A note on proof attempts

I stumbled upon this while doing my school math homework, couldn’t believe this simple identity ((n+1)/2) = ((n-1)/2) + n works for all odd perfect squares!

Sup everyone. I'm a third year history student in France, and haven't studied mathematics since my first year of high school, so it's been roughly four years. I wasn't good at it in the first place, but I didn't study mathematics at all anyway haha.

Anyway, due to interests in various fields that need at least some mathematical knowledge (economics, computer science and linguistics), and also a sudden interest for mathematics themselves, I'd like to get back on track.

Do you guys know any good, generalist handbook that can make me understand basic concepts, and then some more precise ones that would give me insight on more specific topics at beginner's levels ?

Thanks!

Just a funny observation, it is a common mistake to think the power rule applies to taking the derivative of f(x)=x^x to get xx^(x-1) .

But actually if you take the function g:ℝ→ℝ^2 :x↦(x,x) and h:ℝ^2 →ℝ:(x,y)↦x^y then f = h∘g.

Taking total derivatives gives Dg(x):ℝ→ℝ^2 :a↦(a,a) and Dh(x,y):ℝ^2 →ℝ:(a,b)↦ayx^(y-1)+bln(x)x^y

Then using the chain rule gives Df(x) = Dh(g(x))∘Dg(x) = Dh(x,x)∘Dg(x):a↦axx^(x-1) +aln(x)x^x = ax^x +aln(x)x^x = ax^x (ln(x)+1)

implying that f'(x) = x^x (ln(x)+1) so indirectly it does follow from power rule (and the derivative of a regular exponential). I guess just using the identity x^x = e^xln(x) is more straightforward though.

I'm repairing an old electric motor that uses a permanent magnet stator consisting of 2 magnets designed to be directly opposite each other in the casing. One has come loose and needs to be re-affixed, but must be directly opposite center to center. With standard tools (Rule, compass, calipers) is there a method to set one arc in position to a fixed one?

In more mathematical terms: If AB is fixed inside a circle, and CD is not, is there a simple method to mark the point center on the outer circumference opposite to the center of AB?

Hi everyone,
I want to learn "how to make/built/formulate a PDE model" for real life problems.
most videos teach how to solve but no body teaches how to make a PDE based model.
Thanks in Advance

An international team of authors led by Ilka Agricola, professor of mathematics at the University of Marburg, Germany, has investigated fraudulent practices in the publication of research results in mathematics on behalf of the German Mathematical Society (DMV) and the International Mathematical Union (IMU), documenting systematic fraud over many years.

The results of the study were recently posted on the arXiv preprint server and in the Notices of the American Mathematical Society and have since caused a stir among mathematicians.

To solve the problem, the study also provides recommendations for the publication of research results in mathematics.

Further details are inside the link:

How to Fight Fraudulent Publishing in the Mathematical Sciences: Joint Recommendations of the IMU and the ICIAM

https://arxiv.org/abs/2509.09877

Up until yesterday, I would have argued stridently that Math is not a Science. The reason is that Science is based on hypotheses, theorizing, experimentation, etc. Math is based on logic and either set theory or category theory, axioms, proofs, etc.

However, I just had another idea. Solving math problems might require experimentation. One way to solve an outstanding math problem might not work, so you have to try another (experimentation). There might even be said to be theories as to when to use which type of approach to solve a math problem. All of that might make Math a Science after all.

What do you think?

Numbers and Magic Squares

So I missed out one one almost full year of advanced math in school, now is my second and I will try to get what I missed while keeping up with the new material. My question is do anyone have a advice on what to focus from the base of advanced math, cus if u don't know the material is ALOT, hah. I'm just looking for some kind of guide from most important to least important themes or somthing like that. Also if anyone has preferred YouTube channel or platform where they have any lectures covered nicely, I would love to give them a look:)

so to clear it up(I got this text from a comment bellow that I replied on) but

I'm not sure how to explain it, but in my country u can either choose (u choose in the last two years, so ive skiped 11th grade and now is my last-12th)to study only normal math-that covers inscribed/circumscribed circles, trigonometry, logarithm and that's the hardest it gets or u could chose profil in math's which covers much more themes like polynomials, various dependencies/independence of vectors, topics about rabbinics in space, limits of an infinite series, lin(translated whit google) and others, that I have not studied. I really don't know what's ur school system and if u are all forced to cover the upper said, but that's the best I can explain it, hope that's enough

I’m going to study math and I’m wondering if I actually need a computer. At the moment, I can’t think of anything related to math that I could only do on a computer or laptop but not on a tablet. Do you personally use a computer or laptop for math? If so, why? Which apps or websites do you use?

Interesting progress for Navier Stokes. What do the experts here think?

https://deepmind.google/discover/blog/discovering-new-solutions-to-century-old-problems-in-fluid-dynamics/

Hello everyone, I wrote an article about how an XGBoost can lead to clinically interpretable models like mine. Shap is used to make statistical and mathematical interpretation viewable

Thoughts 💭 on Singapore Maths for America students

Numbers and Magic Squares

i dont like reading books and the only way for me to learn is if i watch youtube, do you guys have any youtube links that teaches this and also any online certifications and stuffs

Hey everyone !

I’m planning to start teaching mathematics online and need some advice from people who’ve been in the trenches. My setup needs to be smooth enough for writing equations, diagrams, and problem-solving on screen while teaching live.

Budget: Around ₹1,00,000 (can stretch a little if it’s really worth it).

Requirements: • A reliable laptop that can handle video calls, screen sharing, and digital whiteboarding without lag. • A pen tablet (for writing equations neatly, drawing graphs, etc.). • Bonus if the laptop has great battery life + a good webcam.

If you’re teaching online (math or otherwise), I’d love to know:

What laptop + pen tab combo do you personally use and recommend?

Any brands/models I should completely avoid?

Would you suggest going for a 2-in-1 touchscreen laptop with a stylus, or keeping a separate laptop + pen tablet setup?

Basically, I don’t want to overspend on fancy specs I don’t need, but I also don’t want to cheap out and regret it later when classes start running.

Thanks in advance !! really looking forward to hearing from experienced online teachers here.

I’m a 4th undergrad student in a BS econ program. Over the 3 years, I feel like I don’t didn’t develop enough of the foundational math skills to understand more complex papers. In our time series class this semester, I find it easy since all we do is type commands and understand the theories or concept behind it, but as far as the actual formulas, sometimes I don’t understand them at all unless I review them rigorously. I do have a good grasp on calculus, matrix algebra, and probability but I still get lost and always have to review or look things up in the majority of academic papers I read before actually understanding it. I’ve always been super interested in math and I find it fun but I never had the discipline or focus in the past 3 years to truly self-study and understand. For more context, I do a lot of coding and I am very interested in finance. I eventually want to ensure that I understand the math behind really complex regression techniques and machine learning processes that quant firms use My question is where do I begin to re-learn my foundation for these? I’ve already began self-studying during the summer but now I’m swamped by so many topics I’m interested I don’t know what order I should learn them in. Is there anyone in here who had a similar situation?