/r/mathematics

r/mathematics is a subreddit dedicated to focused questions and discussion concerning mathematics.

/r/mathematics is a subreddit dedicated to focused questions and discussion concerning mathematics. Submissions should state and outline problems or questions about a given field or link to an especially insightful article about a mathematical concept.

/r/mathematics is a moderated community. Please read the submission and comment rules before posting.

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**Please post:**

- Questions, problems and articles which promote discussion about mathematics. Articles must be accompanied by a comment designed to start discussion.

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- Requests for help with homework.
- Homework help
- Jokes, memes, images, infographics, videos or blogspam.

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/r/mathematics

2

Hi everyone, I'm going to college and I'm not good at math, All the time at school I didn't take this subject seriously, and now I'm suffering. I need advice or your personal experience of how you improved your math. thank you have a nice day!

2 Comments

2024/08/11

12:25 UTC

12:25 UTC

0

: currently pursuing statistics degree from a reputed institute in india (i'm in 1st year tho, so can be considered a newbie)

recently while searching for career options, i stumbled upon actuary but cfa as well (frm too, but i do get that it is niche qualification; so let's keep that aside for now)

i went through the study material for actuary exams of india (cs1,cm1,cm2 from iai to be specific) and i think (gut feeling) , i can clear 5( could be 6 but idk anything about buisness finance yet) papers till dec 2025 if i went for it

whereas i also found out about cfa about idk as much as i do for actuary yet, i will be eligible to write cfa level 1 next july, but it is costlier initially. i dont want to burden my parents so soon for exam which i'm unsure of passing for now, since there is so much new syllabus to be studied for cfa (because i come from engineering prep backround)

actuary papers are what i can afford with my stipend and concessions maybe due to the reputation of my college in india

what do i need to know before jumping into these types of certifications while managing college academics side by side ? my 1st priority is my college grade and then the rest. i'm trying to find the rest here. whatever you may know, please type it out. it'll be helpful. thank you :)

0 Comments

2024/08/11

06:33 UTC

06:33 UTC

6

H

5 Comments

2024/08/10

20:53 UTC

20:53 UTC

49

hi, im interested in studying math (pure but taking applied courses and econ minor) and I was wondering if I could actually get a job? or should I just go for engineering? help please!

28 Comments

2024/08/10

20:25 UTC

20:25 UTC

2

Hi everyone. I'm finishing up a master's degree in quantitative methods and would like to do a masters in applied mathematics with an emphasis on epidemiological modelling. I know when applying for graduate programs, it's best to reach out to professors who have similar research interests before you apply to the programs. My question is, does anyone know of any math biology research groups in North America or Europe that are looking for graduate students?

0 Comments

2024/08/10

12:14 UTC

12:14 UTC

2

I don't know anything about control theory, but I have ~2 years and desire to do something interesting in this field. Where should I start? Any suggestions are welcome.

1 Comment

2024/08/10

10:19 UTC

10:19 UTC

20

So i'm not a math person at all, but i'd like someone to explain to me like i'm stupid how this scenario doesn't make sense.

Say you're playing a game and there is a 1 in 14 chance to get an item from a set (say there's 35 pieces of this set) there are other drop tables with random stuff too idk if that's important or not. But say you looted the chest that can drop said item, 100 times and haven't got a single piece from that set. Isn't it more likely you will recieve a piece from that set the next time you loot the chest?

Or isn't it more likely that you will recieve more items from that set in your next say 50 times you loot the chest compared to someone looting it 50 times but started at 0 times looted? Chatgpt says the drop rate is still 1 out of 14 yeah but i've heard that with enough times looted then eventually it will even out to 1 out of 14 for every chest looted. And if that is the case then if you went 1,000,000 times looting the chest without getting a piece you'd say that's super unlikely? Then how is your chance of recieving a piece not dramatically increased on your 1,000,001 time looting the chest?

If i had to bet who would get more pieces within the next 100 chests looted, i'd put my money on the guy who hasn't recieved a single piece in 1,000,000 times looted than someone who is starting at 0 times looted. But apparently i'm wrong in thinking this way and that's gamblers fallacy?

Idk i'm so confused, please someone enlighten me.

12 Comments

2024/08/10

07:36 UTC

07:36 UTC

6

Can somebody help me understand why it is that if we have say 3 equations and 3 unknowns, and 2 of the equations can be combined to make the third equation in the set, that this then means we effectively only have two equations and not three and the third is “redundant”? I’m trying to understand this intuitively but also mathematically.

As a second side question: if we had 4 equations, would the same situation occur except we can not only have two equations that can make a third that’s in our set of equations, but we can have three equations that can make a fourth? I’m guessing we need to do this to be able to know how many “effective” equations we have versus variables to then know if it’s solvable right?

Thanks so much!

9 Comments

2024/08/10

07:33 UTC

07:33 UTC

79

I just want to read your perspective.

We have a lot of geniuses, people who do math for the majority of their lives. We have people who spent countless hours studying math. Yet those giants can’t solve some of the mind boggling math problems. It’s like a race where you are already behind because you started late. It’s like even if you study chess 24/7 you will never beat Magnus Carlsen because you started late. It’s like playing chess for nothing. It’s like doing math for nothing since the giants can’t solve those hard problems, an average Joe won’t be able to, 100% of the time.

Historically, only the giants are able to have a great impact in this particular endeavor or field of knowledge.

P.S. sorry for my bad writing, this is the best writing I can do to write what I want to say/ask. English is not my first language. Also, apologies if this post sounds discouraging, I just want to be realistic since Math is probably 90% genius/brain power and 10% luck.

32 Comments

2024/08/10

06:54 UTC

06:54 UTC

5

plz drop ur maths study routine, like the only resources for us is our textbooks and the questions r not hard enough for the exams. Also how do i just overall get better at maths, cuz like i be doing crazy amount of maths and still get a B. Im in yr 10 qld, and i do methods

6 Comments

2024/08/10

00:21 UTC

00:21 UTC

6

Hello everyone. I've been tutoring a 9th grader in math for several weeks. The tutoring center provides a curriculum, and we've started from multiplying whole numbers through material about fractions/mixed numbers, and now we're on decimals. Understandably, the student is extremely bored and unmotivated by the material. I would move her up to more advanced math if I could, but I've gone over her pretests with her for each of these sections, and it's clear she still needs more practice with this material.

As I see it, the root problem is that this student doesn't know why she should even care about math at all besides the fact that her school will punish her for not being good at it. To be fair it's a legitimate question. As a society we still haven't come up with an answer convincing enough to be effective at motivating the students we force to take math classes.

What do you guys think I should do here? I don't think I'll be able to convince her that learning math is worthwhile using my own personal motivation. For me, the moment I felt like I wanted to study math was in my senior year of working towards my bachelors in mathematics.

I was always naturally good at math in school despite not "getting" it. As an analogy, it's like how someone can be naturally good at basketball during elementary school and middle school despite not having a ghost of a chance of making it to the NBA. In middle school, I knew my natural mathematical ability would serve as a good building block for some sort of professional career. I had missed some pretty important developmental milestones I would have to work hard to make up for, which was a result of my own laziness. i.e. When I was 12 years old, I didn't do enough research about the educational opportunities available in my state, so I didn't realize I had missed the opportunity to enroll in the advanced math program which would've a necessary step to being competitive for a good college.

So when I was in 8th grade, I worked my ass off to get a lot of assignments done before they were even assigned. The idea was to convince my math teacher that by doing the assignments at my current rate, I could finish all of the class's material in two months and I would be able to move on to the next year early. The math teacher talked me out of it, saying it was a bad idea. Even though I was getting all the questions right, I wasn't good enough to move on. Plus, she explained the social isolation that comes with being the "little kid" in a class of students all a whole one year older than you.

So in high school, I tried to see if I could do some mathematical research, and my calculus teacher talked with one of her professor friends to see if that was possible for me to do, but she explained to me that there wasn't any math left that was simple enough for me to do with the meagre faculties of a high school student. So she let me borrow a textbook, and she explained that if I really thought I had what it took to want to do math, then self-learning that textbook should be a piece of cake for me if I was motivated enough. I failed though. I didn't have what it took to be self disciplined enough to read through that textbook on my own. I had to cheat by using outside sources such as Khan Academy and YouTube to understand the material. That way I was able to encounter 3Blue1Brown and Numberphile videos though, and those videos convinced me that math could be seen as interesting.

So next I found out that all of the great mathematicians were able to get started through competition math. So I tried to found a math club at my high school where the goal was to participate in the International Math Olympiad, but apparently I didn't do a good job because not only did all of the other students stop showing up, even the teacher who was supposed to chaperone stopped showing up to the meetings without telling me lol!

In college when I was pursuing my undergraduate degree in mathematics, I again tried to get my hands wet with some research. I spoke with a professor who again told me the same think as my high school teacher did, that people in undergrad aren't able to do research, but that people learn how to do research by self-studying from textbooks. The professor made an arrangement with me, where he gave me a recommendation for a textbook. If I came back to his office having completely read the book and doing all the exercises correctly, he would give me another textbook recommendation to do the same thing, and the cycle would continue. It was a very generous offer, but again I wasn't able to read the textbook. I didn't even start.

It didn't make sense to me what he said, since I knew that "undergraduate research" was technically a thing. I tried messaging the professor in charge of undergraduate research, hoping she might give me a different response. I emailed her multiple times and never got a response. I tried reading that professor's research paper, hoping that displaying an understanding of her research might just be enough to convince her I was taking mathematics seriously.

To help understand the research paper, I asked another professor what the definition of a tensor was (embarassing I know), and she gave me a textbook recommendation, telling me to work through chapters 1-10 of Dummit and Foote.

I only got up through the first 6 chapters or so, but I thought Group Theory was pretty neat, and at that moment I could see a bit of why someone would want to study math full time.

I thought about trying to go for a math PHD, but another PHD student talked me out of it. She said it was a bad idea given my background since I "fucked around in undergrad" too much. (i.e. not building up enough relationships with professors for letters of rec, which would have been the benefit of doing all the extra work of going through those textbooks. I only took two graduate level math classes, which wasn't a lot for grad school, especially since both were topics courses and the professors were unwilling to write letters of rec for those)

So that's why I don't feel like I would do a good job of motivating my current student. I tried to give her a more open ended and challenging questions. Here it is.

A biologist goes into the forest and captures 10 turtles and marks all of them with red paint. The next day the biologist comes back and captures 15 turtles, finding that 5 are marked with red paint. How many turtles are in the forest?

The student said there were 100 turtles. I asked why, and she said because it felt right. I tried to convince her that going just based off of feelings was the same thing as just guessing, but she wouldn't believe me. I showed her how you can get a more accurate estimate using the Lincoln-Petersen estimator, and she said that method made sense too, but that 100 was still a good estimate even if it's less accurate because this question doesn't have a right answer anyways. How should I respond to this?

4 Comments

2024/08/09

23:17 UTC

23:17 UTC

20

I keep seeing this formula pop up occasionally, but I cannot seem to find any evidence that such a formula is valid. How can this possibly work? Is there some sort of definite proof of this?

3 Comments

2024/08/09

20:45 UTC

20:45 UTC

8

Is it time for intuitionist to logic to get a new name? Virtually no one subscribed to intuitionism anymore, and its use in automated proving decidedly runs counter to the idea of intuitionism.

9 Comments

2024/08/09

20:45 UTC

20:45 UTC

2

If a polar curve is connected (ie after 2pi radians the value of f(θ) is the same as the value at 0 radians), is it possible for that curve to have 0 lines of symmetry?

1 Comment

2024/08/09

17:38 UTC

17:38 UTC

3

4 Comments

2024/08/09

12:52 UTC

12:52 UTC

0

Hey everyone,

I'm currently following Benedict Gross's lecture series on Abstract Algebra, which is based on Michael Artin's *Algebra* textbook. In the first lecture, Professor Gross assigns some reading and exercises, specifically:

**Read:**Section 1.1 and pages 38-42 from Artin**Solve:**Problems 1.1.7, 1.1.16, and 1.1.17

However, I'm using the 2nd edition of Artin's *Algebra*, and I'm running into a couple of issues:

**Exercises:**The problem numbers he mentioned (1.1.7, 1.1.16, 1.1.17) don’t seem to match up with anything in my edition.**Pages:**Pages 38-42 in the 2nd edition are in the middle of a section, which is confusing because Professor Gross suggests reading them as a standalone portion.

I'm beginning to think Professor Gross is using the 1st edition, which I don't have. Has anyone else encountered this issue? If so, how did you figure out which exercises from the 2nd edition correspond to the ones assigned in the 1st edition? Also, how can I determine the correct pages to read in the 2nd edition?

Any tips or insights would be greatly appreciated! Should I consider getting the 1st edition, or is there a workaround for this?

Thanks in advance!

4 Comments

2024/08/09

07:59 UTC

07:59 UTC

13

Basically, for functions f & g:

(fg)’=f’g+fg’ (fg)’’=f’’g+2f’g’+fg’’

I tested this out for orders 3 & 4 and it still works. The pattern is that essentially, the k-th derivative of f in the expansion of (fg)^[n] is analogous to x^k in the expansion of (x+y)^n.

I tested it out for (fgh)’ and (fgh)’’ and this even works for the trinomial expansion!

(fgh)’=f’gh+fg’h+fgh’ (fgh)’’=f’’gh+fg’’h+fgh’’+2f’g’h+2f’gh’+2fg’h’

My question is, why is does this relationship exist? And, as a side note, is it possible to map onto this problem the combinatorial argument for the values of binomial expansion coefficients? Essentially, what is the connection here.

8 Comments

2024/08/09

06:22 UTC

06:22 UTC

617

Saw this on a YouTube short. Upon solving it, I decided to make my own question from it and I’m wondering if anyone can provide the same or a different unique solution.

After you solve the question, assume the 2 in question (…b-c=2) can be any positive integer N.

Here’s the Q: Prove that for any value of positive integer N, the answer will always be the same.

177 Comments

2024/08/09

02:27 UTC

02:27 UTC

3

So I’ve been out of school for a couple years, what would be some free courses or websites or anything that I could get a refresher on math before I go and pay for a pre calculus or a statistics class?

1 Comment

2024/08/08

21:44 UTC

21:44 UTC

4

I am a masters student in (pure) math and was wondering if it is possible to get an internship is software engineering over the summer. The masters degree lasts 2 years, so I am referring to the summer after my first year. During my undergrad, I did a CS minor and took the following course: algorithms, operating systems, databases, networks, machine learning.

3 Comments

2024/08/08

17:56 UTC

17:56 UTC

2

Can anyone recommend books on probability theory and descriptive statistics. Preferably ones that actually go into detail, explaining concepts from scratch and don’t just list equations. Thanks in advance!

2 Comments

2024/08/08

17:55 UTC

17:55 UTC

90

People who graduated with a math degree and been in the work force for 3-5 years (excluding academia) , how much math content do you still remember from university and can you still solve those questions in the textbook, be it proving theorems in pure math or computation question in applied math?

30 Comments

2024/08/08

14:55 UTC

14:55 UTC

5

There's something that's very important to me (and mostly my distraught family, and autistic daughter) to work out involving something that happened when we were away.

I have a camera that records at 25 FPS.

I believe the vehicle in the video to cover its car length of 4.88m in 4 to 5FPS (and 5 is GENEROUS). Again, I'll get exact figures when I can later today or tomorrow by marking the roads and measuring accurately and changing the range in the software.

What sort of speed in MPH are we looking at here please? There was ZERO attempt to slow down, swerve, dodge, or otherwise mitigate speed so there are no other factors. The sun is behind the car so no issues with visibility, etc.

It's likely a very simple calc but I'm extremely jetlagged.

Secondary to this, the car weighs AT LEAST ~2,300kg un laden, but it did contain two passengers (it's a 64 plate car, in what looks like fairly poor condition) sop I think it's a 2015 car.

Human reaction time, and braking distance, with the calculated speed in MPH - what would we expect the stopping distance to be?

I am genuinely happy to give someone a small tip (if allowed) for working this out for me, even before I provide exact measurements.

Appreciate you all, many thanks.

7 Comments

2024/08/08

12:26 UTC

12:26 UTC

86

Hi everyone,

I thought I understood lhopital as rule - but then I saw a comment regarding the picture above that said that “if we know g’(x) goes to infinity, we don’t need to know f’(x) goes to infinity for the equality to hold”. Can somebody explain to me why we don’t need what this person calls “unnecessary info”?

Thanks so much!

29 Comments

2024/08/08

06:56 UTC

06:56 UTC

3

Hi! I'm trying to decide my schedule for next school year, and have been wondering what class would be better to take. For part of the scholar designation requirements, you need to take statistics or something equal to it. My school doesn't offer regular or honors statistics, just AP statistics. They also offer honors precalculus. I struggle a bit with math already, so I was wondering what class would be a bit easier to take.

7 Comments

2024/08/08

04:09 UTC

04:09 UTC

3

I asked ChatGPT to take the first 1000 digits of PI and subtract each digit, one from the next, to form a new sequence, then repeat that process on the new sequence, until we come to a sequence where all of the members of the sequence are the same. It took 996 iterations. This would imply (from my very long ago numerical analysis class), that a polynomial of the 996th degree would fit the curve of the first 1000 digits. If we kept going with higher digit counts, I'm assuming we'd keep seeing the order of the polynomial climb as well. Is there some study of this type of approach to PI?

4 Comments

2024/08/07

20:15 UTC

20:15 UTC

1

So I’m reading a book called “When Gödel Walked with Einstein” and wanted to get some opinions on a topic in the book. First, I’ll say I’ve always been fascinated by math but it just has never really clicked for me. Anyway, the question is: do you believe math to be a material part of our universe that is something that must be discovered? Or is it purely a human convention with no material status in our material universe? I think primes may be the easiest example I can come up with. Would an alien civilization understand our concept of prime numbers (or other mathematical concepts) as we do? I tend to think math is not a human abstraction but deeply ingrained in our universe that we unravel. I’d love some actual math brain input.

12 Comments

2024/08/07

19:26 UTC

19:26 UTC

11

Books I see are on philosophy of mathematics but I wanted to know about the mathematics of philosophy. Any suggestions?

9 Comments

2024/08/07

18:07 UTC

18:07 UTC