#INTERMEDIATE MATHS

[retrocgads]

UK 1985

[fortune-maiden]

Intermediate murdles my beloathed

(I fully acknowledge that I am making dumb mistakes but also I just don’t like intermediate murdles x_x)

[bubbloquacious]

You seem to also enjoy talking about space so here's a question about space.

How do we define space?

Like you can't define a space as a collection of points that follow some rules because no other structure is considered or created that way. When we talk about a triangle we don't talk about the specific triangle and it isn't the set of all things triangular either, it's something with three sides.

So is there any way to define space without referencing what that space contains?

It feels like there should be but I can't find it. Don't think about the question too long or it will never leave. (I'm already too far gone). Thank you.

Great question! And like many great questions one that has a great many different answers, depending on what properties of space you care about.

The standard models of what we consider 'spaces' are the Cartesian Euclidean spaces. These are sets consisting of n-tuples of real number coordinates, where the dimension of the space is however many coordinates its points have. These spaces have a notion of points, of subsets, of lines, of incidence, of length, of angle, of continuity, of boundedness, of smoothness, of intermediacy, of convergence, of volume, of polynomials, of vectors, and many more.

What you want a general 'space' to be is entirely dependent on which of these structures you would like to generalize, and for almost any two of these properties you care about there will exist a kind of space that satisfies one of them and not the other.

Indeed when a mathematician says 'consider a triangle' they are not speaking about any specific triangle, but they are in a sense talking about the set of all triangular things. They are referencing an arbitrary triangle, and they make sure whatever they say about it holds true for any specific example. From a proofs-as-programs perspective, what they're doing is creating a function that takes in a triangle and returns a proof that the given proposition holds for that triangle.

And you can definitely define certain kinds of spaces as certain sets of points satisfying some rules. Most, but not all, of the example of spaces in mathematics, in fact. The concept you'll most often see referred to as a 'general space' is what we call a topological space. These spaces are defined to have only notions of points, subsets, and continuity (which is stated in terms of neighbourhoods of points, or open subsets). From these you can also define incidence and convergence, but not length, or angle, or volume, etc. It is possible to leave out any reference to points, though. This starts with the observation that the inverse image function of a continuous transformation encodes almost every bit of data about the transformation, and you can state the properties of the inverse image function abstractly in algebraic terms. This gets you the kind of 'space' known as a locale, for which you only specify particular kinds of 'subsets', and continuity of transformations between locales.

So the answer to 'is there some way to define space without referencing what that space contains' is yes or no, depending on what you want. Certainly to define some structure, you need to specify what that structure is. In a certain sense this is 'data' that the space 'contains', but it might not always consist of actual points or shapes or whatever that lie in the space.

[hella1975]

just picked my final year modules!!! i cant wait!!!! so excited and honoured to be specialising my subject that i love!!!

[probably-just-shitposting]

ADHD + Math = Huh?

I'm slow, not stupid. Yes, there is a difference. I can make all the connections a "smart" person can, it just takes longer because there's like 5 extra steps to every problem because my ADHD brain can't compartmentalize.

This math problem, for example:

15

×20

_____

Now, most people would probably look at this and do it the way taught in school. Multiplying the top ones place by the bottome ones place, then multiplying the top tens place by the bottom ones place, etc, etc.

When I try to solve this problem, I think, okay, so,

1 - 15

2 - 30

3 - 45

4 - 60

5 - 75

6 - 90

7 - 105

8 - 120

9 - 135

10 - 150

150 × 2 = 300

15 × 20 = 300.

On a really good day I might stop at 75 and go, 75 + 75 = 150, 150 × 2 is 300, 15 × 20 = 300. If I were smarter I could even simplify it to 20 × 5 = 100, 100 × 3 = 300, 15 × 20 = 300. However, that probably wouldn't occur to me unless the 20 was on the top of the problem because I read them top to bottom.

Taking all of this into account, Algebra is Hell. You want me to do what?

[caramelmochacrow]

*shaking wet rat* hello.

[herefortheships]

.

[ivccseap]

BridgeCourse Maths - II IMP QS

BCA II

[jandarpan]

BSEB 12th Paper Leak: बिहार में एक बार फिर से पेपर लीक की खबर सामने आ रही है. दरअसल बिहार

BSEB 12th Paper Leak: बिहार में एक बार फिर से पेपर लीक की खबर सामने आ रही है. दरअसल बिहार में आज से बिहार बोर्ड इंटर परीक्षा 2023 की श���रू हो गई है. पहले दिने आज पहली पाली में मैथ्स की परीक्षा हो रही है, लेकिन एग्जाम शुरू होने से पहले ही प्रश्न पत्र वॉट्सऐप ग्रुप में वायरल हो गया. नालंदा: BSEB 12th Paper Leak: बिहार में एक बार फिर से पेपर लीक की खबर सामने आ रही है. दरअसल बिहार में आज से बिहार…

[writing-imagines]

Even Mean Girls Cry // Regina George

Summary: After hooking up with Regina for a year, you finally get to see her vulnerable side after The Plastics reject her at lunch.

Possible warnings: light swearing, bullying, and Regina being Regina

Pairing: Regina George x gender!neutral reader (readers gender literally isn’t mentioned)

A/n: first fic of 2024!! I love Reneé’s Regina so feel free to send me any ideas or thoughts about her

Regina George wasn’t a good person. It was evident ever since the first grade when she told everyone that Peter Howell peed himself after she spilled apple juice on him. So, you did your best to avoid her, and her ever changing minions, every day as you grew up. When you reached high school, Regina’s antics became more frequent and hurtful. By the end of your freshman year, she had at least one embarrassing piece of information on everyone in school, yourself included. 

Your streak of successfully avoiding Regina came to an end after winter break during your sophomore year. Ms. Norbury asked you to be Regina’s Intermediate Math tutor since you had the highest grades in your Algebra 2 class. You were hesitant to accept the opportunity considering Regina’s reputation, but you knew tutoring would look great on your college application. You accepted Ms. Norbury’s request and so started your relationship with Regina George. 

At first, she sat across from you in the empty cafeteria after school, chomping loudly on her gum and texting a thousand words a minute. Her behavior continued every day that week and by Friday, you’d had enough. 

“Regina, stop wasting my time and pay attention.” You finally snapped after she blew an obnoxiously large pink bubble with her gum. Regina’s eyes slowly rose from her phone screen to you. 

“What did you just say to me?” Her eyes resting on you instantly made you lose the confidence you just had. 

“Oh-I…I meant you should pay attention. I’m trying to teach you, so you don’t fail your next algebra test.” You smiled nervously as Regina’s gaze dug further into you. After a few more moments of intense staring, the blonde let out a scoff. 

“You know, you’re actually kind of cute.” Her blue eyes looked you over, this time in a more flirtatious way. You felt like a lamb dangling over a hungry mountain lion. 

“Thanks.” You nervously looked away and rubbed the back of your neck in an attempt to get any relief from Regina’s presence. 

“So, you agree? You think you’re cute.” 

“Umm…I mean, I don’t really know.” Regina’s smile softened and she looked at you as if you were a lost puppy. Without warning, the blonde stood up and made her way to your side of the table. She sat down in the seat beside you and scooted as close as she possibly could, causing your face to warm and your heart to beat faster. 

“Have you ever kissed anyone, Y/n?” Regina questioned with her pointer and middle finger dancing on your thigh. Your throat went dry at the mention of the one thing you were embarrassed of. In a school full of hormonal teenagers, you were truly the only one who hadn’t kissed anyone yet. You were kicking yourself for accidentally telling Karen the sensitive information during a bonfire last year. 

“You know the answer, Regina.” You said with a defeated exhale. You couldn’t bring yourself to look at Regina, instead, you kept your eyes glued to the table. Suddenly, the two fingers that danced on your thigh were placed gently under your chin, forcing you to look at the blonde beside you. Her eyes were kinder, and her smile was still soft, making you feel less embarrassed. 

“It’s okay, you don’t need to be embarrassed.” You didn’t say anything, instead, you softly smiled and took in Regina’s features. You had never noticed how pretty her eyes were or how full her lips were. 

“Do you want to kiss me, Y/n?” Regina’s eyebrows lifted with the question. Without even thinking, you blurted out the answer. 

“Yes.” You swore for a moment Regina began to blush as she pushed a few stray hairs away from her face. 

“Okay. Close your eyes.” 

You did as you were told. For a moment, you were worried it was all just a prank, but when you felt Regina’s lips press against yours, you knew it had to be real. You did your best to reciprocate the kiss, causing Regina to let out a small moan, which caused your stomach to flip about ten times. Suddenly, you felt Regina’s hands find your neck and her perfectly manicured nails rested on the nape of your neck, effectively pulling you in deeper. 

The sound of a door slamming shut caused both of you to pull away quickly. You couldn’t help but stare at Regina with a bewildered look, seriously questioning if the kiss happened. 

“Wow, you're a pretty good kisser, Nerd.” 

“T-Thanks. You’re good too.” You sputtered with the most nervous tone you had ever heard from yourself. The blonde laughed before running her fingers along the edge of her lips to wipe away any smeared lip gloss. 

“I know.”  The two of you sat in silence for what felt like hours before Regina spoke up. 

“So, I’ll see you on Monday then.” She quickly stood up and gathered her things as if nothing had happened. 

“I’ll see you on Monday.” You echoed, wiping Regina’s cherry flavored lip gloss off your lips. 

“Bye, Nerd.” 

“Bye, Regina.” 

Almost a full year later and your hookups with Regina were still going strong. In fact, ever since Cady Heron started causing drama between the girls, you had been spending all of eighth period in the back seat of Regina’s Jeep, making out like it was your last moments on earth. Not to mention, secretly hooking up with the queen bee of North Shore gave you a major confidence boost that even Regina noticed. Your relationship had even gone to the next level: texting each other about things that didn’t involve when and where to hookup. 

You were sitting in Trigonometry when your phone pinged. You quickly checked it, not wanting to risk Ms. Norbury confiscating it. It wasn’t much of a surprise to see that Regina had texted you. 

RG: Sweatpants are the only things that fit me right now 

Y/n: So? 

RG: So? Jesus Y/n. I can’t wear sweatpants to lunch! 

Y/n: Because of the stupid rules YOU made?

RG: They aren’t stupid 

Y/n: I’m sure it’ll be fine. The girls will understand 

“Y/n, care to share with that class what on your phone is so important that you’re missing out on practice test questions?” 

“No. Sorry, Ms. Norbury. It won’t happen again.” 

“Good. Now, as I was saying…” You watched Ms. Norbury turn to write something on the board and quickly sent another text to Regina. 

Y/n: Just got called out by Norbury for texting you. Hope you’re happy 

You went the rest of class without hearing from Regina. In fact, you went most of the day without hearing from her. It was a little weird, but you knew she had a lot going on and it wasn’t like you needed constant communication with each other. 

When lunch came around, it was the same old same old. You sat down with some of your other tutor friends and talked about your day. As Daisy Smith talked about her failed attempt to teach Karen about fractions, you saw Regina walk towards The Plastics. True to her word, she wore gray sweatpants that grabbed your, and several others, attention. You didn’t eye Regina for long, not wanting anyone to accuse you of being a creep or being in love with her. You looked down at your lunch only for the room to suddenly go quiet. 

“You can’t sit with us!” Gretchen’s voice echoed through the silent room. No one dared to even gasp as Regina fired back. 

“Sweatpants are all that fit me right now.” Even though you couldn’t see her face, you could tell Regina was talking through gritted teeth. 

“What do you think, Cady?” Gretchen asked, her voice once again echoing through the room. 

“Sorry, Regina. Rules are rules.” Seeing the sly look on Cady’s face made you want to march over to her and smash a tray of food in her face. You knew that would lead to a suspension, so you made a mental note to figure out some way to get back at Cady that wouldn’t result in a week off school.

“Fine.” 

Regina turned around to see every eye in that room on her. You could tell by the look on her face that for once, she hated the attention. Not a single person in that room moved to make room for Regina as she walked down the aisle. 

“Daisy, scoot down.” You quickly nudged the redhead to make room for Regina.

“Regina, you can sit with us.” You offered, eyes slightly full of hope that she would accept the offer and somehow make the situation better.

“I’m not sitting with you losers.” She spat out as she stormed past your table. 

“What a bitch.” Glenn Coco scoffed. Your blood boiled at Glenn’s comment, but you knew you had to play it cool to avoid any suspicion. 

“Guys, I forgot my math book in Ms. Norbury’s. I’m going to grab it really quick.” 

You quickly got up from the table, leaving your tray behind, and stormed off to find Regina. You searched her usual hangout spots, the maintenance room and the girl’s locker room in the gym. When you didn’t find her in either place, you made your way to the only other place she could be, the parking lot.

Sure enough, as you approached her Jeep, you saw Regina sitting in the passenger seat. Even from far away, you could tell she was crying. Cautiously, you approached the car and tapped on her window. The blonde’s head instantly shot up, revealing her red eyes and mascara stained cheeks. You had never seen Regina cry before, and the sight actually shocked you to your core. Without saying a word, you walked over to the driver’s side and climbed in. 

“What are you doing?” Regina questioned through sniffles as you put the car in reverse and pulled out of the parking spot. 

“I’m taking you home.” Your hands gripped the steering wheel a little tighter when you noticed a picture of Regina, Karen, and Gretchen resting on her dashboard as you drove out of the parking lot. 

“I don’t need you to take me home.” Regina tried to use her usual venomous tone, but it came out shaky and pitiful. 

“I don’t care if you need me to. I want to take you home. That was fucking ridiculous.” 

After a few minutes of silence, you looked over to see tears still rolling down Regina’s face. Based on how her bottom lip was quivering, you knew Regina really needed to cry. You carefully reached your right hand over to Regina and grabbed her hand. 

“It’s okay to cry. They tried to humiliate you in front of the whole school. You don’t have to hide it from me.” You squeezed Regina’s hand, which caused her to quickly pull her hand away. 

“I am not crying because of those bitches. I’m crying because all I can wear is sweatpants and my mascara is ruined.” That time Regina was able to spit out her usual venom. While her tone would intimidate most people, it let you know Regina was going to be okay. 

“Those are still valid reasons to cry.” You said matter-of-factly. You felt Regina’s eyes land on you again, causing you to glance over at her. 

“Why are you so nice to me all the time?” 

“Because I’m a nice person.” You shrugged, not wanting to give away your true feelings for Regina. 

“I think it’s because you like me.” 

“And what if I did?” You replied without missing a beat. Once again, you were kicking yourself for not thinking before you spoke. 

“I’d have to give you a makeover. I can’t date anyone who dresses like that.” 

“What’s wrong with the way I dress?” 

“Nothing, if you’re going for a grocery store clerk.” You scoffed and acted offended by Regina’s words, which made the blonde crack a smile. 

“I do not dress like a grocery store clerk.” 

You both chuckled as you pulled up to the George's home. You instantly took note that Mrs. George’s car was missing from the driveway. 

“Do you want to come in? My mom isn’t home.” Regina looked at you with hopeful eyes. Not wanting to leave Regina alone after a traumatic event, you decided that it would be a good idea for you to stick around for a little while longer.

“Yeah, I’ll come in for a little bit.” 

You turned off the car and let Regina take the lead into her home. The second the front door closed behind you, Regina took your hand and led you up to her room. 

“Shoes off and get on the bed.” The blonde commanded.

“Regina, I don’t think we should-”

“Relax, Nerd. I just want you to hold me and tell me I’m pretty.” 

You quickly kicked your shoes off and lied down on the right side of the bed. Once you were comfortable, Regina joined you. Within seconds, her head found a comfortable spot on your chest, resting between your jaw and collarbone. Her hand found its way down to your stomach and balled the fabric of your shirt into her hand. After Regina was comfortable, you snaked your arm around her and held her close. You couldn’t help but look down at the blonde with a smile. When she wasn’t ruining people’s lives, Regina was actually kind of sweet. 

“Hey, Regina?”

“What, Nerd?” 

“You’re the most beautiful girl I’ve ever seen.” 

“Yeah, I know.” You could feel Regina’s smirk against your neck, which only made you fall a little harder for her.

You laid there, holding the blonde like your life depended on it. Your mind couldn’t help but wonder about finally telling Regina how you felt about her. It seemed like a good idea, especially after a hard day, but the thought of losing her stopped you. So, you just let Regina George, the meanest girl in North Shore, sleep on your chest while you held her close. 

[patricia-taxxon]

any advice on getting my paws wet with music theory? i realize that this probably doesn't actually mean all that much, but every time i use a daw without a "highlight every note in the scale" feature, programming midi suddenly becomes very cerebral and i have to repeatedly mentally calculate which notes are in the scale ("okay" to use), which is frustrating. my spatial reasoning is incredibly poor and i can't just go off of vibes anymore. i feel like i'm missing the point, or something

Honestly, this might be a disappointing answer, but in order to gain intuition with it you probably need to gain beginner/intermediate level proficiency with a musical instrument, it's gonna be memorization and math until you can get those ideas out of your paws. It's just the shape of the information, a lot of jazz theory is based on the spacial quality of the piano keys, a lot of rock theory is based on the spacial quality of the fretboard, etc. And listen to a lot of music, of course. Once you can feel the diatonicism on your clawtips, you're gucci.

[sexhaver]

ok im pretty sure most MTG players following me have already heard of this one but i just realized i can nerd snipe math majors following me with it so here goes. imagine a game of Magic with the following board state:

your opponent controls a Leonin Elder

you control a Filigree Sages, a Wirefly Hive, and some arbitrary source of infinite mana

somehow, despite having the format-warping power of Wirefly Hive on your side, you are going to lose the game unless you win on your next turn. maybe you only have one card left in your deck or something, idk, figure it out

it is your opponent's end step, and they're low on life

so obviously the play is to flip coins to make wireflies until you have enough to overwhelm their life total. however, the Leonin Elder complicates this. say they start with 2 life:

you can lose the first flip as many times as you want with no consequences

once you win your first flip, you make a 2/2 flyer, but your opponent goes up to 3 life, so you need to make another one for lethal

if you win the second flip in a row, then congrats! you have two 2/2 flyers vs an opponent with 4 life. you start your turn and swing for lethal

but if you lose that flip. hoo boy. now you start over from square one, but your opponent has 3 life, so you need to win 3 flips in a row! (one 2/2 -> 4 life, two 2/2s -> 5 life, three 2/2s -> 6 life -> lethal)

and of course if you lose any of the intermediate flips in THAT chain you dig yourself even deeper

and this is all assuming they started at just 2 life

so the math questions here are as follows:

are you mathematically guaranteed to eventually flip enough heads in a row for lethal, or does the series not converge like that?

if the answer to 1 is "no", then what are the odds of success as a function of how much life your opponent had at the start of this process? show your work.

if the answer to 1 is "yes", could you use that to argue with a judge that you should be allowed to shortcut the process (see MTG Comprehensive Rule 727) and just jump straight to the win without having to flip infinite coins? (this one is less of a math question and more of an MTG rules question unfortunately)

[studentbyday]

week 2 / small commitments challenge

Sometimes I think too much about the intermediate (a few months from now) and far future (a year or years from now) and get so worried that I won't "make it" in whatever way I determine is "making it" for a certain goal that I can't focus very well on the present. This week, this mostly happened at night when I finally go to or get ready for bed. The ochem midterm is coming up, which is forcing me to stay in the present more during the day. I think if that wasn't happening, I would be even more of a runaway train 😭 And yet when I focus on school, I just feel so sad being cooped up indoors, where I focus best, when the weather is so nice outside. The second half of the semester is always the hardest on my psyche. I want to remember why I'm doing this. But the reason is out there in the world, not at my desk...

In other news, I adjusted my study routine so that I try to do an hour of learning R (typically first thing...at first I tried for 2h but that never happened and I just felt discouraged), followed by ochem work, then driving practice. Much less overwhelming BUT still making decent progress on the highest-priority side projects when I can keep up with them... I'll need to keep at this routine or smth similar for a while tho because I fell off the bandwagon towards the end of the week, trying to focus on ochem. Whenever I end up feeling ready, I want to add in an hour of math bc that will open many doors for understanding cool computational biology stuff...or maybe I'll add in some music theory instead... Who knows, my priorities may change again by that point. 🤷🏻‍♀️ One step at a time! 👣 I also struggled to stick to a consistent sleep schedule this week...again. Briefly, before this challenge, I had been able to do this while I was on habitica...but then the novelty faded and I stopped keeping myself accountable for it as I tried to keep track of everything else on the app lol. So now I'll just use habitica to keep track of my sleep/wake times, using the minus button when I miss out on the habit. I also struggled with the meditating thing...meditation is one of those things where the benefits are subtle and last longer the more regularly I do it, so I think I just have to stick with it until that happens and serves as a stronger motivator...Maybe I'll just make meditating at night the "mandatory" one since that really helps me feel peaceful enough to sleep. Aaand I completely forgot about exercise. I haven't been doing that consistently either this week 🙃 Lots of room for improvement. 🪄

[asexualbookbird]

Top 5 craft projects you made?

IN NO PARTICULAR ORDER!

We have Beeby, the Minecraft Bee! It was announced and I KNEW I had to make one haha I made each minecraft pixel one centimeter I think? And used that as a guide. There's a felted heart inside too :)

THE MOMOFUKU MILK BAR BIRTHDAY CAKE, for my sisters birthday in 2020. So no I didn't even get to taste it. It took me like three days. It was fun and very impressive and it looks VERY COOL!

HOT OFF THE PRESSES WE HAVE TINY BOUND BOOK EARRINGS (LOCKED TOMB STYLE) This was a gift and the reason this ask has been sitting in my inbox. The recipient has opened them , gift has been GIVEN! lots of fun! I couldn't find hi res images of the entire cover spread so I scanned them myself! Got my math wrong and had to trim the book parts after they were bound! Used silver plated earring because nickel allergies are no joke. Would do again!

Someone on instagram is making these giant piped flower pieces and it looked so fun I tried it myself. This was my first (and so far only lol) attempt and I think it came out cool! It was a lot of fun and I DO want to do it again, but I've never so much as piped a flower in frosting so it's a new skill I have to learn. I'm still looking for one of those. Stick things. That cake artists use to make frosting flowers. The only place I've found one is Hobby Lobby and well :/ I'd really like to make a larger piece of lilies for my mom!

AND FINALLY! MY FIRST BIG CROCHET PROJECT! THE RADIANCE BLANKET! This was in a mart maxim magazine that was sent to our house and I said WOW I WANNA DO THAT so my mom bought me the pattern and about ten rows in I was struggling and noticed. Oh. This is an Intermediate pattern. I'd only ever made amigurumi at the time, so all I knew was single crochet and slip stitches LOL it was an ambitious first project but I learned a lot! This is on my moms large queen sized bed so its BIG! Took me about a year to finish, with a long break over the summer because it was too hot to work on it.

THANKS FOR ASKING SORRY IT TOOK SO LONG HOPE YOU HAVE A GOOD DAY!

[corvidcleric]

[start i.d.: a drawing of my fantasy high sona character. they have gray-green toned skin with cattails sticking out of muddy brown hair, gazing off to the side. they wear earthy tones, with a green sweater, brown carpenters pants, a silver sword hanging at their side, and converse. text on the side reads “juno / swamp genasi / paladin 6 sorcerer 3.” another chunk reads “courses: math and meta magic / advanced aura studies / area of effect - spellcasting and community / elementary action economy / intermediate elvish.” end i.d.]

we making fhsonas on twitter. get in

[ivccseap]

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