/math/: Math general

Is Calculus 3 worth learning? It isn't in the curriculum and I have been told Cal 2 is all I will need.

Starting mechanical engineering in college this September.

What is kans acadimy?

>>7774635
define worth taking

>>7774635
What kind of shitty fucking school do you go to where calc 3 (that's vector calc at your school, right?) is not required for mech eng?

>>7774631
Could anyone recommendate me a texbook all about college advice?

>>7774631
Could anyone give me advice for college about what textbooks should I be getting?

>>7774655
A Mathematician's Survival Guide: Graduate School and Early Career Development by Krantz

>>7774651
>Mech E.
>Calc 3 not required
At first I was like "go easy most schools don't require computer science students to take it" and then I saw that...

>>7774631
It is a well-known fact that an operator A (on a separable Hilbert space) which is normal modulo compact operators happens to be unitarily equivalent to a Wiener-Hopf operator B. What does the shape of the essential spectrum of A tell us about the index of B?

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Could someone please explain this?

Why doesn't this rule apply to the second?

>>7775128
It didnt apply to the first. Both are odd functions. The negative sign of the denominator is not considered in the first equation.

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>>7775136
Then pls explain this

>>7775146
In your one you forgot the minus in front

>>7775149
Fuck me I need glasses

Coming from EE undergrad, doing physics theory now for grad school. I've taken courses in calc 1-3 and ODE's, never a formal algebra (linear or otherwise) class, and no analysis or topology. Somewhat good at linear algebra from my quantum coursework.

I feel behind my group mates in math, who all did physics or math/physics undergrad. Is there a good resource for catching up, so I'm more fluent in math necessary to do work at this level? Texts on "math for physicists" with problems I could work? I can Wikipedia a lot of stuff to get through papers, but I don't know the basics life they do to pull things up and know where to work from.

>>7774631
Does anyone know if there has been any verification of the validity of the work published by Mochizuki dealing with the abc conjecture?

>>7775146
Is high school fun for you so far?

>>7775363
There was a conference in England. It didn't get anywhere.

>>7775392
Does order matter?

>>7775405
idk senpai that's all the problem says

lol idk why i am asking this on /sci/ i am a fucking retarded ass person who should go off themselves lmao

>>7775411
Either [math]\binom{30}{20}[/math] or [math]\frac{30!}{10!}[/math]

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>>7775427

>>7775469
You are welcome.

>>7775469
use the 30!/10!
the way the question is phrased means that order definitely matters

>>7775332
Mathematical methods in the physical sciences by Boas
Mathematical methods of classical mechanics by Arnold
Mathematics of Classical and Quantum Physics by Byron and Fuller (Dover = cheap)
Mathematics for Physicists by Krzywicki and Dennery (also dover)

Trying to show this limit exists (not necessarily estimate its value):
[eqn]\lim_{t\to+\infty}\int_0^1{\frac{\mathrm{d}x}{\sqrt{1 - x^2}}\,\log\left[1 - \sin^2(x t)\,\frac{1 - x^2}{1 + a x^2}\right]},[/eqn]
with [math]a \ge 0[/math].

No luck on Math Exchange so far, I wonder if /sci/ can help me with this.

I'm getting my BEng in a few months. Supposedly my major is one that most heavily relies on probability, statistics etc (describing signals), but I never really got my head around it. Is there a good video (series?) I can watch to learn about it?

>>7776063
Ok, not sure with it didn't format that, trying with inline TeX:
[math]\lim_{t\to+\infty}\int_0^1 \frac{\mathrm{d}x}{\sqrt{1 - x^2}}\,\log\left[1 - \sin^2(x t)\,\frac{1 - x^2}{1 + a x^2}\right][/math]

>>7776063

The answer is 6

>>7776073
That's some shitty notation. What's the scope of x?

>>7776138
What do you mean? This is an integral over the reals, with the integration variable x in [0, 1]. It is standard notation.

>>7776144
I mean, is the integrand just 1/sqrt(...) and x is free in the log[...], or is x bound in the whole thing?

Also, what is a? Is it real, complex, natural?

>>7776164
x is bound to the whole integral (or I would have used a different name for the variable).
As for a, as I specified in my original post it is a non negative (real) constant.

Hope that clarifies everything.

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Hello /sci/ How do I get disposable income out of this equation?

I'm really stuck and any help is appreciated

The equilibrium is normally

Y= C0+C1(Yd)+I+G-T

Yd can also be (Y-T)

Thanks

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Is the determinant of a tensor product the product of the determinants?
If so, would this be true in the infinite dimensional case?

>>7775611
I agree senpai, thanks Im just retarded, I am really stupid loll fuck

What's your favorite maths book?

>>7776604
For finite dimension you're close but it's the product of the determinants raised to the dimension of each of the original spaces, see:

https://en.wikipedia.org/wiki/Kronecker_product#Relations_to_other_matrix_operations

What exactly is the notion of determinant you're using for infinite dimensional matrices?

2x-1
------- > 0
X

I am taking both Calc 3 and Linear Algebra over the summer in 8 weeks

Will I struggle? (Only taking these two classes)

>>7776073
t only appear in the sin term, which averages to 1/2 for all practical purposes since the other stuff is continuous, differentiable and has all the usual boring properties

>>7776668
Nice. Thanks for that.
I'm calculating functional integrals to find gap equations. To evaluate them I need to find the determinants of the Dirac operator (amongst other things)