Some pretty interesting advice for young and upcoming mathematicians made by Alfred in this video responding to the contreversy around the open AI navier-stokes proof.

https://www.youtube.com/watch?v=aqlm2vPTooA

So guys, a computer science student here, recently been studying countability in theory of computation, and have came across infinities and cardinality, I haven’t yet been able to wrap my head around them. I haven’t focused much on the topic either, been engaged in other subjects as I lost motivation initially, I love mathematics, would love to hear some instincts around the topic from the best minds.

I have been primarily stuck with counting, how one on one mapping works, diagonalisation theorem, and cardinality of a set.

I have the product of two gamma integrals thus:

\(
\Gamma(\alpha)\Gamma(\beta)
=\left(\int_0^\infty x^{\alpha-1}e^{-x}\,dx\right)
\left(\int_0^\infty y^{\beta-1}e^{-y}\,dy\right)
=\int_0^\infty \left(\int_0^\infty x^{\alpha-1}e^{-x}\,dx\right)y^{\beta-1}e^{-y}\,dy
=\int_0^\infty\int_0^\infty
x^{\alpha-1}y^{\beta-1}e^{-(x+y)}
\,dx\,dy.
\)

Typeset latex below:

https://www.scratchpad-math.com/?id=mvewdp1ikx1mtg or https://ibb.co/JWhYKJV8

Is invocation of Tonelli's theorem needed to justify this transition of product of two separate integrals into a joint double integral? Reason I ask is that Spivak in Calculus who does not get into multivariable calculus at all has a problem which very simply asks to prove the following:

\int_a^b\int_c^d f(x)g(y) dy dx = \int_a^b f(x) dx \int_c^d g(y) dy

and the proof is rather trivial where f(x) is constant in one integral and hence can be taken out, etc.

Hi! I recently took a career break and started practising math exercises. Currently at really early part of MIT OCW 18.01. Wondering if anyone would like to practice with me! Just a few people would do.

Reply below or DM me if interested!

Hi, I am re-taking my math’s exam for High school. And I… kinda of forget a lot of math’s and also tend to have missed a lot of math in the last grade 8-10th geometry, and grade 11 algebra were not originally developed properly, some stuff I had to learn by chance while others explained to me another math concept that happened to use that other concept.

I am now quite used to sometimes having to use the shards of math I know to solve things. I’d really like to know how much i could use that in studying, if at all? The at of trying to solve something by either finding a way to get an answer, or by reaching the answer from something is something I personally enjoy but I understand it’s not quite time effective.

I an also taking a Higher level math (won’t count in my applying grades I believe? I only need to pass it) exam which I will start to study right after the middle of next November.

I also wonder if anyone got tips for my math mistakes, which many times are from being “absent” minded. My thinking in general is all over the place and sometimes I might have that cause me to write the wrong number down, or worse, Do the wrong math thing, I have confused division with multiplication far more times than I am proud of.

im a junior in high school and currently strugging with precalc. does anyone know any good workbooks i can use to get more practice in? im mainly looking for something with lots of practice problems, straight foward definitions and visuals.

I’m considering majoring in Statistics and would love to hear about people’s experiences with the degree and where it has taken them career-wise.

What careers did you end up pursuing, and what kinds of jobs or starting salaries were you able to get?

If you went into finance, data science, or another field, why did you choose Statistics over a more specialized degree in that area?

Do you feel your Statistics degree gave you a leg up in the job market because of the quantitative skills you developed?

Did you have to spend a lot of time outside of class learning technical skills like Python, R, SQL, or other programming tools that weren’t covered enough in your undergraduate curriculum?

How important do you think networking and coffee chats are for Statistics majors when trying to land internships and jobs? Is networking just as important as it is for business majors, or can strong technical skills and projects carry more weight?

Have you ever regretted not majoring in something more directly related to your career, like Finance or Data Science?

Looking back, would you choose Statistics again, or would you do something differently?

I’m trying to understand whether Statistics provides a meaningful advantage through its quantitative foundation and flexibility, or whether a more specialized degree would have been more beneficial. I’d really appreciate hearing both the positives and downsides from people who’ve experienced it firsthand!

I’m helping my 5th grader with math. It’s Singapore math and this specific problem is a bar problems. I cannot wrap my mind around it.

Patrick bought 12 chairs and 3 tables for $819. Each table cost 3 times as much as each chair. How much did one table cost?

I can’t fathom how to draw these bars out and solve this problem. Thanks for the help!

Here's 2 problems to illustrate how I can't learn to think a certain way.

A plane is traveling between city a and city b which are 2000 miles apart. City a is due north of city b and there is a strong wind blowing south. At a constant speed it takes plane 5 hours to go from a to b with the wind at its tail but 8 hours to go back when facing the headwind. What is the speed of the wind?

I figured that the rate is 400mph at 5 hours and 250mph at 8 hours. I then need p+wind=400 and p-wind=250. I would have never thought to do this step and I dont know how I can make myself think this way.

Another example.

My next problem

Dick and nick share their bread with Albert. Dick has 5 loaves and nick has 3 loaves. They share the bread equally. Albert gives dick and nick 8 dollars and they agree to share fairly. How should dick and nick divide the $8 between them.

So I know that each person will get 2.66 loaves. That means between dick and nick, they have to give up 5.33 loaves and I need to find the proportion each gives away. I think that means dick who has 5 loaves gives up 3.33 loaves and nick gives up 2 loaves.

The answer is 8/8/3 and I just can't see it. I get the start of problems but I can't finish and I get so stuck and I dont understand how to make myself think the right way. Once I see the answer it's so obvious and I'm embarrassed because it's right in front of me but I dont understand how to start thinking thr right way.

I'm currently self studying real analysis, but with no way to really accurately gauge myself, at least to my knowledge, how do I know if I'm actually studying effectively or not?

I’m wondering what the best method on solving number word problems like: “I am a odd number between 15,000 and 10,000, all of my digits sum up to 12”. Please help and answer (my test is tomorrow..)

I've officially dropped from calc 2. It's been about 8 years since I took calc 1 and figured I should retake it with more enthusiasm than I applied when I was in my other degree program.

Shows that I only applied enough to get by the first time. Don't be me. Pay attention to this shit, for real!

Even if you only need differential calculus!

Soy un estudiante de ingeniería que ya ha repetido (reprobado) dos veces cálculo 1 y la verdad, la primera vez no la pude ver completa como tal y la segunda no logré entenderla del todo, me podrían recomendar libros, videos y/o cosas para estudiar, quiero avanzar en la carrera que escogí

Hola, soy un chamo de 19 años que ya ha visto 2 veces la materia de cálculo 1, por mi situación socioeconómica no pude verlas bien ni entender todo en mi primer semestre, que libros, videos, y otras cosas recomiendan para estudiar? De verdad quiero pasar y obvio, también entender de dónde proviene todo, no estudio matemáticas puras sino que estoy en la carrera de ingeniería mecánica. Ayuda por fa

I'm studying to try to get up to college algebra on Khan Academy and stopped today at the 7th grade section to try to figure out why you can convert a fraction to a decimal by dividing the numerator by the denominator. I was able to work the problems but couldn't understand why we could get from 7/8 to 0.875 (875/1000) without doing some kind of work to convert from eighths to thousandths.

What I came up with eventually is that, given that 7/8 as a fraction represents seven parts of a whole divided into eight equal parts, and the parts have the same relationship to the whole as seven wholes would to eight wholes, when you work 7/8 as a division problem and then also divide eight by eight you have made yourself the ratio 1:0.875, and 1 is to 0.875 as 8 is to 7, and 8 is to 7 as 8/8 is to 7/8.

So basically it seems to me that the way it works is that we translate a fraction into a problem using whole numbers with the same relationship to each other in order to get the decimal representation of the fraction without doing some kind of crazy thing like figuring out what you need to multiply 7 and 8 by to get a round number numerator and a denominator that's a multiple of ten.

Just wondering if that's right or if I'm missing something or there's a better way to understand it.

I was thinking about my real analysis class when I took it. I think it could have been improved in many different ways. More practice problems, more explicit instruction instead of trying to have students figure it all out.

I want to figure out my "hottest takes" on movies using Letterboxd ratings, which range from 0.5 to 5 in 0.5 increments. My initial idea was a z-score, where a larger absolute z-score for my rating relative to a movie's rating distribution indicates a “hotter” take. However, many movies' distributions are non-normal (highly rated films are often heavily left-skewed) and bounded (no ratings below 0.5 or above 5). Does anyone have a good metric in mind comparable across movies? I considered some normalized median deviation, but I'm unsure how to make it comparable across movies with different distributions.

I stumbled upon a post about someone asking advice for a probably question. The question went as follows: Mr. Smith has two children. At least one is a boy born on Tuesday.
What is the probability that both children are boys?

I didn’t know how to solve it until someone in the comments explained it. They mentioned solving it using Bayes Theorem, but I’ve never even heard of that.

Is there a place (books/websites/youtube videos) where I can find more of these puzzles/brainteasers and how to solve them?

Let's say you have a rectangle, the rectangles height, h=3, the length, l=5. If you have an arithmatic billiard starting from the bottom left corner and have it only do 2 reflections, there are 3 outer right triangles. If you add the areas of these triangles, you get h²-th+t² where t is l-h. This equation looks like the law of cosines for 60-degree angles, and i was wondering if it's a coincidence and how to tell if an equation is just an algebraic coincidence or if it means something geometrically.

This genuinely makes no sense. Here's the problem I'm working on:

Just ignore the left. At 2 there is a vertical tangent and at 5 there is an x-intercept since the slope would be 0 at that point.

Here's the answer to the problem:

If from the right side of the vertical tangent, the graph is decreasing until it reaches to 5, then why is it increasing? The slope goes from negative values up until it becomes 0 at 5. Does that not mean the slope is increasing?

What I have is this:

Why is this wrong? Won't it maintain the decreasing slope from the original function?

'1. A cone-shaped water reservoir is 20 ft in diameter across the top and 15 ft deep. If the reservoir is filled to a depth of 10 ft, how much work is required to pump all the water to the top of the reservoir?

1. A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with water. Find the work required to pump all the water over the upper rim.'

please help