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I'm trying to understand the construction of the dirac operator on a manifold, but actually I guess that doesn't really matter for the question ...
How do I prove the following statement by induction? $$n^2 \lt 2^n$$ $P(n)$ is the statement $n^2 \lt 2^n$ Claim: For all $n \gt k$, where $k$ is any inte...
I realise how to find the sum up a finite arithmetic series when the common ratio is the same each time. 1/2n(2a+(n-1)d) However what happens when d (the ...
How do we show that equality holds in the triangle inequality $|a+b|=|a|+|b|$ iff both numbers are positive, both are negative or one is zero? I already s...
Imagine if we used a base $\pi$ number system, what would it look like? Wouldn't it make certain problems more intuitive (eg: area and volume calcula...
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I'm having difficulty entering the the correct syntax into my ti 89 calculator to differentiate logarithms. So far this is what I cam up with for f&#...
In my Engineering Dynamics class, I've encountered this equation $ads=vdv$. I could not wrap my head around why it was true, but I was able to come u...
In the figure given below, PQR is a triangle with sides PQ=10, PR=17, QR=21. ABCD is a square inscribed in the triangle. I want to find perimeter of squar...
Let $A$ be an algebra over a field $K$. If $D_1$ and $D_2$ are derivations of $A$, show that $D_1 \circ D_2$ is not necessarily a derivation (it is if $D_...
Suppose we have the matrix $A = \begin{bmatrix} 4 &6 \\ -8 &-12\\ \end{bmatrix} $ and the vector $b = \begin{bmatrix} 3\\ -6 \end{bmatrix} $. So I...
