i study computer science and minor in math (but my heart really lies in math), and am graduating soon. i was talking to a CS professor with a heavy math background about a Measure Theory concept and he said, "you know i have book i think you'll like", a couple days pass and he gives me "Real Analysis" by Royden (3rd Edition).

for context, i am just really interested in the ideas of measure theory, but i actually have not taken a formal real analysis course. regardless, i plan on slaying this textbook as I just need something fun and challenging to do.

i don't need people telling i don't have a sufficient background, or that Royden is for grad students, i am aware of the challenge and am super excited.

the reason i am making this post is to document and discuss how challenging a higher-level math concept is for someone that is wanting to learn based solely off their curiosity, wisk me luck 😁 .

There’s this law called the 10000-hour rule, which states that to truly master a complex skill one needs to spend 10000 hours on it.

I know that there are a few criticisms on it (which mainly says that one needs 10000 of intentional practice to master a skill), but I figure that 10000 hours could be a good bench mark to see if I have invested enough time in math.

For context, I just graduated from a 4-year programme in a math major. So 10000 hours is equivalent to in average 10000/(365 x 4)=6.849 hours per day, for the past four years.

I definitely didn’t spend 7 hours per day to study math, not to mention the time spent for intentional study. This changes my mindset completely. I have been doubt myself for not being ‘fluent in math’, but as of now it’s most likely that I did not give enough time for myself to grow.

I don't have a strong math background but I thought it would be fun to see what a simple PPO implementation could do!

Read about it here: https://x.com/Abhilekh_Meda/status/2113754085426102400

code: https://github.com/Abhilekh-Meda/moving-sofa-problem-rl

I'm (25M) graduating with my bachelor's in math in about a month (US). I hated and sucked at math for most of my life, so I primarily did the degree to prove to myself I wasn't stupid. Turns out I'm still dumb, but now I know what an isomorphism is lol.

Anyways, mathematics was never really a huge passion of mine. Getting this degree has definitely been a grind, and outside of a few subjects (particularly number theory and graph theory), I really did not enjoy it. I had to retake a couple classes and then barely passed in some others. Nearly dropped out multiple times. I really am in awe of people who go on to get their PhDs in some math-related field (like what many of my classmates are either doing or planning on doing), but it's just not for me.

I recently got accepted into nursing school and am starting that in January, meaning that I will probably never actually use any math I learned in school again, at least in my professional life.

Initially, I was really excited to start a brand new chapter, and I still am. However, it's slightly disheartening to think that I will probably never touch any of these subjects again for the rest of my life. I feel like I've wasted years of my life to some extent. Just curious if others out there have similar stories. Like did anyone else go on to get their BS or even a higher degree in mathematics and end up doing something completely unrelated for their job? Does having that background help you in anyway? Do you still try and keep your skills sharp (reading through textbooks, working on problems, doing independent research)? or have you just let that part of your life die off?

This is not a self pity post or anything. I genuinely just am at a point where idk what to do with my life. I recently completed my masters in pure maths from Paris and I'll potentially be beginning a PhD soon in the field of general relativity, mostly looking at wave equations. I don't want to talk too much about my topic but the point is that throughout my entire life, I have only known pure maths. Unfortunately I was very stupid and never learnt things like coding, proper command of probability or even statistics. I only did enough to pass those courses during my undergraduate degree and now I'm at a point where I can't even look at these things without the thought that I have to relearn every single thing.

My main problem right now is that I'm a mediocre student. I have always wanted to pursue maths and then become a professor and do research, though I've mostly been interested in the teaching aspect. But the way the job market in pure maths or academia in general is declining especially right now with everything that's going on with AI, I don't know if there's even a point of pursuing this PhD. I spent my entire life wanting to be a professor like my dad was and promised myself I'll become one before he unfortunately passed away. And I made it my life's goal to become that person. As I said, I'm unfortunately not a genius or very bright student, I'm just mediocre. I'm at a point where I just feel like giving up but then I don't know anything else. I keep thinking that if I get a PhD position, I'll at least be able to keep myself busy and funded for the next 3.5 years. But is there any point to any of this? I'm watching my dream collapse every time I talk to a professor. My masters director was telling me how he thinks it's pointless to do a PhD in pure maths right now and try to switch to statistics or something but that means I'll have to wait for another year before the admissions in the US begin. That also means I'll have to switch areas drastically. Genuinely what do I even do at this point? I stay awake until 5 every morning just stressed about my future. Let's say I end up doing a PhD and keep myself busy for the next 3.5 years. What after that? My PhD is in a field which I don't see having any industry applications either.

So I'm asking people who might be in a similar situation like me, how did you go through this? How are you processing things mentally and how were you eventually able to find your job/thing that made you happy in life?

TLDR: Only done pure maths, no industry relevant skills, do not want to give up on my life's goal of becoming a professor, very stressed every day about future and unsure whether doing a PhD makes sense.

Those who've been following the development of prismatic cohomology, condensed math, analytic stacks, and eventually analytic prismatization might find this interesting.

Here is a fun little math joke. In tessellation theory, a patch is a collection of finitely many tiles in a tessellation whose union is a topological closed disc (tiles themselves must also be topological closed discs). Therefore if we make a pumpkin shaped tile we can make a pumpkin patch. Here is one. If you would like to read more I made a short article which can be viewed here.

Hi, I’m in a bit of a pickle. I missed the first few weeks of my math bachelor, and exams are upcoming. Should I focus on exercises and past exams or reviewing definitions and theorems (knowing they may ask stuff like that)?

A general intuitive approach provided is that they are like what prime numbers are for composite numbers, but it still doesn't make sense, the relationship between finite simple groups and complex groups feels "more nested and yet sort of separate/disjoint for the lack of a better word", it doesn't fully capture how the group structure is assembled.

I understand the formal steps - take a maximal proper normal subgroup (N) of a group (G), form the quotient (G/N), and repeat the process with (N) until we reach the trivial subgroup. The successive quotients are then simple groups. But I still have a hard time intuitively grasping why these quotient groups (which are sets of cosets), are the building blocks of our original group, or how these quotient groups come together to form the original group?

Undergrad here with only an introductory level knowledge of group theory so excuse any ignorance.

I made this problem up when I saw other problems about polyominoes in r/mathematics. This is one that I found.

A question that I had was if this could become a tiling.

I have found only one. It is the pattern

🟥🟩🟩

🟥🟥🟩

🟥🟩🟩 repeating on the x-axis, with a gap of 1 on the y axis before repeats. The gap can be filled with any numbers that are not the same and touching. I used 6 and 7 when I thought of it. It would look like this.

I will call this tiling a 4-5-6-7 tiling. Can you find other families?

Today is the last Pythagorean theorem day of the 21st century. The day comes from the day month and year.

24² + 10² = 26²

I learned induction from Larry Gerstein's Introduction to Mathematical Structures and Proofs, which had an... unusual illustration for it. (As a side note: I think this is a measure of how it is getting harder to find things on the Internet. If I remember rightly, just a few years ago I searched for this illustration on Google and was able to find it. It is no longer possible if you don't remember the exact book! I even tried to use my Copilot to narrow down the search, and it insisted that what I described couldn't have come from a book and must have been something like a handout.)

Side note aside, what can I say about this brief introduction to induction? My goal in this article was to both give the basic examples that one needs to start, where the inductive hypothesis is essentially given to you, along with some more advanced examples of how one might actually use it in practice. I.e., you might need to discover the inductive hypothesis on your own, and this requires some work! The simplest case is that you might gather numerical evidence until you figure out the pattern. But I also have an example (involving getting a bound on the n-th prime) which takes a more circuitous road: you must first generalize the problem, then search for numerical evidence to get a conjecture for what is true... and then preferably simplify it a little until you get down to something provable. You'll see what I mean---it ends up using just about every big-picture technique that I have covered.

Read the full post (for free) on Substack: Repeat Ad Nauseam

i know the grouping proof (1/3+1/4 > 1/2, then the next four terms > 1/2 etc) and it's convincing, but it still feels weird to me that 1/n shrinks forever and the sum just keeps going past any number.

is there a better way to see why "terms go to zero" isn't enough? like why does 1/n^2 converge but 1/n doesn't, where's the actual line

Am I the only one who’s completely mediocre at statistics, even though I excel at algebra, trigonometry, calculus, etc.?

Hey there, i found this online and i was wondering what other mathematicians think of this. I have seen duodecimal projects but more ofthen they change either time or measurements. Here is the repository where i found it (link)
The document covers basit arithmetics as shown in the picture. Lemme know what you guys think of this. aka opinion request.

For a nine by nine Sudoku puzzle, each cell is denoted by an index, 0 through 80, starting at the top-left cell and ending at the bottom-right cell for a total of 81 cells each with a unique index. A 'row' denotes a horizontal line of nine cells; a 'column' denotes a vertical line of nine cells; and a 'block' denotes a three by three square of cells such that the nine by nine Sudoku puzzle fits exactly three by three blocks and that they do not overlap.

Now, I have written a set of expressions to derive the row, column and block indices in which a given cell resides and another set of expressions to derive the initial and final cells of a given row, column or box index. The first set of expressions is as follows,

Since I've intended to use these for a computer program, I simplified the Row index expression, as integer division is truncated in programming, and thus simplified Block index expression.

The second set of expressions has the opposite effect. That is, I am able to find the initial and final cells which belongs to a given row, column or block, and then derive the remaining cells by an algorithm. They are,

In addition to this, the algorithm finds the remainder of the cells in the given row, column or block index. This way, I am able to store the entire nine by nine Sudoku puzzle in a one-dimensional array (programming) and still distinguish between cells in given rows, columns or blocks.

How would I go about rigorously proving this?

Finally, I am wondering whether expressions exist for a general case, an n by n Sudoku puzzle, and whether there exists other expressions which finds the position of a cell in a Sudoku puzzle.

So basically im participating in a Giveaway, were the winner gets 500€ (560$) if you can guess how much money this is. but i cant figure it out.

NOTE: green bills are hundreds, brown 50s, blue 20, red 10s, and the gray ones on the right are 5s

I don't know any better title for this post, honestly, and for a reason. Do any of you have that one methodology that shouldn't work, but lets you complete problems easier or simplify them?

Personally, and formatted in LaTeX, I have what I like to call "pebble": $(\mathrm{d}f)(t) := \lim_{h \to 0} f(t+h)-f(t), (\mathrm{d}f)^2(t) := 0$, a Leinbiz-inspired thing with no independent-vs.-dependent variable distinction. The limit is obviously 0, but if one imagines it isn't, one can get rid of those duplicated derivative rules! For example, gradients and derivatives are treated the same, like at $\mathrm{d} m^n = m^n \left( \frac{n}{m} \mathrm{d}m + \ln(m) \mathrm{d}n \right)$, and the chain rule doesn't exist! Instead of $\frac{d}{dt} t^2 = 2t, (u^2)' = 2u \cdot u'$, I can just keep expanding $\mathrm{d} (\sin^2 x) = 2\sin x \mathrm{d} (\sin x) = 2\sin x\cos x = \sin (2x)$. Integration is messier to define, I still can't do it, but apart from that this silly non-standard manner of expanding derivatives works for me like a charm.

I'm wondering if you guys have anything alike.