Check out this video: https://www.khanacademy.org/math/recreational-math/puzzles/brain-teasers/v/3-d-path-counting-brain-teaser
Look at trinomial functions for general case
I had a 3.6 gpa and 3.9 math gpa... Some leadership experiences / TA.
Post college won a 2 national tech competitions
I guess one of my problems is how to focus my interests
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?
Ha ha ha! This is imranq from the MEGA Society! I bet you can feel my overwhelming intellect already. And as you can see, even my own initials spell IQ. How I laugh at you mere mortals...
On a more serious note, however, the Stanford-Binet scale (if I remember correctly) was not used to measure...
Actually in my university (which is somewhat well regarded), you can easily get a math major without taking number theory (but you may be forced to take something like partial differential equations).
Grad school seems to be a general route (for anything really since math majors have analytical skills to pursue medicine, law, MBA, etc.). However, if the economy were better, you could be working for investment banks (contrary to popular perception, they still exist) and make 300k+ to make even...
I don't know much about the inherent nature of mass (or matter) but I do know that no "matter" what happens, we will constantly be explaining the meanings behind the meanings behind the meanings forever, (I mean, what is energy per say?). Instead, take a look at the different types of mass and...
So I went ahead and got it (without a response from PF!). Luckily, the book is amazing in depth and accessibility. It is hefty, a full 1000 pages and costs $99 (but I got it for $50 through a border's deal). I can see this becoming useful in explaining some of the conceptual stuff in future math...
For your information, you don't have to take both Math I and IIC since they are looked at separately and are counted equally in college admissions. Personally, I would recommend you take Math IIC since it is curved very well (you can get 8 wrong and still get an 800!), but it is harder than Math...
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...
Personally, I liked that \[\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}
= \dfrac{1}{1 + \dfrac{1}{1+\frac{1}{1+...}}} = \phi\] or the golden ratio. Also, note (since phi is defined by those recursive sequences) that \frac{1}{\phi} = \phi -1
Thanks, now I get it.
But is there a way to find out where the sequence converges? We do know that \sqrt{3} < \lim_{n\rightarrow\infty} f(1,n) < 2 . Where:
f(a, b) = \begin{cases}
\sqrt{a + f(a+1, b-1)} & b > 0
\0 & b = 0 \end{cases}