Problem 42 is simple as (Z,+) is an abelian group isomorphic to mZ

Problem 39 Z7 which is a cyclic of order 7 generated by 1 so order of 2 is 3 as 2^3 is isomorphic to 1 mod(7)

Regarding level 43 it's has simple pole at Z=1 and use Cauchy residue theorem which lets to 2πi Res(f,1) which is 2πi

Make a video on vector I am able to understand the formula but i cannot use it in real life so i think i am weak in applications so if u can make a video on that it will be helpful

Roots of x^4-2 are 2^1/4 ,-2^1/4,2^1/4i and -2^1/4i so its splliting field is Q(2^1/4,-2^1/4,2^1/4i,-2^1/4i)=Q(2^1/4,i) To show the irreducibility just use eisenstien critirion And degree of splliting field is [Q(2^1/4,i):Q]=[Q(2^1/4):Q(i)][Q(i):Q] Which is 4×2 which is 8 which we can easily find the degrees of the minimal polynomial of the roots over their extension Solution of problems 48 pretty easy

The same logic is not used in the first two examples when solving for the second set of two numbers. It’s contradicts itself.

4:07 I'm in high school and I love this part of math :) Calculus

Mine lvl 21 im in class X (India) Ap comes before log Log comes in 11th Mostly everything in 11th n 12th The vectors is also in 11th physics

9025

Isn’t this cool ? No

Made to lv50 but I think most math students can make to roughly this level, with probably a few levels missing (I know some people don’t do Galois theory, differential geometry or algebraic topology). And anything after level 50 is hell.

25

This is racist...

Great problem ❤ Seems difficult, but it’s just „base × height“ 😅 The problem is therefore reduced to figuring out the base area 😊 Draw a perpendicular from the circle center to the dashed line, from there follow the dashed line until it touches the circle, then connect this point with the center. This is a right triangle, with side lengths 2, 4 and 2√3. Therefore, it is also a 30º-60º-90º triangle which has half the area of an equilateral triangle. So the total base area is given by „area of the full circle - area of a 120º circle sector + area of an equlateral triangle with side length 4“ or 16π - 16π/3 + 4√3 = 4(8π/3 + √3). So the volume is 40(8π/3 + √3).

היכן רשום בשרטוט התחלתי מרובע משיק בנקודה מרכז המעגל כל זה לא שווה כלום

2:06 it's 19446 easy thanks for it tricks 😊👍

I am amongst the top 5% yayy

Can we differentiate by taking equation as lnx=ln25/x I dont know please reply

This can't be it. I'm a physics student and can do all of these with the exception of topology (I can work only with the basics). Is this enough for a math major, actually?

1st cookie: 0:45 2nd cookie: 1:52 3rd cookie: 3:06

Thumbnail : gauss divergence theorem

Then try some advanced determinant calculus

That thumbnail is so disrespectful bro

3:56 1093

1944.6

3:35 9025

Oh wow! I never knew you could do it like that! This helped so much! Thank you!

301.59 cubic metres ❤

Wait eigens value in level 35 isn't in jee syllabus yet. how y'all covered it?? Have you been preparing btech syllabus as well

Bru some of the higher levels are easier than lower ones

me watching as a middle schooler

9025

Thanks from Morocco

320pi/3+20sqrt(12) 320pi/3+40sqrt(3)

If you don't feel geometry you can't do it. Cuz maths isn't all about just answers, it's an art.