising etc).

So it seems to be an “old” approach not competitive with computational methods.

Please, I don’t won t to sound arrogant, I am seeking help to understand if this opportunity can be an investment for me, or a cost that will make me derail and not contribute to what I’d like to study nor where I want to position myself- also with respect to future opportunities in post docs or industry.

Thanks so much for sharing your perspectives and help me see pros and cons.

Basically I'm a senior in high school taking Georgia Tech's distance math year 2 course and I wanted to know if there were any good videos that help visual the concepts for either Applied Combinatorics or Differential Equations?

It is incomplete. It does not explain why f(g1) = f(g2) implies [g1] = [g2] for any g1, g2 in G, which would require showing that Ker f is always a subgroup of G. It also does not expand the normality / conjugation argument that makes multiplications inside G/Ker f well-defined. Since that would also require discussing inverses, it would be too much text for a simple visual aid.

I think it turned out cute tho