the Galois fields can't be isomorphic that is

Hm I think you can actually prove it if the degrees mismatch too. Since you assume the rep g has degree strictly less than f1, then g*f2/f1 should have degree strictly less than f2

yes you can prove that

it's quite easy actually

the degrees part htat is

we know the exact # of elements in F[x]/f1(x)

it's going to be q^n

i'm assuming q is prime btw

Sure since it's irreducible. Otherwise, hm...

If a polynomial has a non-prime degree, to guarantee reducibility you need to allow complex coefficients, right?

i don't think it matters what the degree of the polynomial is

like if it's prime or not

i think what matters are the coefficients

if you don't have prime coefficients, your polynomials stop being a field

the reason why F[x] is a field is because Z_q is a field when q is prime

if q is not prime, Z_q is not a field

and therefore F[x] is not guaranteed to be a field

Why is Z_q not a field when q is, say, 4?

the very basic example is that say if you have Z_4, the polynomial "2" does not have a multiplicative inverse

Ohh

Neat

Z_4 is not a field because 2 does not have a multiplicative inverse

Yeah haha been a while

and since Z_q is a subfield of F_q[x]

yeah I've literally pullen out my abstract alg. book out today

i need some cryptography knowledge from it

i learned all of this again today 😛

That's neat. I enjoyed abstract algebra but mostly only needed the linear algebra part since then (11 years ago). Rotation groups and some other stuff relevant to geometry, but not much more. Cryptography seems interesting, we did cover RSA at some point, I only remember the main idea, that factoring is hard 😁

@ThisIsChris wellyeah, some pajeets found a way to crack RSA with you guessed it, Galois fields

Is that a recent thing?

yeah

like a year or so

it's amazing how irrelevant Abstract Algebra used to be until computers, and now it's hella important

Huh no kidding. Guess I better put 2FA on my bank accounts then

yep

idk about you, my dad make me take applied math

it was "fun" i guess, but I really want to go back to college and get a pure math degree

later

😛

pure math is so much more fun that learning about how to earn money at google

"pure math is fun" I will never understand you types

https://giphy.com/gifs/frog-get-out-U9DiGJDKfbwGY

@Deleted User

@ThisIsChris

I'll stop there

@YourFundamentalTheorum haha I like the sigma algebra one but don't get the epic one? It's a true statement if f is 1-1 and onto. Not sure what else.

@ThisIsChris epic means an epimorphism

which is literally defined by that equation

so f is epic

https://en.wikipedia.org/wiki/Epimorphism

So this Julian Von Abele's phsyics QCI theory of physics- anyone think anything of it?

@Jonaltright I'm thinking of buying the book to support him, I don't really know what his theory is. I did take a physics class in college so I hope I can understand something of it 😁

Yeah I saw people doing that. I'm sure they'll suspend publication once they see an uptick in sales though :(

Hopefully he makes out ok. Doxxing has been devastating for me

@ThisIsChris Physics classes can be harsh. I took some to fulfill return requirements for a computer science degree. Are they actually useful in your career?

@Jacob Some intro to physics is a "now to know" but not "need to know". The main use in my career has been to better understand some calculus concepts, since the beginnings of calculus and physics are tightly connected.

😳

you actually use calculus in your job?

I heard programmers don't actually use it

I'll DM you

based

https://www.ted.com/talks/tamas_kocsis_the_case_for_a_decentralized_internet/transcript?language=en

Hey, has anyone here changed careers using a 'code bootcamp'? Or is anyone a front-end web developer? I want to get a new job as a web developer this summer.

I’m currently trying to do that. Just going off of free courses online as of now

Cool @VinceChaos. I've been doing that for a few years now, but wasn't really taking it seriously. Now I'm doing a code bootcamp. What courses are you doing? Codecademy? W3Schools?

@NuclearReactionary Khan Academy, the Odin project, SoloLearn, and another that I can’t remember the name of rn

I use w3schools as a reference

Learning form multiple so I don’t miss anything and get different teaching types

Upskill! That was the last one. I really like using that one if you want to learn full stack

Nice. I haven't heard of Odin Project, SoloLearn or Upskill! I'll check them out!

The bootcamp I'm doing rn is $200/mo. but it's self-paced. I'm hoping to finish it in 3 months and then start applying for jobs lol

Oh yeah these are all free before I go for something like that

What’s your camp called

Treehouse. They have what they call a "TechDegree" for front end web development.

There's also one for full-stack if that's your thing, or iOS, too, I think.

A friend of mine is a web developer and he says the projects in this program are representative of the real world, so I'm confident I'll get a job when I'm done

Nice I actually did hear of that one maybe I’ll spend the cash

If you do, I can refer you for a discount, I think

@NuclearReactionary @VinceChaos vast majority of new front end devs in my experience now are coming out of code bootcamps, good choice!

starting salary at my company for fresh code camp grads is around 65-70k

Good to hear @ThisIsChris ! Do you know anyone that did Treehouse, specifically?

@NuclearReactionary I know a lot of people who've used Tree House to learn tools, myself included, but this is the first I'm hearing of their credential.

The main thing I would look for from a bootcamp graduate is do you have a portfolio to present? Most code camps spend a lot of time getting you to develop one.

Ok. Yeah, Treehouse does that. And like I said, a friend of mine said he thinks it represents real world work.

I’m gonna be disappointed if the starting salary isn’t more than that here, though. That would actually be a pay cut for me 😂 and I’m a teacher

Looking at indeed and paysa, I’m hopeful.

@NuclearReactionary where's "here"? my company's in manhattan which is usually pretty top dollar location. Only place I'm seen on the paycharts that regularly exceeds it is San Francisco.

Also, I don't want to judge, but if I could teach at a comparable or better salary then I would probably choose that, why do you want to change jobs?

My dad was a teacher, pretty good benefits, though I'm aware they've gotten worse depending on when you got into the system. But if you're making more as a teacher than 65k then you've probably been in it for a while.

I often recommend front-end dev work for people without a college degree or people who got a degree in underwater basket weaving and just woke up. 65k coding certainly beats retail, diner serving, or being a journalist as a career path. But I wouldn't take a pay cut from a respected job to do it. The pay scale does go up, of course, with years of experience. But life experience isn't going to transfer over that much, I'm sorry to say.

If you want to make a bigger salary and really need to code then it would make more sense to get a Computer Science degree. Since you have a Bachelor's already (I assume since you're a teacher) then I guess you would go for a Master's in CS degree.

They can make big bucks. With a Master's in CS degree + some internships, you can easily get 125k. (Not my field, I just know the salaries, kinda wish I had done more CS in school!)

Were you genuinely interested in coding/CS before you got started on this path or was it more pragmatism that took you this direction? For me it'd be more pragmatism. I feel like I could do it, it's just not a passion of mine.

I got a general business degree and I’m not even working in my chosen field. Considering a masters too but idk if I wanna spend way more money

Instead*

@Mick is that a question for me or NuclearReactionary?

@VinceChaos A Master's in what?

CS

@VinceChaos The opportunities with a Master's in CS are unparalleled. If you really like computers

That’s what I understand. You’ll get an offer months ahead of time in anticipation of graduation

It’s just the price

Yeah pretty much. Ideally you have time for a (paid) internship between your first and second year.

Nice. Yeah I’m using free products as of now. We’ll see what’s next

@ThisIsChris for you, but I'd love to hear what you have to say @NuclearReactionary

I heard of this great apprenticeship program from LinkedIn called Reach for programmers from non traditional backgrounds

@Mick yes I was very interested in coding. It really helps because even when you start working you learn a lot on the job but it helps a lot to learn outside of work too.

Recommending the podcast “learn to code with me” if you drive a lot like I do and feel guilty if you can’t seem to find the time to code

@ThisIsChris I've only taken a couple of introductory courses when I was younger. So I only have a very basic understanding of what goes into coding. Just made a basic website once really. It was actually kind of fun. I've the means to go back to school, eventually, it's just a matter of when at this point really. And for what.

@Mick I'll DM you

Sorry, lotta questions to answer. In order:
1. "Here" is San Jose.
2. I fell into teaching and I'm not crazy about it. Also, I'm at a private school, which doesn't necessarily mean high salary (you'd assume that, but it's not always the case). Most importantly: no pension.
3. Yes, I'm interested in CS now. Hindsight being 20-20, I definitely got the wrong degree: Music Business/Technology. I just was never exposed to CS or didn't think I could do it.
4. A Masters in CS isn't really an option; schools won't consider a BA good enough.

indeed.com

paysa.com

@Mick

@VinceChaos I've always been a little put-off by that learntocodewith.me site. That's the podcast you're referring to, right?

But I've never listened to her podcast. It's good, you say?

I got valuable info the first episode I listened to

About that reach program

Never visited the site

@NuclearReactionary San Jose is basically same as SF, in which case any salary I quoted for NY you can tack on 10-15% on. But I'm skepical of those payscale estimates for front end devs unless you qualified them as people with a Bachelor's in CS, or who have many years of experience.

Ok @ThisIsChris . Hmm. Well, we'll see what happens. I teach web dev anyway, so this program isn't terribly expensive as a form of professional development.

Another thing to consider: In my current position my salary isn't likely to grow much, if at all. Meanwhile, the salaries as a web dev _start_ maybe a bit below what I make now and grow far above whatever I'll ever make in my current employment.

@NuclearReactionary yes, also with respect to you pointing out you teach at a private school, I see what you mean. Private school teaching, afaik from my dad, doesn't compensate nearly as much.

$142,000 avg salary in San Jose, CA
$143,000 avg annual rent for 1br apartment in San Jose, CA

😛

@Tanner - SC The Bay is bananas!

BS! A 12k/month apartment?! That’s not an avg apartment!

Last time I was out there, a small 2 bedroom ranch outside the city was ~$800k

@micbwilli what do you think of "the singularity" and brain emulation? I was talking to a friend about it earlier today.

I listened to Kaczynski manifesto on the progress of man and industrialization. I got 2 big take aways from it.

You can't end the progress due to an inability to make a simultaneous revolutionary impact.

Who controls and builds the last machine brain build by a man will ever build might decide if human existence continues.

@micbwilli 😢 scary stuff

Does anyone have any experience with visual basic and the correct way to save a project's files? Gotta love putting in extra hours at school just to get a zero on something because it didn't save properly... 😡

<@&387091385075105804> <@&435155896780324864> ?

^

Did you get any feedback on what was wrong with your submission

"does not have all project files to run the program"

Using visual studio?

Yup

I've never used vb, but you'll want to include all of the cls, frm, and bas files as well as the visual studio project file (maybe .sln). If you want to test it, move the whole thing to a different folder and see if it runs. That'll help you understand all the files you need.

I basically need to know how to save both the design and code files and then put them in a .zip file.

To make a zip file, select all the files you want, right click -> send to -> compressed folder

The files should all be saved all ready in your project folder

Do we have any actuaries or CFAs in here?

Pic somewhat related. I want to work with him.

@Ekdromoi ^

😂

okay can someone help me with this?

Determine which books cost less than the average cost of books in the same category.List the title, the category, and the cost of these books.

apparently this is the answer, but I don't really get it

```SQL
SELECT a.title, b.category, a.cost
FROM books a,
(SELECT category, AVG(cost) averagecost
FROM books
GROUP BY category) b
WHERE a.category = b.category
AND a.cost < b.averagecost;
```

I see no numbers

it's not a math question

it's just SQL

oh ya I forgot to tag <@&435155896780324864>

I ended up writing my own solution like this

```SQL
SELECT BOOKS.Title, BOOKS.Category, BOOKS.Cost
FROM BOOKS, (SELECT BOOKS.Category, AVG(BOOKS.Cost) AverageCost
FROM BOOKS
GROUP BY BOOKS.Category) AverageCosts
WHERE BOOKS.Category = AverageCosts.Category
AND BOOKS.Cost < AverageCosts.AverageCost
```

idk if the first one is better

mine feels less convoluted

@Jacob I agree yours is less convoluted that the first one, but I would do
```sql
SELECT Title, Category, Cost FROM
(
BOOKS
INNER JOIN
(
SELECT Category, AVG(Cost) as avg_cost FROM
BOOKS GROUP BY Category
)
)
WHERE Cost < avg_cost
```

haha wow that's a lot less

I think our teacher wants us to get practice with subqueries on this assignment, though

@Jacob well the avg cost part is calculated with a subquery

oh that's right

I don't think we officially learned to do subqueries in the JOIN clause yet

but that looks like a better solution for the future, thanks

Pretty cool article: https://www.sciencehistory.org/distillations/magazine/isaac-newton-and-the-american-alchemist