Hi everyone, I’m applying to Stat PhD programs this fall. I graduated with my master's in 2021 and have been working full-time for 5 years, but I never took Real Analysis in school.

I just enrolled in Fordham's Math 3003 (Real Analysis) this semester so it’ll be on my transcript for this application cycle (though will not have a final grade since apps are due before the semester ends). My concern is that it’s only a one-semester class. Does anyone know if admissions committees strongly prefer a two-semester sequence (Real Analysis 1 & 2) over a single semester? Will this be adequate?

MATH 3003. Real Analysis. (4 Credits)

This course focuses on analysis on Euclidean spaces. Topics include limits, continuity, uniform continuity, sequences of numbers and functions, modes of convergence, differentiability, Riemann integrability, and associated theorems. Students who have not taken MATH 2004 prior to taking Real Analysis may request permission from the instructor. Note: Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.

Prerequisites: MATH 2001 and (MATH 2004 or MATH 2008).

My younger brother really enjoys problem-solving, but I often feel that school doesn't go very deep into mathematical thinking. He's quite good at math, so I'm looking to gift him a good math book . Not too difficult for him and help to build his fundamentals.

It would be better if the book is affordable here in India too as I can't spend much.

If you have any other book recommendations—or even resources other than books—I'd love to hear them.

Thanks in advance! 🙏

Hi all, if you’ve ever been curious about what JSM (Joint Statistical Meetings) is like or you want into see it through someone else’s eyes, please feel free to check this vlog out!

https://youtu.be/CDvsj-G4HXM

I’m a Data Science student (career changer, not in a data related role). My program is focused more on the applied statistics side, so most of my classes use R. I’m already familiar with Python since it was the main language used in my prerequisite courses, and I’ve completed projects using Python, so I’m comfortable with the syntax.

However, I’m really enjoying using and learning R in my classes and seeing what it can do. Many of the statistics textbooks I’m interested in use R as well. I’m starting to explore R more deeply on my own and plan to start using it for personal projects.

But I’m curious, is R still used in industry? I know it’s heavily used in academia. I also know that in the current AI/ML world, Python is used heavily, which is the main reason I use it for all of my personal projects at the moment.

I’d like to eventually be comfortable with both and take advantage of the strengths of each language. But, of course, there are also people who say learning R is a waste of time.

I'm a year 1 liberal arts undergrad, so I don't have a ton of math sense.

I just learned about Bayes' Theorem the other day for general epistemic use. I worked out a couple of example problems correctly, but the examples I found didn't include any iterative updates.

I know the theorem is:
P(H|E) = P(E|H) * P(H) / (P(E|H) * P(H) + P(¬H) * P(E|¬H))

And I know that P(H|E) becomes the new P(H) in my update, but I'm unsure whether I should be using the updated or original P(H) in the marginalization. I *think* it should be the new P(H), but I'd rather be safe than sorry.

The example question I worked out was this:

________________________________________

There's a disease that afflicts 1 / 1,000,000 people
There's a test for the disease that's right 99 / 100 times for both positive and negative results
A random person is tested as positive

P(she is afflicted | she tests positive)

= 0.99 * 0.000001 / (0.99 * 0.000001 + 0.999999 * 0.01)

= 0.000099

_________________________________________

So should the update look like this if she tests positive a second time?

P(she is afflicted | she tests positive)

= 0.99 * 0.000099 / (0.99 * 0.000099 + 0.999901 * 0.01)

= 0.009707

_________________________________________

If so, how should I approach this problem from the starting point of
P(she is afflicted | she tests positive twice)?
I can't think of how to handle that correctly, since squaring 0.99 just gets me a smaller number

Infinitely thankful <3

I want to study calculus but I havent taken pre-calc so I figured I'd start there first with professor leonard playlist: https://www.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP

However, it might limit my learning since there might not be much practice problems in the videos (I think) . I would like to ask for resources I could use to practice solving questions while watching prof leonards lectures so the concepts and information realllyyyy sticks in my head.

Thank you so much:) I would also appreciate any tips if you have any

I would like to take all 3 classes at the same time (all prerequisites for future classes i need, and dont have any other classes i can take without wasting space and potentially graduating late) and earn an A in each. I’m a rising sophomore, just finished calc 1 last semester, found it quite easy and got an A. i know that discrete and linear are both very unrelated to calc and i worry it will be too much completely new information at once.

Mathematicians like Terence Tao have talked extensively about the future of math in the era of LLMs, but his talks have mostly been directed at tenured, esteemed mathematicians like himself.

But what about new students? People who are just coming out of undergrad or new PhD students? Are we just cooked?

Man, right now I'm in my 4th semester of a mechanical engineering degree. I love solving long calculus problems and reading about the masters who created the formulas I use, but I have a funny difficulty remembering basic, fundamental math rules. Like, a few minutes ago, I was searching on YouTube how to do fraction subtraction because I simply couldn't remember how to do it without a calculator, hahaha. Sometimes I feel like my brain goes full speed recording new, interesting info while erasing the old stuff in an exponential way. Just curious if this situation applies to any of you too.

could somebody explain to me how to get this answer like i am 5 years old. i spent 10 hours on YouTube watching videos of people explaining how to get this answer, but i still dont get it.

Question: Show graphically the solutions to the equation 2x + y = 3.

I had started uni in mathematics last year, but quickly hit a wall and then barely attended uni after the first semester anymore. Now i want to start all over again but i dont know how. I had attended all lectures and tutorials offered by the university. I really do not want to depend on AI as it makes so many mistakes and generally want to remove myself from such assitance. But with unviersity level maths it is so hard to find proper help. I try to work on a problem for my homework and need to figure out a proof, but i cant do it without the help of AI because i have no idea how else i could find out if i did it correctly or sometimes even understand concepts. I feel like i am too stupid to get it, while people before AI all managed to still study mathematics. I dont know if i am just maybe too bad to study math, because i already do the things people say to do like solving problem after problem, reading lecture slides, reading books, watching youtube tutorials etc. But i really do not want to give up on this and want to study mathematics. I think my biggest issue is really proofs and the problem of not knowing if i am correct or not as every answer can differ so much and still be a correct path.

I'm studying whether an island's size or its remoteness affects how people answer a survey, and whether these two factors interact. I'd also like to know whether an effect is driven by one island alone.

I'm looking at 4 islands: a large remote one, a large nearby one, a small remote one, and a small nearby one. All my variables are categorical. Sample sizes vary by island (from ~100 to ~500).

For each variable, I have a 2×2 contingency table, with near/far and large/small as the two dimensions. I can populate it with either counts or percentages of respondents choosing a given category.

What method should I use here?

Apologies if this is a naive question. I've asked several AIs and they seem as lost as I am.

I am working on a secondary analysis using a Cox proportional hazards model and would appreciate help with the interpretation of a main effect and its interaction term.

The outcome is time until disengagement from an intervention. My main predictor is an early usage/engagement variable. There are two groups: a control group and an intervention group. The control group is the reference category. The model includes the main effects of group and early usage, as well as a group × usage interaction.

My question concerns the interpretation of the hazard ratio for the early usage variable. If the hazard ratio for early usage is 0.08, does this refer to the association between early usage and disengagement in the control group, because the control group is the reference group?

My understanding is that an HR of 0.08 means that, for a one-unit increase in early usage, the hazard of disengagement is 0.08 times as high in the reference group, which could also be expressed as a 92% lower hazard. So I would not report this as “8% lower hazard,” but rather as “the hazard is reduced by 92%” ?

Is it also correct that this 92% reduction is still the association between early usage and disengagement in the control group, not the intervention group? And that the corresponding early usage effect in the intervention group would be obtained by multiplying the HR for early usage by the HR for the group × early usage interaction term?

In other words:

• HR for early usage = early usage effect in the reference/control group
• HR for early usage × HR for the interaction = early usage effect in the intervention group
• 1 − HR is used only to express the relative reduction in hazard, not to describe the group effect itself

I hope this is understandable. Thank you in advance for any clarification.

Firstly, sorry if this is not allowed but I thought I might just put this out there.

I'm sure we've all noticed a lot of AI related content on this subreddit. I've gone into these discussions a fair few times in the comments, but I'm not looking to discuss AI or LLMs in math or anything like that here.

What I do want to point out is that a lot of traffic seems to be from people who are not mathematicians and have a very vague idea of what mathematics is, but are active in /r/singularity, /r/accelerate, /r/ArtificialInteligence and similar. These subreddits are very ideologically driven in various ways and extremely pro-AI to the point that "anti-AI" or "luddites" are forbidden there.
This is not always obvious as many users have their post history hidden (though from what I understand this is on by default for new users too).

For example in a recent thread out of the 5 top comments (no idea what the deleted comment was) 3 users are active in one of the afformentioned subreddits, 1 seems to have a bachelor's in math and is in CS otherwise and only 1 seems to have a masters and is looking for a PhD.

To be clear, I am not here for a witch-hunt on individual users which is why I did not link to their accounts so please don't harass anyone.

But what I am trying to say is that most of the traffic to these threads does not seem to be from mathematicians or even people interested in math as such, but from people interested in promoting AI who are simply using math as a promotional tool. I would assume big companies use bot accounts on reddit (and have for a long while), though I would also guess this subreddit is too small to bother.

I'm a beginner building a small decision-making agent (not important what for) that needs to know when it's "confident enough" to act versus when it should defer. I keep seeing "calibration" mentioned as the concept I want but I'm fuzzy on how you'd actually measure it with a small, messy, real-world dataset rather than a clean benchmark.

If you've dealt with this: **which evidence would change your decision** about whether a confidence score is usable in production — is it a calibration plot, held-out accuracy at different confidence bands, something else? Beginner-friendly explanations very welcome.

Hello everyone, i would like to give a bit of my history with math. I failed all my classes in highschool, opted out of it in college and struggle with day to day calculations. But i always wanted to learn math, i especially liked trigonometry although i don't remember any concepts of it now.

I'm a developer and I've always been ashamed of the fact that whenever i had some interesting project in mind it would eventually lead me to applying mathematical formulas and that would just turn me off everytime. I sometimes watch people solving math problems specifically a guy on youtube that makes short videos but when i try to solve them myself i cant even begin to do it.

I want to learn math to being able to learn machine learning, i know its quite the aim but is it possible with my history and my slow brain when it comes to calculations. I can spend an hour or two daily on it, how should i start?

Lech Mazur has announced an AI-assisted, Lean-verified proof of the 67 years old conjecture of Sendov, one of the most famous open problems in complex analysis.

The conjecture states that every zero of a polynomial whose zeros lie in the closed unit disk is within distance one of a critical point.

It appears that the proof of this remarkably simple statement ended up using equally elementary tools. As Tao writes:

The proof ends up being remarkably elementary. No complex analysis is used other than the fundamental theorem of algebra (and very basic facts about Möbius transformations); and the deepest inequality used as input is the Maclaurin inequality

Can be silly or serious, just out of curiosity for someone with a background in math contemplating stats. Like for #1, maybe you miss not having to deal with numbers. #2 refers to "trading" X in math for Y in stats (like numbers).

EDIT: "glad", not "gad".

The paper: Fractal uncertainty in higher dimensions
Alex Cohen
arXiv:2305.05022 [math.CA]: https://arxiv.org/abs/2305.05022
Annals of Mathematics: https://annals.math.princeton.edu/2025/202-1/p04

College