This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with prime numbers, but other tha...

From the Question $y''=1+(y')^2$ I used Reduction of Order by taking $y'=z$ to get, $$z\left(\frac{dz}{dy}\right)=1+z^2$$ Solve the eq...

Long ago I realized that manipulation of derivatives was possible using algebraic quantities. One could take a differential instead of derivatives $$ d[\s...

I've been using the book "Topoi: A Categorial Analysis of Logic" by Robert Goldblatt. I found it intuitive and fun, but I feel like some parts are mi...

Assuming that I know that: 1) A plane isometry is either a rotation, a traslation, a reflection, or a glide reflection 2) Every isometry can be expressed ...

How do I go about proving this? Two subspaces $V$ and $W$ of $\mathbb{R}^n$ are called complements if any vector $x$ in $\mathbb{R}^n$ can be expressed un...

Q&A for people studying math at any level and professionals in related fields

If $A, B$ and $A + B$ are all $n × n$ invertible matrices. Prove that $A^{−1} + B^{−1}$ is invertible and the inverse is $A(A + B) ^{−1}B$. I am afraid I ...

For which $n$ is the sum: $$\sum_{k=0}^{n}10^k$$ a prime number? Are they finite?

I found that Kullback-Leibler loss, log-loss or cross-entropy is the same loss function. Is the logistic-loss function used in logistic regression equival...