/math/: Math general

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Anonymous

/math/: Math general 2016-01-10 22:34:34 Post No. 7774631

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/math/: Math general 2016-01-10 22:34:34 Post No. 7774631

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You know the drill:

Ask math-related questions or post math problems, have people discuss them with you.

No college advice, no textbook recs.

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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.

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What is kans acadimy?

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>>7774635

define worth taking

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>>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?

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>>7774631

Could anyone recommendate me a texbook all about college advice?

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>>7774631

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

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>>7774655

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

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>>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...

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>>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?

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>>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

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>>7775146

In your one you forgot the minus in front

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>>7775149

Fuck me I need glasses

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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.

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>>7774631

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

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>>7775146

Is high school fun for you so far?

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>>7775363

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

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>>7775392

Does order matter?

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>>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

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>>7775411

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

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>>7775469

You are welcome.

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>>7775469

use the 30!/10!

the way the question is phrased means that order definitely matters

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>>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)

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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.

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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?

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>>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]

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>>7776063

The answer is 6

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>>7776073

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

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>>7776138

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

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>>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?

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>>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?

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>>7775611

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

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What's your favorite maths book?

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>>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?

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2x-1

------- > 0

X

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

Will I struggle? (Only taking these two classes)

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>>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

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>>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)

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