Cubers and math

[Abram Grimsley]

(If anyone wants to read my B- paper I can DM it to you lol)

I might not understand all of it, but I would like to read it, please.

 

[ruffleduck]

All of mathematics is imaginary at the end of the day. (I align mostly with the formalist philosophy on math.)

 

[Caleb Valenzuela]

the only imaginary math I know is mental math (I imagine the numbers)

 

[qwr]

All of mathematics is imaginary at the end of the day. (I align mostly with the formalist philosophy on math.)

What about Platonism

 

[ruffleduck]

What about Platonism

I don't buy it as much. Although maybe classical logic and natural numbers are more "real" in a sense, than other math objects / constructions.

 

[BenChristman1]

Well, how's everyone's math endeavors going? Since last spring when this thread was alive I've taken Calc 3 and Abstract Algebra. This semester I'm not doing too much, just a geometry class (I hate geometry) and LaTeX (wish I knew what this was when I was writing my math papers a year ago lol) Also, maybe this thread should be moved to off-topic?

 

[SpeedCubingLord]

Well, how's everyone's math endeavors going? Since last spring when this thread was alive I've taken Calc 3 and Abstract Algebra. This semester I'm not doing too much, just a geometry class (I hate geometry) and LaTeX (wish I knew what this was when I was writing my math papers a year ago lol) Also, maybe this thread should be moved to off-topic?

Im in 7th grade, but since about fifth grade I started learning and speedrunning algebra 1. ever since then i have been number 1 in both school i have been to. i have been introduced to calculus and knkw what integration and derivation are, and i know the bare basics of limits. i still feel like algebra is more fun and interesting because of all its irl applications and variety, but everythings cooler than the peasnatry called arithmetic they taught me before my math speedrun.

we have this thing called thr MAP test, and i got the highest in the school by 14 points, 287.

so it think im doing pretty good.

overall math has helped me feel good about myself, and i am decent at all subjects, straight A+ (98%+) and have on 97 in history

lowk i just realized how much of a nerd i am how do i even have time for cubing sports AND gaming lol

do i have a good trajectory for UCLA guys? @abunickabhi do you think i have a good trajectory for IIT bombay?

 

[ruffleduck]

Well, how's everyone's math endeavors going? Since last spring when this thread was alive I've taken Calc 3 and Abstract Algebra. This semester I'm not doing too much, just a geometry class (I hate geometry) and LaTeX (wish I knew what this was when I was writing my math papers a year ago lol) Also, maybe this thread should be moved to off-topic?

Last semester, I took measure theory and abstract algebra 1. This semester I'm taking differential geometry, Fourier analysis, and grad cryptography (I get to do a research project!)

I'm also doing a directed reading program (DRP) for toric topology where i'm reading and writing a report on selected material from Buchstaber Toric Topology and Lee Smooth Manifolds

 

[SpeedCubingLord]

Last semester, I took measure theory and abstract algebra 1. This semester I'm taking differential geometry, Fourier analysis, and grad cryptography (I get to do a research project!)

I'm also doing a directed reading program (DRP) for toric topology where i'm reading and writing a report on selected material from Buchstaber Toric Topology and Lee Smooth Manifolds

I am not too into geometry, is differential geometry and differential calculus similar in any aspect?

 

[Abram Grimsley]

Well, how's everyone's math endeavors going? Since last spring when this thread was alive I've taken Calc 3 and Abstract Algebra. This semester I'm not doing too much, just a geometry class (I hate geometry) and LaTeX (wish I knew what this was when I was writing my math papers a year ago lol) Also, maybe this thread should be moved to off-topic?

I am having fun! Last semester I finished Calc 1, am currently studying Calc 2, and will be studying Calc 3 and Linear Algebra next semester.

 

[SpeedCubingLord]

I am having fun! Last semester I finished Calc 1, am currently studying Calc 2, and will be studying Calc 3 and Linear Algebra next semester.

calc 3 is 3 dimensional right? gl bro!

 

[ruffleduck]

I am not too into geometry, is differential geometry and differential calculus similar in any aspect?

Differential geometry is the study of smooth manifolds and smooth maps between manifolds. You're correct to note that "differential" in diffgeo relates to differential calculus! I'll do my best to explain how differentiation works here:
- You may be familiar with the single-variable derivative---the slope (tangent line) of a one-dimensional function at a point.
- You can generalize this to any dimension! Imagine a smooth surface. You can have a tangent plane to that surface instead of a tangent line.
- That's called multi-variable calculus or "Analysis on R^n" when studied more formally/theoretically/technically.
- Manifolds are spaces that locally "look" like a multi-dimensional Euclidean space (R^n) but globally may be curved.
- Classic example: Imagine an ant on a big sphere, or us on Earth. To the ant (or us), the ground looks totally flat (locally). But in reality, it's curved (globally).
- So differential geometry is applying (multi-variable) calculus locally on smooth manifolds and considering smooth maps between smooth manifolds in that sense.

Edit: What I described is mostly limited to differential topology, differential geometry technically adds in other geometric concepts such as metrics, geodesics, curvature, etc that aren't necessarily present in a topological space. The focus is more Riemannian manifolds rather than smooth manifolds in general.

 

[Abram Grimsley]

calc 3 is 3 dimensional right? gl bro!

yeah, Calc 3 is also known as multivariable calculus, which deals with functions in three dimensional fields (I think lol).

 

[SpeedCubingLord]

Differential geometry is the study of smooth manifolds and smooth maps between manifolds. You're correct to note that "differential" in diffgeo relates to differential calculus! I'll do my best to explain how differentiation works here:
- You may be familiar with the single-variable derivative---the slope (tangent line) of a one-dimensional function at a point.
- You can generalize this to any dimension! Imagine a smooth surface. You can have a tangent plane to that surface instead of a tangent line.
- That's called multi-variable calculus or "Analysis on R^n" when studied more formally/theoretically/technically.
- Manifolds are spaces that locally "look" like a multi-dimensional Euclidean space (R^n) but globally may be twisted.
- Classic example: Imagine an ant on a big sphere, or us being on Earth. To us, the ground looks totally flat (locally). But in reality, it's curved (globally).
- So differential geometry is applying (multi-variable) calculus locally on smooth manifolds and considering the possible smooth maps between smooth manifolds in that sense

i feel like this relates to space time in someway. you mentioned how something may appear flat locally but is curved globally, which relates to einsteins theory of relativity, and also how the universe might be a loop of curved spacetime the leads us to the same spot after after trying to travel to the "end" of the universe.

this also seems to relate how if you draw 2 parralell straight lines on a ball, they will intersect, which disproves the fifth axiom (i dont remember where the axiom was tho). i learned everything in this msg from vsauce and veritasium btw!

 

[ruffleduck]

i feel like this relates to space time in someway.

Yes, exactly!! Physicists use differential geometry to study space-time exactly as you said. Differential geometry is extremely important in theoretical physics, maybe the most important aside from like PDE theory.

you mentioned how something may appear flat locally but is curved globally, which relates to einsteins theory of relativity, and also how the universe might be a loop of curved spacetime the leads us to the same spot after after trying to travel to the "end" of the universe.

Yes, Einstein was a huge pioneer of differential geometry! Definitely highly relevant.

this also seems to relate how if you draw 2 parralell straight lines on a ball, they will intersect, which disproves the fifth axiom (i dont remember where the axiom was tho). i learned everything in this msg from vsauce and veritasium btw!

The concept of "straight lines on a ball" is geodesics from differential geometry. It doesn't disprove the fifth axiom though because the parallel postulate is only stated to hold for flat (Euclidean) geometry. But yeah, it wouldn't hold necessarily for all curved surfaces.

 

[SpeedCubingLord]

Yes, exactly!! Physicists use differential geometry to study space-time exactly as you said. Differential geometry is extremely important in theoretical physics, maybe the most important aside from like PDE theory.

Yes, Einstein was a huge pioneer of differential geometry! Definitely highly relevant.

The concept of "straight lines on a ball" is geodesics from differential geometry. It doesn't disprove the fifth axiom though because the parallel postulate is only stated to hold for flat (Euclidean) geometry. But yeah, it wouldn't hold necessarily for all curved surfaces.

grasping concepts fast has given me an advantage in my mathematical speedrun. good luck in your mathematical journey bro!!! thanks for helping me understand what diffgeo is!!

 

[BenChristman1]

Im in 7th grade, but since about fifth grade I started learning and speedrunning algebra 1. ever since then i have been number 1 in both school i have been to. i have been introduced to calculus and knkw what integration and derivation are, and i know the bare basics of limits. i still feel like algebra is more fun and interesting because of all its irl applications and variety, but everythings cooler than the peasnatry called arithmetic they taught me before my math speedrun.

we have this thing called thr MAP test, and i got the highest in the school by 14 points, 287.

so it think im doing pretty good.

overall math has helped me feel gkd about myself, and i am decent at all subjects, straight A+ (98%+) and have on 97 in history

lowk i just realized how much of a nerd i am how do i even have time for cubing sports AND gaming lol

do i have a good trajectory for UCLA guys? @abunickabhi do you think i have a good trajectory for IIT bombay?

Dang, even knowing that much of calculus in 7th grade is very impressive, well done! I hope you're able to continue to be challenged in math; seems like you'll be very good at it!

I am having fun! Last semester I finished Calc 1, am currently studying Calc 2, and will be studying Calc 3 and Linear Algebra next semester.

Good luck! I personally was not a huge fan of Calc 2 or 3 (I know a lot of people who loved them though), but Linear Algebra is definitely a super fun field!

Last semester, I took measure theory and abstract algebra 1. This semester I'm taking differential geometry, Fourier analysis, and grad cryptography (I get to do a research project!)

I'm also doing a directed reading program (DRP) for toric topology where i'm reading and writing a report on selected material from Buchstaber Toric Topology and Lee Smooth Manifolds

Differential geometry is the study of smooth manifolds and smooth maps between manifolds. You're correct to note that "differential" in diffgeo relates to differential calculus! I'll do my best to explain how differentiation works here:
- You may be familiar with the single-variable derivative---the slope (tangent line) of a one-dimensional function at a point.
- You can generalize this to any dimension! Imagine a smooth surface. You can have a tangent plane to that surface instead of a tangent line.
- That's called multi-variable calculus or "Analysis on R^n" when studied more formally/theoretically/technically.
- Manifolds are spaces that locally "look" like a multi-dimensional Euclidean space (R^n) but globally may be curved.
- Classic example: Imagine an ant on a big sphere, or us on Earth. To the ant (or us), the ground looks totally flat (locally). But in reality, it's curved (globally).
- So differential geometry is applying (multi-variable) calculus locally on smooth manifolds and considering smooth maps between smooth manifolds in that sense.

Edit: What I described is mostly limited to differential topology, differential geometry technically adds in other geometric concepts such as metrics, geodesics, curvature, etc that aren't necessarily present in a topological space. The focus is more Riemannian manifolds rather than smooth manifolds in general.

Yes, exactly!! Physicists use differential geometry to study space-time exactly as you said. Differential geometry is extremely important in theoretical physics, maybe the most important aside from like PDE theory.

Yes, Einstein was a huge pioneer of differential geometry! Definitely highly relevant.

The concept of "straight lines on a ball" is geodesics from differential geometry. It doesn't disprove the fifth axiom though because the parallel postulate is only stated to hold for flat (Euclidean) geometry. But yeah, it wouldn't hold necessarily for all curved surfaces.

Wow, some of that stuff seems pretty crazy! I appreciate the explanation of differential geometry; it sounds super interesting, although I most likely will not get that far in math haha

 

[SpeedCubingLord]

algebra is pretty fun right now imo

what are you guys in the phillipines learning? my math teacher is trying to teach us geometric transformations and half the class knows it bro before and half class is too stupid too understand it even though we are in a honors class

like @qwr said, real math isnt being taught in middle school, and ive barely hit the tip of the iceberg. i hope the one subject i like except science does not make me scared.

 

[Caleb Valenzuela]

what are you guys in the phillipines learning? my math teacher is trying to teach us geometric transformations and half the class knows it bro before and half class is too stupid too understand it even though we are in a honors class

like @qwr said, real math isnt being taught in middle school, and ive barely hit the tip of the iceberg. i hope the one subject i like except science does not make me scared.

I just started 7th grade like one or two months ago (yeah uhh don’t question that) and currently i’m learning about square roots and cube roots (pretty easy so far), and before that i was learning about sets and set notation. I seem to be pretty far behind compared to everyone else here. I think i need to lock in on school. I am homeschooled though so i study everything mostly by myself (it’s like 85 myself, 5% ChatGPT, 5% parents, and 5% books when it comes to basic lessons.

 

[SpeedCubingLord]

I just started 7th grade like one or two months ago (yeah uhh don’t question that) and currently i’m learning about square roots and cube roots (pretty easy so far), and before that i was learning about sets and set notation. I seem to be pretty far behind compared to everyone else here. I think i need to lock in on school. I am homeschooled though so i study everything mostly by myself (it’s like 85 myself, 5% ChatGPT, 5% parents, and 5% books when it comes to basic lessons.

umm, caleb. you are 13 years old. square and chbe roots are learnt in 6th grade. and its compulsory.
bro lock in youre being homeschooled you dont have to got at the same pace as others, so go faster, not slower. how about i tutor you in math and you tutor me in cubing?