A bit of a emotional talk rather than talking about theory. I never thought I would end up studying maths. I started uni in summer last year and there I met Real Analysis, and boy... just proofing things in general, I feel like I'm so bad at it, or at least not as good as I should be.
The worst part is I could technically graduate while being bad at Real Analysis, but it feels wrong: how could I call myself a mathematician if I struggle with the area of math that embodies proofing and the showing the "truth" of a statement? How could I call myself a mathematician if I struggle so much with the rigorousness? Not a little, but a lot.
I love the rigorousness because it makes me feel stable. Imagine the great things humans have been able to do just because 1+1 is always equal to 2. It's not up to God's attitude today, if he wakes up with the left foot and says "Today, I wanna make it so 1+1=3. *poof* Done!" No. 1+1 always equals 2. Always. And it's because of this "always" that we've came to construct great, useful and still rigorous ideas over 1+1=2.
But me struggling to what is probably the essence of math, at least in my eyes, makes me feel dirty. For context, maybe I want to pursue a carrer in quantitative finance, which means learning stochastic calculus, which seems an awesome branch from the little I've seem so far, but requires also having a good ability to proof things.
Even if someone with more experience in the field tells me that not that much mastery in proofing is necessary, I still feel like a fraud if I never get satisfied with my ability to proof things.
Finally, I feel like, to cope with this situation, I'm starting to value the usefulness of math over its rigorousness.
Ok, maybe to spark discussion: in your stage in life now, do you feel satisfied with your ability to proof things? If you consider yourself not good at proofing rigorously stuff, does it bother you or it isn't important to you? I'm just a naive math student wanting to explore others' perspectives. Thanks for your time. :)
Warning: Many Mathematical terms being used in this post. Fun-to-play player discretion is advised
Have you ever wondered why when you state something about a card and the amazing possibilities it can get, you get criticized by someone else who said that the possibilities are not consistent enough and the card isn't good? Well, it turns out there are way more into that, and that player saying your combos are not consistent, he didn't say that out of nowhere. There's a whole algorithm around this, in any card game out there, to find out the odds for everything.
I know, so many players just don't want to hear about competitive plays, because they just want to play for fun, and I am completely fine with that. But I want to tell you, if you're going to claim a card is good, at least back it up with the right statistics for the card, don't just list out the possibilities. I'll explain why in following paragraphs
Mathematical terms
Independence: Two or more events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the others (equivalently, does not affect the odds). Similarly, 2 or more random variables are independent if the realization of one does not affect the probability distribution of the other. We use this term to describe two scenario that doesn't affect each other, such as 2 different games of PvZ Heroes or 2 times the block meter roll.
Expected Value (EV): this is the term for the anticipated value for an investment at some point in the future. In Statistics and Probability analysis, the expected value is calculated by multiplying each of the possible independent outcomes by the likelihood each outcome will occur and then summing all of those values. By calculating expected values, investors can choose the scenario most likely to give the desired outcome.
Formula:
https://preview.redd.it/oxt4ayyq5v081.png?width=658&format=png&auto=webp&s=f4992d287635372c89f3c462750f46dc8583cd61
Best Outcome: or best case scenario, highroll, is the best value you can get from an investment at some point in the future. In Statistics and Probability analysis, it's the greatest result(s) you can get from one or multiple draws.
Variance: the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spre
... keep reading on reddit ➡Foreword:
Hey everyone, awhile ago I made a post on how to get into stochastic analysis. Since it was pretty well recieved, and people expressed interest in a similar guide for dynamical systems, I thought I'd write it up.
In contrast to stochastic analysis, dynamical systems is far less linear in the progression of topics. My friend once fondly described it as "the completionist's nightmare". As such it's hard to even pinpoint a "core reading" list for the subject, and not all prerequisites will be needed for all topics. So the guide will be divided into general reading and further topics, instead of core reading per se.
This is also more of a secondary interest of mine, so my knowledge of topics and the associated literature will not be as good as with stochastic analysis. As such, feel free to post up some other recommendations in the comments!
General prerequisites:
As stated in the foreword, not all prerequisites will be needed for all topics. I'll state briefly the required prerequisites for each topic as needed, but among the stuff that will come up are measure theory, functional analysis, general topology, differential geometry, differential topology, and a bit of algebraic topology.
General reading:
-
To get your feet wet with the subject, Brin and Stuck's Introduction to Dynamical Systems has a really nice selection of topics - covering stuff like topological dynamics, complex dynamics, ergodic theory, bifurcation theory, etc. A few words of warning though - their chapters on hyperbolic dynamics are borderline unreadable on a first go. Also there are quite many typos and the writing is pretty terse. Nevertheless it's still my favourite introduction to the field.
-
For a (much) more in depth general overview, you can't do much better than Katok Hasselblatt's Introduction to the Modern Theory of Dynamical Systems. I would recommend only using the first three parts - the last part on hyperbolic dynamics is rather messy, and other dedicated resources would better here. I'll mention them later in the topics section.
-
Finally, there is the monstrous four volume Handbook of Dynamical Systems. These consist of extremely comprehensive survey articles written by leading experts in their respective fields. I don't think anyone should, or would want to read these in full, so probably it's better to pinpoint a topic of interest and then
Official DD theme music: MEGA NRG MAN - BACK ON THE ROCKS and [Manuel - GAS GAS GAS] (https://www.youtube.com/watch?v=atuFSv2bLa8) and Ken Blast - The Top please listen to this as you read. Eurobeat music will give you Adderall like effects and help you read/comprehend this DD. The lyrics are also quite stock-y.
“When you get to the top
You ever been to the top?
Just listen... let me tell ya
Hear what you're missin'
Shut up and listen!
In the beginning you'll get crazy
Spending all the money you got
No more women to love you now
You gotta go and leave town“
So I’ve taken my daily Adderall, caffeine, and nicotine; I’m in a DD mood. I was requested by a few users to write an $MU (Micron Technology) DD.
Company profile:
“The world is moving to a new economic model, where data is driving value creation in ways we had not imagined just a few years ago. Data is today’s new business currency, and memory and storage are strategic differentiators which will redefine how we extract value from data to expand the global economy and transform our society.
As the leader in innovative memory solutions, Micron is helping the world make sense of data by delivering technology that is transforming how the world uses information to enrich life for all. Through our global brands — Micron and Crucial — we offer the industry’s broadest portfolio. We are the only company manufacturing today’s major memory and storage technologies: DRAM, NAND, and NOR technology.
By providing foundational capability for innovations like AI and 5G across data center, the intelligent edge, and consumer devices, we unlock innovation across industries including healthcare, automotive and communications. Our technology and expertise are central to maximizing value from cutting-edge computing applications and new business models which disrupt and advance the industry.
*From our roots in Boise, Idaho, Micron has grown into an influential global presence committed to being the best memory company in the world. This means conducting business with integrity, accountability, and prof
... keep reading on reddit ➡I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.
Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.
Do your worst!
For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.
I said "hey look, an escaPEA"
No one near me but it didn't half make me laugh for a good hour or so!
Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂
It really does, I swear!
Buenosdillas
They’re on standbi
Pilot on me!!
Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.
This sub is mostly just NSFW puns now.
If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.
Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.
When I got home, they were still there.
A few weeks ago, I made a post discussing what COVID-19 would look like in Singapore in the long term after the situation stabilizes. I created a simple model with the naive assumption that the daily case rate would be constant at 1000 for 28 days based off what European countries are seeing after their respective exit waves. Since then, I have further improved the model to account for the daily trends and dynamic nature of the disease spreading throughout our community today, allowing me to make day-by-day predictions instead of averaging over a whole month. In this post, I will present the results of my simulations and modeling, hopefully giving us a preview of what the next few weeks might look like.
TL;DR is coming up first for those lazy to read through the whole analysis.
#Summary
We can expect a peak 7-day average of around 2.7k daily cases on October 11, roughly 2 weeks from today. Of these, approximately 620 will be seniors over the age of 60 and among whom 120 will be unvaccinated and at risk of severe illness.
Due to the time delay between cases being detected and developing severe symptoms, we can expect the maximum hospital utilization to be in the second half of October, with the maximum ICU load at the end of the month. Of the projected 850 cases of serious illness on October 21, around 720 will be seniors above the age of 60. Approximately 500 of these cases will be unvaccinated. We can also expect a peak of 13 patients passing away each day occurring around October 26. Of these, we expect 3 to be fully vaccinated while 10 will be unvaccinated.
Adding up the values over the month of October gives the following projections:
| Total Cases | Ever Required Oxygen Supplementation | Ever Admitted to ICU | Deceased |
|---|---|---|---|
| 64,959 | 1,830 (2.8%) | 397 (0.6%) | 291 (0.4%) |
#Methodology
Creating a Mathematical Model
In order to make predictions about the trajectory of the virus, we must first find a way to mathematically describe the trends observed today. Simply connecting the dots will not give us any insight into future numbers, but finding a mathematical description allows us to extrapolate the values today into the future. The mil
... keep reading on reddit ➡I won't be doing that today!
[Removed]
You take away their little brooms
This morning, my 4 year old daughter.
Daughter: I'm hungry
Me: nerves building, smile widening
Me: Hi hungry, I'm dad.
She had no idea what was going on but I finally did it.
Thank you all for listening.
Nothing, he was gladiator.
It’s pronounced “Noel.”
After all his first name is No-vac
What, then, is Chinese rap?
Edit:
Notable mentions from the comments:
-
Spanish/Swedish/Swiss/Serbian hits
-
French/Finnish art
-
Country/Canadian rap
-
Chinese/Country/Canadian rock
-
Turkish/Tunisian/Taiwanese rap
There hasn't been a single post this year!
(Happy 2022 from New Zealand)
Nothing, it just waved
Him: I can explain everything!
(It's his best joke yet I think)
Bob
So that I could frequently say, "I am going to walk 5 miles now."
Edit: My most popular post on Reddit! 😀 Thank you for the awards.
Just to clarify, 12345678
Me grabbing a soda from my (what I thought was) half full 12pk...
Notices there's only 2;
Me: "Awe man... This is a damn bird box!" Her: "What the hell does that mean?!" Me: (Pulls both cans out & shows them to her) "It's only got Toucans."
I'm not ashamed to admit the look on her face was glorious.
Official DD theme music: MEGA NRG MAN - BACK ON THE ROCKS and [Manuel - GAS GAS GAS] (https://www.youtube.com/watch?v=atuFSv2bLa8) and Ken Blast - The Top please listen to this as you read. Eurobeat music will give you Adderall like effects and help you read/comprehend this DD. The lyrics are also quite stock-y.
“When you get to the top
You ever been to the top?
Just listen... let me tell ya
Hear what you're missin'
Shut up and listen!
In the beginning you'll get crazy
Spending all the money you got
No more women to love you now
You gotta go and leave town“
So I’ve taken my daily Adderall, caffeine, and nicotine; I’m in a DD mood. I was requested by a few users to write an $MU (Micron Technology) DD. Apologies for posting this so soon after my Logitech DD, but the weekend is when I have time to write stimulant-fueled DD’s.
A lot of people didn’t like how long my Logitech DD was, so I’ll shorten my MU DD and make it more readable for you illiterate regards.
Company profile:
“The world is moving to a new economic model, where data is driving value creation in ways we had not imagined just a few years ago. Data is today’s new business currency, and memory and storage are strategic differentiators which will redefine how we extract value from data to expand the global economy and transform our society.
As the leader in innovative memory solutions, Micron is helping the world make sense of data by delivering technology that is transforming how the world uses information to enrich life for all. Through our global brands — Micron and Crucial — we offer the industry’s broadest portfolio. We are the only company manufacturing today’s major memory and storage technologies: DRAM, NAND, and NOR technology.
By providing foundational capability for innovations like AI and 5G across data center, the intelligent edge, and consumer devices, we unlock innovation across industries including healthcare, automotive and communications. Our technology and expertise are central to maximizing value from cutting-edge computing applications and new business models which disrupt and advance the industry.
*From our roots in Boise, Idaho, Micron has grown into an influential global presence committed to being the best memory company in the world. This means conducting business with integrity, accountability, and professionalism and supporting our
... keep reading on reddit ➡I'm surprised it hasn't decade.
What did 0 say to 8 ?
" Nice Belt "
So What did 3 say to 8 ?
" Hey, you two stop making out "
There hasn't been a post all year!
