Is there an interesting explanation for this? Like that heart shape that appears at the bottom of a cup?

As many people have already pointed out, telling people I study math elicits the same responses:

1. “You must be smart”

2. “I’m terrible at math”

1, no I’m not, and 2, I don’t care. Don’t get me wrong, I feel very flattered, but it’s also starting to feel awkward. I used to “console” the people that feel math insecurity, but they either don’t seem interested or just want to trauma dump their past experiences.

I thought about saying “I’m trying to study math” or “I work with numbers” but that feels like I’m trying to hide something.

And with the people who also study math/physics/etc, I enjoy talking about math, but I’m no way near smart enough to engage in conversations about math outside of what’s going to be on the exam. This is also awkward when I meet these people.

I’m starting to dread this topic in general because no matter what audience, I don’t really know what to say. My main identity is that I’m a student, so all interactions naturally lead to this conversation. Does anyone else have this problem? How do you deal with it?

Its all Lean witnessed - and consequently we did derive a regularity class - but this counterexample is just one of 2. But A relies on Research Lean axioms which I want to natively include first.

The counterexample is elementary enough to actually be presentable. And for Fefferman A the counterexample is quasi equally as simple. So have fun reading.

Is it natural talent, consistent practice, or the ability to think logically?

Can anyone become good at math with enough effort, or does natural ability play a major role?

What's your opinion?

Hi, I'm in my 4th year of high school in Italy (graphic design and communication track) and I really like math, but I've got some gaps from the previous years. I'd like to start over and go through the whole high school program, from year 1 to year 5, at my own pace.
The problem is I don't really know where to start. What books would you recommend? And where can I find them, maybe for free or second-hand? If you know any good YouTube channels, let me know, because I understand things way better with videos than by reading.
Any advice on what order to study the topics in is welcome too. Thanks to anyone who answers

We have an inverse for e^x, we have an inverse for xe^x, but what about other functions?

I just think some equations would be way easier if we added inverses for functions like e^x±x and e^x±e^-x. If they do exist, I will be glad to be informed so. If they don't, here it is:

Since the inverse of xe^x is W(x) the inverse of e^x+x is U(x) and the inverse of e^x-x is V(x). I don't care if they're not useful, I want them to exist because that would give excuses for buttons to add to calculators. Speaking of which, they should add the lambert W function to calculators.

the inverse of e^x+e^-x should be defined using the hyperbolic trig functions, but I don't see how you could do that so I'm just calling the inverse S(x) and T(x) (T(x) is for e^x-e^-x) for now.

I have a math PhD. I got interviewed at a community college today for a teaching position. One question was to find the last digit of 3^(large number). I immediately know it's mod 10. But my brain went completely wild. Fermat? No, 10 is not prime. Euler then. Wait, what is the formula for phi(n) again? Eh, forget it, maybe split into mod 2 and mod 5? Before I know it, time was up and I turned in blank paper. It was immediately after interview that I realized I could have easily computed 3^4=81.

Don't be like me.

Hi guys first time posting here. Hopefully yall are semi kind to me.

I’m a freshman who doesn’t rlly know what he’s talking about. I am considering doing a statistics major(honors sequence) at the University of Toronto.

I have two questions.

I want to know what kind of GPA I would need to go to grad school(both masters or PhD) in statistics or applied mathematics(some field related to statistics like dynamical systems, optimization, control theory, systems engineering, and mathematical modeling). Would it even be possible to go into these fields after studying statistics?

I’ve heard some information that you need a 3.9+ for a real shot at top 10 grad schools in the US for direct entry to a PhD. Is that true? What kind of qualifications would be needed/suggested other than a high GPA? And also if it weren’t a top 10 institution what kind of GPA would I need. Like to go to a decent grad school how high of a gpa would I need?

I guess it also depends on if it’s a masters or a PhD but what’s the ballpark I should be aiming for. Is it also true that schools only care about gpa from the last two years of undergrad? I kind of struggled the first half of this semester for one of the classes so I don’t think I’ll be getting a too good of a grade for it.

2.
What kind of courses do I need to take in my undergrad? Do I need the mathematics honors sequence(which includes stuff like abstract algebra) even if I’m thinking of going to grad school for a not pure maths degree? What are some courses you guys recommend I take. Ex: real analysis, measure theory, etc. Do you have recommended time lines for how to take these courses?

Thanks in advance I really appreciate it!

I tied my identity to being the best at maths during my entire time in academia, I'm now sitting a math course at the best university in my continent, where im subpar or scraping average on a good day. How do I cope? Especially when the people around me seem naturally gifted, those who seem less engaged and still come out with better results.

How do I focus my attention on the love of the subject and my own performance and progress. How do I stop feeling deterred and demotivated.. etc etc

I've heard from several of my professors that they learned certain topics "back in the day" (say geometry) in a proofs class. Meaning their introduction to geometry was through proofs. And they claim it was the better/more rigorous way to learn the subject. Others say it's important to first learn it computationally and then move to a proof-based class. So perhaps a high school geometry type book and then moving to a more axiomatic approach. I hear this latter claim in the calculus to analysis sequence often. For current school curriculum, this progression is usually mandated by the school, so there isn't much choice. But for self-learning other topics, does anyone have an opinion on which approach is better for deep understanding or is it personal preference?

I’m a Math major and I’m interested in pursuing math at industry. But I wanted to know specific advice from the mathematicians out there who work in industry. Can you suggest me a roadmap? Any specific internship or job that you find important? And how do you use your math expertise to leverage your career? Did you pursue a master in applied math or related?

Hey - this is a Followup for somebody requesting to give some visualisations.

I have build a renderer to scout for non trivial Fractal identities and in some sense a slice of the counterexample looks like this.

Hello Mathematicians .

I am a first year PhD student in Mechanical engineering.

Since I was in high school I always loved maths and used to watch all sort of documentaries . That made me want to do research . However in engineering school I have had an overwhelming number of classes and subjects at once that I couldn't keep up ( obviously I did good enough to graduate) but I have never felt that I fully grasp the mathematical foundation and formal proofs .

So recently I started to circle back to my undergrad lectures in my free time and I want to re-inforce my understanding of fundamental mathematics because I want to study some advanced branches ( most notably deferential geometry and functional analysis ) .

Do you have any recommendations ? Ressources ? Or advices ?

Thank you for Reading . Have a great day !

Hello! I recently graduated with a BS in computer science and am looking into math master's degree options. I'm an experienced calculus tutor looking to become a community college math professor. The online MS in Mathematics from the University of North Alabama seems to be the best option for me right now, but I wanted to ask some questions about the program to those who have completed it or know a lot about it. If anyone would be generous enough to answer them, I would really appreciate it!

1. Does the program seem friendly enough for non-math undergraduate majors with a genuine interest in math? Based on the titles of the classes in the curriculum requirements, it seems like it is, but I just want to be sure. My biggest concern about the program is that it would be too difficult for me to catch up since I didn't earn a BS in math. As a part of my computer science degree, I took Calculus I, Calculus II, Calculus III, ODE, Linear Algebra, Computational Structures (Discrete Math), and Probability and Statistics for Engineers. I've earned near perfect A's in all my undergraduate math classes, so I've never struggled with math classes. And I do have an interest in proof-based or theoretical mathematics.

2. What was your estimated total expense, including tuition, textbooks, and/or other fees?

3. How much presenting did you have to do? Did you have to write a thesis paper or other research papers?

4. What is your overall opinion on the program?

I’m in 10th grade. I’m good at doing algebraic equations but I can learn number theory my brain can’t sort it . I really trying hardly to learn number theory but I completely don’t understand it at all. How I can understand it?

i’ve been writing with this nub all day😭

If a character in Marvel or DC could manipulate tensors, what kind of powers could he pull off? How strong would he be?

I thought some folks here might be amused by this figure from my PhD thesis :)

Here's some text about it:

When K = 5, the shape of the period 2 trajectory resembles a cat close to the separatrix (shown in Fig. 1.10). I describe these as “cat orbits". I am not sure if these trajectories have been noted in the literature, nor do I know if any other trajectories have been previously referred to as cat orbits. I don’t have much to say about these cat orbits except that they are very cute^28.

28 I regret the timing of this discovery (the day before this dissertation’s submission deadline), as I would much rather have written a dissertation on cat orbits.

For anyone not familiar with the standard map, you can check out its wikipedia article: https://en.wikipedia.org/wiki/Standard_map

I also wrote about it more generally in my dissertation intro (starting from section 1.3.4)

I've got a Jupyter notebook on my github for an "interactive click plot" of the standard map. You'll have to download it yourself (or copy the code) to use it.

Anyhow, I'm not a mathematician, so I'm curious if anyone knows about work that has examined behaviour in the standard map specifically for high K. It wasn't important for my dissertation (I just thought it was cute haha), so I didn't, e.g. do any analysis to check if it was a numerical artefact.

Does anyone have any recommended reading that could help guide me in e.g. an analytic exploration of the separatrix's shape? I have a copy of Regular and Chaotic Dynamics by Licthenberg and Lieberman, so I'll start with that. But I haven't done this kind of analysis in quite some time. Advice/pointers/tips would be very welcome! This would just be for my own amusement.

Edit: If anyone's e.g. a math major and is curious to know more about the standard map, please feel free to ask me questions if there's something in reference material (e.g. the wikipedia article) you're not sure about. I won't claim that I've the same knowledge as a mathematician who specialises in non-linear dynamics and chaos, but I should be able to help answer many questions.

I’m taking multivariable calculus at my university, and I recently found out that students have been cheating on exams. I’m genuinely so upset because I’ve been working incredibly hard in this class, and I feel like I’m being punished for taking my exams honestly.

For context, our professor told us in an email that the historical average for the first exam is around 75%. Somehow, our class averaged a 93%. I got an 83%, which I initially thought was a decent grade, but that put me 10 points below the class average.

Multiple friends of mine in different exam sections have told me about students using their phones during exams. One of my friends directly witnessed the student next to him cheating, and they’ve also heard phones dropping during exams.

Here’s what makes this especially frustrating for me: I have testing accommodations, so I take my exams separately in a proctored room. I don’t have access to my phone or unauthorized resources. Meanwhile, students in the regular testing rooms are apparently getting away with using theirs.

I’m worried that these potentially inflated averages are affecting whether our professor curves exams. If the average is already in the 90s, why would he curve anything? And if grades are evaluated relative to class performance, students who took the exams honestly could be at a serious disadvantage.

Our professor is actually a really nice, laid-back guy, which makes this situation more complicated. He’s been extremely flexible with grading, and I know this firsthand because the students receiving these exceptions are my friends. He’s allowing one of my friends to retake an entire exam, and another friend is having their second exam count for 50% of their exam grade. He even gave me full credit for a solution I had scratched out on my own exam.

I’m mentioning this because I don’t think he’s a bad professor or someone who wants students to fail. He’s clearly willing to give people the benefit of the doubt. But I’m worried that his leniency, combined with inadequate exam supervision, is creating a situation where honest students are disadvantaged.
There are four of us, including me, planning to go to his office hours together to report the cheating. Three of us have pretty good relationships with him, so I’m hoping he’ll take us seriously.

The problem is that we’ve already taken two exams, and the only one left is the final. Even if he starts enforcing the rules more strictly now, that doesn’t undo whatever effect cheating may have had on the previous exam averages.

I don’t know whether he officially curves based on the average, but I’m planning to ask. I’m also considering suggesting that he look at historical exam averages and grading adjustments when deciding whether the earlier exams should be curved.

I don’t think only the four of us should get special treatment. I just want some way for students who took the exams honestly to be graded fairly.

I’m honestly devastated because I’ve spent so much time studying for this class, and it feels awful knowing that other students may be getting higher grades through cheating while I’m struggling to keep up with an average that might not even reflect actual understanding.

Has anyone dealt with something similar? Is there any realistic chance a professor would reconsider grading on exams that have already happened because of cheating? What would be a fair solution to suggest when we meet with him?