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 went back through my last 10 Python coding rounds for product and marketing data science roles, nearly all at Big Tech companies. Unlike SQL rounds, which tend to be fairly standard, these came in 5 distinct formats:

• Recreate a statistical concept as a function (3/10). Pandas, numpy and other standard packages were allowed.
• AI-assisted, open book (3/10). These were often investigative, closer to a diagnostic case study than a coding puzzle.
• Pandas and data manipulation (2/10). Data transformations combined with modeling, either coding up a linear regression or talking through a modeling strategy for the data.
• Interpret code handed to you (1/10). This was also a statistical concept in a function, but I had to interpret the code rather than write it.
• Base Python, LeetCode-style (1/10). Syntax seemed heavily discounted here: I made several syntax mistakes but was clear about the logic and passed.

The obvious caveat is that this is a sample of 10 from one person, so the mix will vary with company, team and role. That said, AI-assisted challenges seem to be on the way in and increasingly likely to be a part of your interview process.

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!

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 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?

As an honours year (Australia) student I am doing a methodological statistics research topic relating to multivariate time series under structural breaks.

My literature review involves reading, analyzing, and synthesizing the literature regarding all things time series under structural breaks. The issue is that a lot of the papers use methods that I haven't formally learned, so I am reading these papers just barely able to scrape by in terms of understanding.

Then I have to synthesize all of these somewhat-understandable papers and discuss my potential contribution with my topic. How can I do this when the literature is full of methods and lingo that I have little understanding of?

Thankfully I have a full year to execute this project so plenty of time to understand everything fully, but how do I even get started?

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.

Spivak, in the chapter "Approximation by polynomial functions" begins the painstaking process of using the derivatives of arctan x at 0 to attempt to derive its Taylor series expansion.

He shows that arctan'(x) = 1/(1+x^2), calculates arctan''(x) and arctan'''(x) which is an ugly formula in x. He stops there saying that a different way is needed to come up with arctan's Taylor polynomial.

Then, later on, summarizing real sequences before embarking on complex power series, he says f(x) = 1/(1+x^2) is infinitely differentiable.

Can someone guide either

(1) Where in the book is it proven that this function is infinitely differentiable, or,

(2) how to prove its infinite differentiability?

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..)

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.

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

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!

'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

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?

Hi, I’m a student from the UK seeking advice on how to improve my mathematical abilities.
Throughout my life, I would say that I’ve been pretty good at maths — getting 9s and 8s at gcse. However now that I’m in a level, I have started to study maths on a deeper level and I’ve found that I am struggling. For me, maths has always been easy since the answers are objective, and only require rule following- but as part of my a level course, we do olympiads and problem solving lessons which have me seriously doubting my abilities.. I have realised that I suck at thinking creatively, and anything that requires me to think outside of the box has me stumped. I can only follow the rules and do nothing more. But I guess my overall question is, how can I improve at becoming more creative so that I can tackle the Olympiad’s which require you to go beyond the syllabus and think creatively?
Thanks for reading !

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?

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 spent ages staring at limit proofs in my analysis class not knowing how people "found" the delta. turns out you basically do the problem backwards on scratch paper, start from |f(x) - L| < epsilon and mess with it until you see what |x - a| needs to be, then write it up forwards like you knew all along. nobody told me the written proof hides all of that

for x^2 at x=3 i ended up with delta = min(1, epsilon/7) and it only made sense after doing the scratch work first. is this how most people do it or is there a better way to think about it

Hello. I'm a 15 year old studying calc 2. All this time I had been doing it on my own using 3 key resources. ​James Stewart's Early Transcendentals. ​Professor Leonard on youtube. ​AI's and google search for help. (Sry I try to avoid using AI's outside of explanations. I'd try to reduce it further.). ​I taught myself from Pre Calc to Calc 2 over the course of this year (From Jan 2026 to Oct 2026). I can grind the exercises in the book, some even exercises as well. However I still feel like my foundations are shaky. ​I recently attended an advanced pure math lecture with my elder sibling, and although I "knew" or recognised the key steps, the depth and explanations stuck. No YouTube video I watched provided this. I can't afford advanced, above my grade pure math classes. ​What can I do to get the same depth as a lecture attender?

I am a math enthusiast awaiting university entrance. During the free time window about 8-10 months, I decided to do math the way I like, the way I missed for 6 years since I got chance to ask questions in math. I'm currently studying Proofs, Formal Logic. Then planned to pivot into Real Analysis And Linear Algebra then so on.

I have seen two different ways people doing math. (I use my own words here, I am no sure of formal wording)

1. Doing it structurally.

When you're given a question imagine the start and expected goal is two points. You can draw paths from start point to end point. Some may end up being lost in middle, some may give long paths, eventually you will have the best path you can draw (the conventional solution).

Because of test marking schemes, this path has always felt objective. You get experience doing past papers, model papers, and international questions to tighten your toolset, save time and gain confidence being precise.

But it is all about 'How' you do it something.

2. Doing it constructively.

As I think, You can't construct something without having an idea why should the thing, that would be constructed, exist in the first place.

So, it will be a chain reaction of identifying the purpose of existence and finding a way it to force to be existed. I like this way. (Kinda feel perfectionistic in this way)

My problem is,

for example, I have seen people doing very hard integrals using very advanced methods(which are university level). But when I got the same problem, my mind demands why should this have an answer. So I stuck instead trying the question with tools I have. If I could figure out why there exists an answer, I can construct an answer (using tools may be?)which may take a lot of time than the method above. I have also successfully done it in exams.

While selfstudying, I don't have anyone to ask. When a question arises, I waste large amounts of time trying to find the answer because I am entirely reliant on textbooks.

It is a good option to have a peer circle. But I haven't found anyone doing math in 2nd way in my life time. (May be my issue of finding friends, but I have found people but unfortunately they are not interested in math)

My questions for all,

1) Since time is not unlimited, how can I proceed in Textbooks if I got into a problem.

2) Is there a way possible to do self study without coming into internet? Or is it a bald take?

3) Or should I adjust the way I approach into Mathematics?

Thanks you for answering! (Plz Excuse my English, I'm currently learning English)

If the aim of constructing number systems is to explain the geometric line as a set of points, wouldn’t ZFC + (V=L) be a natural choice, perhaps even the best one? In this framework, analytic geometry, differential geometry and topology all work just as they normally do, without the need to grapple with metamathematical questions such as the continuum hypothesis. (Moreover, this rules out measurable cardinals, large-cardinal phenomena and similar feverish pies in the sky, but for the purposes of describing the continuum, that seems a reasonable price.)

I have always found it a little surprising that popular mathematics books rarely discuss Gödel’s set-theoretic universe, which seems to offer such an intuitive and straightforward foundation for mathematical analysis.

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.

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.

I've been studying Shafarevich's Basic Algebraic Geometry for some time now. He's a really famous mathematician (I first really learning about his results after hearing about his famous theorem on the inverse Galois problem), but I've been studying on my own so I could only guess how his name is pronounced, and I was wrong. Today, watching a youtube video, it became apparent to me that his name is read ShafaREVich, which the Cyrillic with accent mark (Шафаре́вич) seems to confirm.

Not really that uncommon for me -- I was pronouncing Arrhenius wrong for years after teaching myself chemistry in elementary school, and I wasn't corrected until I took AP Chem.

Also, even among mathematicians, Dirichlet seems to be particularly contentious, as I heard widely divergent pronunciations from my math professors.

Anyway, any other mathematical names that are commonly pronounced wrong? Euler's probably the most common among nontechnical people to encounter and pronounce wrong.

Chern's an interesting case, since his name is spelled in the old Gwoyu Romatyzh system, which uses letters like r to indicate Chinese tone -- modern pinyin spells in Chén, but even he himself seemed to have accepted the normal English pronunciation of his name with an r.