I finished my bachelors a 2-3 years back in mathematics and working a pretty good job in New York in the tech industry, but I am having trouble deciding what to do next!
My options are either continue down this route and become a product manager, go more heavily into software engineering...
Homework Statement
Hey I'm trying to get a sense of this problem, just starting pde class:
au_x+bu_y+cu=0
Homework Equations
The Attempt at a Solution
Dunno what to do with that last term
Homework Statement
Homework Equations
An equivalence relation on a set A, is for a,b,c in A if:
a~a
a~b => b~a
a~b and b~c => a~c
The Attempt at a Solution
It seems uncomplicated, but I don't know how I would write down a proof. The book I'm using is Topics in Algebra, 1st Edition Herstein
edit: whoops, the title should read, "what to do about textbooks with no solutions"
So I'm trying to learn real analysis (using C.C. Pugh's book) and its going alright until I hit the exercises. There are no solutions! How am I supposed to know I proved something correctly? Is there a website...
Homework Statement
We have a corollary that if f(x) is in the set of Riemann Integrable functions and g(x) is continuous, then g(f(x)) is also a riemann integrable function
Show that if g(x) is piecewise continuous then this is not true
Homework Equations
Hint: take f to be a ruler...
Homework Statement
Given x > 0 and n \in N, prove that there is a unique y > 0 s.t. y^n = x exists and is unique
Homework Equations
Hint is given: consider y = 1. u.b. \{s \in R : s^n < x\}
The Attempt at a Solution
I'm not used to this style of proof (real analysis I), help would be...
Homework Statement
Find the number of roots for the equation x^2+1=0 \mod n \: for \: n = 8,9,10,45
Homework Equations
The Attempt at a Solution
I have no idea where to start. Could someone help me understand?
So we were going over geometric series in my calc class (basic, I know), however I was intrigued by one point that the prof. made during lecture
\frac{\pi^2}{6} = \sum^{\infty}_{n=1}\frac{1}{n^2} = \zeta (2)
That's amazing (at least to me). Looking for the explanation for this, I found a...
I been trying to solve some nested radicals. I've been able to do:
\[\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}\]
Which is pretty cool since it equals to the "Golden Ratio" or \[\frac{\sqrt{5}+1}{2}\]
But I can't seem to do the following:
\[\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\cdots}}}}\]
Using a...
The other day I decided to calculate 1.225 x 36 in my head (this was a calculation in one of my problem sets) and I found that it took me a lot longer than I originally thought. So I was wondering if there was any sort of strategy to gradually improve this skill.
Here's a strategy I am...
Homework Statement
You have a chain of length 10m with 80kg, how much work does it take to lift this chain from one end to 6ft?
Homework Equations
\delta = \frac{10}{80} = .125
The Attempt at a Solution
W = \int{F(x)}\,dx = \int^{6}_{0}{\delta lg}\,dl = \frac{\delta l^2g}{2}...
Homework Statement
It looks deceptively easy, but I can't seem to get it...
\int^{\frac{\pi}{4}}_{0}{\\sec^4{x}\tan^4{x}}\,dx
Homework Equations
\sec^2{x} = \tan^2{x} +1
The Attempt at a Solution
I've tried, but they all end up as trigonometric polynomials
I've already self-studied calculus, so I wanted to go on and learn it in multiple variables. Generally, Apostol seems to have had good reviews for 'pure, prose learning', but how is it to actually learn from it? And if I do should I read the single-variable calculus section?
Thanks
Homework Statement
A crest is created on a string by vibrating it. The crests have two periods on the string which is 3 m long. At what point will the crest have an acceleration of zero?
I had gotten this problem from a science competition and really had no idea how to do it. But I assumed...
Homework Statement
I'm just trying to solve this
\int {\sec^3{x} dx
Homework Equations
sec^2{x} = 1 + tan^2{x}
The Attempt at a Solution
well i was able to simplify it to this:
\int {\sec{x}*\tan^2{x}} dx + \ln{|\sec{x} + \tan{x}|}
but I still was not able to find that new integral
Suppose you have a Cartesian coordinate system with:
a 2uC charge at (0,0) and a -8uC charge at (4,0), why is there only one point in which the EFI is zero (-4,0)? Shouldn't that be the first point where the EFI is zero (so (-5,0),(-6,0)... all have Electric Fields of zero)
The reason I...