Hi everyone,

I'm considering applying for master's programs in pure mathematics at good universities in Europe (excluding the UK), such as Bonn, Paris Saclay, ETH, EPFL, TUM, University of Vienna, etc. However, my bachelor's degree focused heavily on applied mathematics, statistics, and some physics.

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To summarise, I completed a bachelor's degree in statistics, with mathematics and physics as my minors. My coursework included calculus (including multivariable), linear algebra, differential equations, statistics, and physics (mechanics, optics, thermodynamics, quantum mechanics). And I am also dedicating my free time to self-studying extra math courses to further deepen my understanding of mathematics

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I understand the importance of researching specializations based on my interests, but as someone who recently discovered a passion for mathematics, I'm still exploring specific areas of focus. While I'm actively engaging in my studies and hope to identify my particular interests in the coming months, as an international student, I need to apply to universities soon and am seeking advice on transitioning from an applied mathematics background to pursuing pure mathematics master's programs in Europe.

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So i wanted to ask how feasible is it to transition from an applied mathematics background to studying pure mathematics at the graduate level? And Do top EU universities welcome applicants with applied mathematics backgrounds who want to pursue pure mathematics? Should I just apply for applied mathematics master's programs initially and then shift towards pure mathematics if possible?
I apologise if this is the wrong sub to post this query.

Hi, I am doing my master's in applied mathematics and looking forward to learn a programming language. In my bachelor's I have studied C and R at beginners level and during my master's I have been introduced to MATLAB, MAPEL and MATHEMATICA. Even though each one of these have their merits and flaws can you please suggest me what should I have command on. (For me MATLAB is more intuitive because of my experience with C. ) Also would you suggest me to learn PYTHON except these. Can you also suggest me some books which contains mathematics problem on these languages ( with solved examples will be good). Thanks for your help 🙂🙂

I’m planning a shift towards a Master’s in Applied Math and could use some guidance on strengthening my application for next fall.

Background:

• In mid-30s, got a Bachelor’s in Math over decades ago from a less recognized US college.
• My GPA was decent. Overall: 3.6; Major(Math): 3.8
• Won a regional math competition during senior year back in college
• Didn’t get around to doing any research tho
• Jumped straight into work post-college due to financial constraints, sidelining any plans for further education
• Had climbed to a management position over the years, but my roles have not been tech-oriented

The Plan: Now that I’m in a better spot financially, and I plan to apply Master in Applied Math for next fall. I aim to apply to top 10 or top 20 applied math graduate programs, considering schools in the US but also looking at Canada, UK or EU.

Need some guidance:

For the US: Considering my non-technical work experience and the time since I last engaged in serious math, I’m thinking of aiming for a high score on the GRE Math Subject Test (rather than the general GRE) to show I still got it. Is this a good approach, or are there other steps I should consider to strengthen my application for these top programs?

For Canada, UK or EU: With many top programs outside the US not requiring the GRE and considering my background, any advice on how I can make my application stand out?

I just found out about fractional calculus and this popped in my head, For example D^ε [f(x)] is it possible to do? Does It has a meaning

For example, 15 rounds up to 20, and not 10, even though it is exactly halfway between them.

From my (surface-level) Googling, and checking other subreddits, it appears to be a random rule, and just convention.

Are there are any other “random” rules in math?

I mean I just started with the book "Jay Cummings - Proofs - A Long Form Mathematics Textbook" and I am interested initially for learning proofs.

But I lack discipline which makes things harder for me. So what would be the best approach to study proofs and practice if you can site any extra references. These days I am able to focus so I just need some guidance so I don't really lose interest in it.

I can put 2-3 hours everyday to it but going in wrong direction would do not good. I have prerequisite knowledge about real analysis and stuff but not being able write proofs makes things harder for me.

formula for g(x) until k then f(x) is

((f(x)+g(x))/2)+(((g(x)-f(x))(|x-k|))/(2(x-k)))

this can be iterated to make any piecewise function desirable. This image shows a basic example of the formula.

Hello, I am in my mid 30s haven’t been in school for 15 years and now getting sick of what I do for a living and considering college. I’ve always been good at math and genuinely liked Math. But to get back into it I know I need to give myself a refresher and wondering what I should focus on. Any help or advice would be appreciated. Thank you

In application, I can apply the t-test, and I know that the t-distribution allows me to calculate the probability of the t-stat for a given degree of freedom.

My confusion comes from where does the t-distribution comes from intuitively. (The PDF and the proof are quite complicated.)

Can people confirm if this is a correct way to think about the t-distribution?

1. There exists a population from which we wish to sample n observations.
2. We take our first sample with n observation, then find the t-stat. Then you repeat the process.

3.This would lead to a distribution of T's and given you a representation of the t-distribution (pdf).

And is this other way correct?
For all samples of n size that meet the criteria to run a t-stat. When the t-stat is run, it will follow the t-dist with n-1 degrees of freedom. Then you can use those probabilities.

Where can I find questions very similar to AMC 12? I don't want to waste all of the AMC 12 questions

I have a question about the online math degree.

Here is the background story. I graduated 9 years ago. My major is secondary education in mathematics. Recently I am interested in getting a master degree in pure math. I did some research and knew that I need to cover a lot of credits for the bachelor's degree in pure math before I start the master's degree program.

Those credits needed to be covered is like starting over again to get a bachelor's degree in pure math as a freshman.

So I think why don't I just get a bachelor's degree in pure math. That will be much easier to think about what class I already took or I need to take.

Financially, I can do part time student only because I need to pay for the international student tuition fee. That can be expensive in some of the university in US. Also, I can do online class only because I work full time as a high school / community college teacher.

Could you guys give me any advise or suggestions for which university I should apply to?

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I’m currently reading Journey to the Edge of Reason – an insightful biography of Kurt Gödel. It’s a stellar example of situating someone within their era and the importance of broader cultural-intellectual-artistic currents shaping someone. For instance how the physicist Ernest Mach and artist Gustav Klimt both shaped the pre-war Vienna Gödel came of age in. Philosophy, art, modern languages, and not just math and science mattered to him. (And he was not unique in this regard. This was common to everyone of his class background) This has made me wonder how do people think mathematics and science fit within contemporary culture now. Is there still a cross-dialogue? Should there be?

How can I solve an equation of the third degree or higher that contains natural numbers (not coefficients of anything)? Without this number it is easy, but when I try to solve it, it is impossible to add it to the parentheses using the factorization method.

x^4 + 7x = 0 is eazy(it can be lonnger its just an example)

x(x^3 + 7) =0

x = 0

x = square -7

but if i got a normal number - like 1 of 3 and bot x or 3x so i cant solve it!

like x^4 + 7x + 2 = 0

how can i solve it?!

i know its sound stupied but i am 7 grade and i cant understand it.

I got a B.S. in Pure Mathematics from Florida State University four years ago, and I'm planning on applying to grad schools this fall (so starting Fall 2025 if accepted). I'm reasonably confident I can get some decent recommendation letters, and I did do an honors thesis in undergrad, though it was more of just a summary of what I read rather than producing any research. I'm trying to get into as good of a school as I can, given that my chances at academia will likely be slimmer than slim if I don't.

I got a 3.2 GPA in undergrad, which is low for some of these top universities, and I'm trying to figure out how to make the rest of my resume shine. That's where research comes in. Currently, I'm going through the basic graduate courses by carefully studying the textbooks used in those courses, and I intend to go deeper if I have time after that survey.

I was wondering though, after seeing that some people have REU experience, if it's possible to do something like that while not actually an undergrad anymore. I also have a job and need to keep it, so it would have to be part time. If that's possible, is it worth doing? I'd love to do some research, so if there's another way to find open research areas that might be accessible to me, that would help too.

Is it true that (2/1)(2/1)(4/3)(4/3)(6/5)(6/5)...=(2/3)(2/3)(4/5)(4/5)(6/7)(6/7)...? As there is the same amount of every digit on each side of the equation, I don't see any reason for it to not be the same. Yet the left is the product of numbers greater than 1 and the right is a product of numbers all less than 1 so how would they be equal? The problem is not due to the product not converging in general, as it is The Wallis Product which converges to π/2. Is it possible for a product to both diverge and converge just due to the rearangment? Shouldn't work like that. Also when taking log on both sides, the left is clearly positive and the right is negative so how can they be the same thing. Please help

I've only ever seen chaotic behaviour arise from iteration (like the logistic map and mandelbrot set) and was wondering if perhaps you could find it in a regular function or something else. Also, I was wondering if fractals could arise out of non iterative processes.

My differential equations professor is a very nice and smart old dude who has overall made the class very pleasant. The issue is, he's an applied mathematician, and he loooooves physics. We are extremely behind the other sections of the same class because we'll learn a concept then learn how it's applied to like 5 different physical relationships. I like physics too, but I don't want to spend entire lectures watching the derivation of Torricelli's law in a math class. We've literally done physics experiments in class. I like the class but feel like I won't be prepared for the math in E&M or classical mechanics. Should I tell him to try and speed up the class a bit or should I just prepare to self study on the rest of the class during the summer?

Let me preface this with the fact I’m a musician not a mathematician, so I’m not sure if this is a fairly obvious/easy question.

So, I am a drummer and I was interested in trying to find all possible combinations of 4 limbs in a certain space of time, let’s just say 1 bar of 4/4 in quavers (8 quavers in total).

My first logical step was to figure out how many possibilities there are for each singular 8th note. I have no idea how to find that with a formula, but I brute forced it and found: (where Left hand = L; Right hand = R; Left foot = H; Right foot = K)

1. (none)
2. L
3. R
4. H
5. K
6. LR
7. LH
8. LK
9. RH
10. RK
11. HK
12. LRH
13. LRK
14. LHK
15. RHK
16. LRHK

Here obviously order doesn’t matter, and you can’t have repetitions of any element.

(Side question: Is there a formula to calculate these possibilities? What if I wanted to calculate the possibilities where the right hand can now choose between 2 different drums? Or possibilities if I can accent (make louder) notes?)

But now my next step was to think of each possibility as single elements (1-16), then try to figure out how many ways you could choose these elements in a certain order and with repetitions. So in this case I’m trying to find how many ways 16 elements can go into 8 quavers. Each possibility would choose 8 of these 16 elements.

So I tried to figure this out, but it’s too huge for me to brute force, and I tried online to find a formula, but I have no idea which ones are applicable to this problem, there are so many different looking formulas online. And I have a concern which will affect the outcome if the formula doesn’t take this into account:

My concern is, in this case the order of elements will matter, but only the order of distinctly different elements. If there are 2 identical elements, their order doesn’t matter if they’re swapped around.

For example, if it’s a 3-note combination using the 16 elements:

if you swap the 1 and 2 around:

1 - 1 - 2 is different to 1 - 2 - 1

but if you swap two 1’s around:

1 - 1 - 2 is counted the same as 1 - 1 - 2

So, my main question is: Is there a formula to calculate all permutations of choosing X elements from a set of Y elements, which takes these things into account:

• You can have repetitions / choose the same element multiple times.
• The order of elements matters, but identical items’ order doesn’t matter.

Thanks!

The common “guesses” to solving differential equations involve linear combinations of exponential or complex exponentials, or solutions of the form x*e^x. It makes sense that these guesses are common because of the derivative, but i have little to no knowledge on how you would know to ‘guess’ a solution to a differential equation. Can anyone provide insight?

My son is a junior undergrad majoring in business at a top-tier US university. Alongside his business courses, he's excelled at advanced math (binary/binomial probability, matrix/linear algebra, multi variable calculus, etc). He got a perfect score on the math SAT and tutors kids in subjects from basic geometry through calc 3.

He sees his math abilities as a unique strength that sets him apart from other business students - and it's what he loves doing. He wants to find a career path that would take advantage of these skills. He's got some coding experience (Python, SQL, a few others), and great people skills.

He doesn't want to go the conventional route of most B-school students into finance or consulting. What other avenues do you think would be worth investigating?

Thank you all in advance!

https://preview.redd.it/1opwa9nre4tc1.png?width=3046&format=png&auto=webp&s=70599bc7290f37868ba705df045b4f1754661cb3

https://preview.redd.it/2h5uvszre4tc1.png?width=3046&format=png&auto=webp&s=b54543f66000246c34590f61a419b13c58f6ee99

It basically goes through each (x,y) position on an n by n grid with that double-sum and counts the ratio between number of points that are inside of biggest possible circle in that grid (by checking if the norm of the vector from the each point to the center of the grid is bigger or equal to the radius of the circle) and the total number of points and guesses pi based off of it. Since the grid has a size of n by n and is approximating pi based off of the ratio of the number points in the grid that are in the circle and the total number points in the grid, making n infinitely big gets to pi.

I had previously asked something similar here about this but now I am deciding between a data science or stats minor as a mathematics major. Between the two, which is in more demand as a skill and/or career?

During the COVID lockdown I started watching Numberphile and playing around with mathematics as a hobby. This was one of my coolest results and I thought I'd share it with you guys!

Hello!

I want to solve equations step by step, but I don't want to do it on paper and I don't want to do all the tedious rewriting and manual application of rules.

Something like where I can start with the equation

a/b = x/b where I then can select b, right-click and select "multiply on both sides".

Ideally I would be able to have multiple simultaneous equations that I can work on independently and then later combine for example when I have solved for x in one of them I could replace all occurrences of x in the other.

I have failed to find any software like this, all I find is, on the one end full-fledged equation solvers and on the other end fully-manual (LaTeX).

Another software I would expect to exist is one where I draw a picture using circles/rectangles, add knowns & unknown lengths to the image and then can select unknowns to get an equation for that variable.

It seems to me that such software should exist, what would it be called? Have any examples?
Both commercial and non-commercial software would work fine!

I have trying to self learn combinations and permutations. During theory I understand each and every thing but when going to do questions I don't understand how to approach it. I can decide whether this combination question or a permutations question. But can't find the approach.

I’m a junior American college student about to graduate from a t20 college with a finance and applied math double major. I only have a couple classes left to take for my applied math portion of the major and they should not be too bad besides numerical analysis. I have gotten almost all As in my applied math classes yet I do not actually know how to do any math it seems like I forget everything the second the final is over. I have taken through calc 3 yet could probably barely pass a calc one test right now. I have international friends who show me their local country’s college entrance math exams and I can only do a few of the problems. It really doesn’t matter to me too much since I’m going to a career using my finance degree but still can’t help but feel a bit stupid and also disappointed with the American education system for letting someone like me graduate with technically a math major from a top university despite me probably not even being able to get a 4 on a Calc AB AP test right now(which I never took in high school). Am I the only one or are there other fraudulent math majors out there lol?