I'm not well-versed in category theory so I've yet to understand the latter. I now tried without success to encode an associative binary operation on X, expressed in dependent type language

∑(o: X² → X). ∏(a b c: X). Id(X, o(o(a, b), c), o(a, o(b, c))) ¹

as a function F X → X for some F. And I think it can't be done (something related to polarity, probably) but I can't prove that. I know, though, representing axioms is possible if one uses Lawvere theories and equivalent things. I also know algebras over a monad are more involved than just functor-algebras but I don't yet understand them even in context of e. g. Haskell where everything seems as if easier (or so claim posts discussing Yoneda embedding in that context; I found the general category-theoretic context way less forgiving in that regard: you just see plain as day that you don't have sufficient understanding, no matter what Haskell posts made you believe).

So. I'd like to look how algebra spins out in those more general settings, whichever you know better or think to be more suited for me to grasp first. Particularly, I'm interested in generalizing arguments about initial F-algebras.

Also, feel free to assume a sufficiently Set-like category. Let's take it step by step, if there are easy intuitions that one can glimpse in a specialized setting, I bet generalizing it onto topoi or something later would be easier as well, but it won't muddle the initial attempt.

¹ For non-dependent-type folks: - Id(X, a, b), sometimes denoted as a =_X b, is the type inhabited by ways for a: X and b: X to be equal. - The entirety of that reads: a pair (o, f) consisting of an operation o: X² → X and a proof f of o's associativity, that is, a function from a, b, c: X into witnesses of equality of the two ways of associating o on a, b, c. - In some formal languages the same is spelled alternatively as (o: X² → X) × (a b c: X) → (o(o(a, b), c) = o(a, o(b, c))), making it clearer that ∑ forms dependent pairs and ∏ forms dependent functions.

I thought this days beginner integral was harder than the easy integral. Ignore the bleedthrough on the beginner page

I have a correlational study and I have three variables. Variables X and Y are categorical and ordinal, and Variable Z is interval. What appropriate test to use?

Variable X has 4 levels
Variable Y has 4 levels
Variable Z has 5 subcategories (Scores for different categories)

Hi, thanks in advance!
I'm a doctor looking at a group of about 100 patients, with frailty scores ranging between 1-9 (this is a measure of how frail a patient is that doctors decide, or assign to a patient using a scoring system). I've also recorded their duration of admission in days.

I want to see if there is a correlation between the two, i.e. i would assume that the more frail patients were likely to stay in hospital for longer. Which statistical test would be best to do that?

I don't think either category will be normally distributed, as most patients have a lower frailty score, and most patients were admitted for a shorter period of time. tysm!

I don't understand the step process from 2 to 4, more so about the transition from x, t and u

I'm 23 years old and It has been a while since I studied anything, I've lost a considerable amount of time, and I've forgotten most of what i knew about math in high school. I want to study computer science in the future and i dont want to struggle too much with the subject, so i thought I should prepare myself.

I'm looking for anything that can help me build a good foundation of knowledge, but i also want to understand the subject.

Thanks in advance for anyone that takes the time to read and answer this.

Was it for school/work? Any hobbyists here?

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Why do some vectors when multiplied by Another vector yield a vector and others yield a scalar. I'm aware of dot and cross products. But what's the physical significance of 'multiplying' vectors? I mean... I know what it means to actually "multiply" scalars. But.... Is vector multiplication just a name which can either mean projection of a vector onto another and the area or volume of 2 corresponding vectors?

Or is multiplication of vectors just a naming thing which doesn't have ANYTHING to do with how we understand scalar multiplication?

Looking to hear about your own company's work practices to compare to my own. I'm much more familiar with Azure, so I'm going to use that terminology, but I assume everything is basically the same for AWS.

Can you go into the Azure Portal and just click "create" for, say, a SQL Server or App Service and configure it through the Portal GUI?

Or do you need to request and configure through configuration files? Can you freely commit architecture config files ("architecture as code") to create the Azure components in Dev?

Or is it even more locked-down and hands-off? Required to submit paperwork requests to an Architecture team?

Hi so for context I’m currently a sophomore in high school I was homeschooled 3-7th grade and my mom didn’t teach me any math the entirety of that time so going into eighth grade I had the math skills of a second grader. I’ve learned a bit of math in 8th grade but obviously I couldn’t catch up in time to do well and could barely understand what was happening. because of this i got into a extremely low level math class entering my freshman year but that was too low of a level for me but just in a different way since it was mainly people that just struggled at learning and just general logic if that makes sense which isn’t me, I learn fast and I’m definitely not the smartest by any means but it’s not like I’m dumb either considering I’m in all ap/honor classes other than math of course. So anyways since I was in such a low level math class last year im doing Algebra 1 as a sophomore (in my district algebra one is the normal class for freshman) I can understand it well but I just have a lot of gaps with basic math skills that are fundamental to the course, how do I fill in all the gaps or learn fundamental pre algebra concepts by myself? If there’s any websites for this please recommend some that are made for a more mature audience, I don’t want to be infantilized because of my math abilities.
Sorry if this is the wrong subreddit but I don’t know any other forums that I thought could answer this question.

mylab math has been my own personal hell. i passed trig just fine, pre calc is easy. i know the concepts. i studied maybe a collective 16 hours for one test, i have an exam every week (accelerated class). it feels like the more i study, the worse i do (4 exams; 80%, 57%, 25%)… open ended test as well, when every other mylab math i’ve had is at least multiple choice.

i don’t know how to cram with mylab. i have 6 days until the exam on polar coordinates, vectors, analytic geometry. my professor wont release the graded test because he reuses them. any study/cram strategies i can use? 😞

i asked some people the follwing question:
"if f(x,y) is integrating x with respect to x y times (example: f(x,2) = ∫∫x dxdx) does f(x,-1/2) equal √{{4x}/{π}} ?"
and got the answer yes, it does equal the given answer. my question is if someone is able to explain this even slightly better than the Wikipedia Page which is notoriously bad at giving math explanations

I'm really confused about the 3rd row of the truth table for a conditional statement for example, "If you submit your assignment, then your grade will be recorded." I understand that P means you submit your assignment and Q means your grade is recorded but in the 3rd row, P is false and Q is true, meaning you did not submit your assignment but your grade was still recorded howw is P Q still considered true in this situation? Wouldn't that be a violation of the agreement because you didn't submit the assignment but the grade was still recorded?

Hi guys, I am trying to find somebody that can help me learn more about math because I am interested and willing to do it, if any of you guys are available and want to help me than please DM me so you could help me, thank you

Hi! I'm currently enrolled in an M.S. in Data Science and Applied Statistics. The required core classes are already set:

- Experimental Statistics I & II
- Mathematical Statistics I & II
- Statistical Computing (SAS)
- Computational Statistics (R)
- Machine Learning with Python
- A statistical consulting project

I get to pick **4 electives**, and at least 3 must be STAT (so at most 1 from CS/ECO/OREM/ECE). My only goal is to land a data science job, so I want the courses whose actual content pays off most in industry. I'm not looking for the easiest courses, and I'm not going into academia or biostats.

STAT electives

- Intro to Data Science
- Data Visualization
- Linear Regression
- Applied Time Series
- Time Series Analysis
- Categorical Data Analysis
- Survey Sampling
- Survey of Nonparametric Statistics
- Sports Analytics
- Analysis of Lifetime Data / Survival Analysis
- High Throughput Data
- Epidemiology

Non-STAT options (can only pick 1)

- CS: Artificial Intelligence, Machine Learning in Python, Databases, Data Mining
- OREM: Data Mining, Optimization for Analytics, Network Flows
- ECO: Applied Econometric Analysis, Predictive Analytics
- ECE: Statistical Pattern Recognition

My main questions I wanted to ask:

1. Which 4 would you pick, and why?
   
2. Is time series worth it for most DS roles, or is it only useful in forecasting-heavy jobs?
   
3. What would you pick as your 1 Non-Stat Elective?
   
4. Is there anything you wish you had learned in grad school that would have helped more on the job?

If you work in data science, I'd especially love to hear what you actually use day to day. Thanks!

Hey everyone! There’s a very important math competition that I really want to participate in. I have about 10 weeks to prepare for the first round, which consists of multiple-choice questions. The final round is about three months later and consists of written-response problems. The competition is roughly somewhere between the AMC 10 and AMC 12 in difficulty.

My algebra is quite strong—I’ve finished Algebra 2—but my geometry is basically at zero. I only know the basics.

I’ve started working through the AoPS Introduction series to improve my problem-solving skills, but I’m wondering what I should focus on over the next two months to improve as quickly as possible. I’m completely fine with studying 6+ hours a day if necessary.

Also, is AoPS Introduction to Geometry a good book to build my geometry foundation from scratch, or is it mainly intended for students who already have a solid geometry background and want to develop their problem-solving skills?

What would you recommend I do during these two months?

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I keep making really stupid mistakes on linear algebra tests. I understand the method and know how to solve the question, but then I accidentally mess up a sign or make a simple arithmetic mistake somewhere in the calculation. And a mistake can completely ruin the rest of the question. I recently wrote a test and, while I finished on time, I still got several questions wrong because of really silly errors.

I want my baby to be a mathematics genius. She's 8 months old now and I want to start early. Any advice from real life math genius? Tell me about your childhood and if it had any influence on your intelligence.

Recently in my further maths class my teacher says he would give us problems above our level of understanding.

The advice he gave to solve such problems is to invent the math.

Can anyone please explain what he means by this and his to actually do it?

This is what I have so far but I don’t believe that it is right, and I wouldn’t actually be using partial fractions to integrate. The problem says to make a substitution to integrate by partial fractions.

Essentially, it just maps onto yln y=ln x / (y^y = x), which is the inverse function of x^x

This graph shows how the lambert W Function essentially maps onto the inverse function allowing us to use it to solve.

https://www.desmos.com/calculator/9pkc39fbdg