The best you can do to start, @Bhavay, is think about how $(2x+1)/2x$ is slighly more than $1$ when $x\ge 1$. So you have $\log 4 + y\log 3$ where $y$ is a bit more than $1$.
I see. So they don't want you to try to solve it. They want you to understand how many solutions it will have. Are you allowed to use graphing calculators?
@Arjun: You are lazy and rude beyond belief. Go away.
Hey everyone, a quick question (sorry for the bad terminology...) - for abelian groups, when I see $\bigoplus_{i \in I} A_i$, should this mean the colimit of the discrete diagram ( discrete = no non-identity morphisms) (where this discrete diagram has $I$ many objects, even if $A_i = A_j$ etc.)
@TedShifrin But it requires some thinking and manipulation and then finding values of t , is there a procedural way to approach these kinds of problem?
one day I shall learn about smooth toposes only to annoy you all by constantly talking about how and why they are definitely the only natural setting for doing differential geometry
Assume consciousness is the experiential manifestation of thought and that thought and physicality are dual mathematical objects in the spirit of Gromov. $F:P \to T$
Hm, interesting. We know rational cohomology of Lie groups completely, $H^*(G; \Bbb Q)$ is just an exterior algebra on odd-dimensional generators. So the EMSS should tell something about cohomology of $G/H$, yeah.
It's fascinating that for a compact Lie group $G$ (or a symmetric space in general I suppose but I don't understand these well), its invariant forms complex determines the homotopy type of $G$.
@TedShifrin Hello Professor. I solved the next question. I have another question, whose answer i know but i don't know why is the answer is answer to that question.
Yeah I have good skills with algebra, but trigo: i have skills, but i used to rote learn (I know how to use stuff but I dont know what would be going on)
There are beautiful ideas in calculus and linear algebra, @icecream. If you want to get into computer graphics/games programming, you want some linear algebra understanding for sure.
I'm going to try to come up with a proof of CGB. It must come from understanding the top Chern class (the Euler class) by reading it off of the characteristic polynomial for the connection.
Yeah, I know lots of my friends who got 95+ but without actually understanding the course. They just got that high because they memorized the questions and how to solve them. BUT im not like them. Well, maybe just recently I've been trying to change.
You should figure out my "embedded" proof as well. For bonus, @Balarka, figure out the boundary term for manifolds with boundary. I've actually not done this in courses. Chern's original proof did this.
Anyhow, if you're going to take a discrete math class for your computer science degree, you might like a book like "How to Think Like a Mathematician," by Houston, @icecream.
If you really want to go back through high school algebra/trig stuff you can, but I'm suggesting a new start that will be more helpful going forward. It doesn't hurt to do a few algebra problems every day "for fun."
It's hard to speak broadly, but I think confidence should ultimately come from understanding. What comes from doing certain standard computations over and over is familiarity. Both are important.
Yup. Sometimes having someone to explain things to also is helpful for building understanding and confidence. Maybe you can find a (remote) study partner :)
Logarithm is a tricky concept for many people. A biologist relative asked me what the point of it is; I had to explain it to her using infection growth.
For computer scientists the point is data is written in binary, and there are $2^n$ binary strings of length $n$.
Thus the famous joke that $\log$ for mathematicians is log base e, $\log$ for biologists is log base 10 and $\log$ for computer scientists is log base 2
$e=\prod_{n=1}^{\infty}\left(1-\frac{1}{\tau^n}\right)^{\frac{\mu(n)-\varphi(n)}{n}}$, where $\mu$ is the Möbius function, $\varphi$ is the Euler function and $\tau$ is the golden ratio
