updates
Proving Handshake Theorem.
I am currently learning Graph Theory and I've decided to prove the Handshake Theorem which states that for all undirected graph, $$\sum_{u\in V}\deg(...
Apr 22, 2026
Archive: Updates
![Remainder when $5^{5555}$ is divided by $10000$. [duplicate]](https://news.conceivablytech.com/uploads/remainder-when-5-5555-is-divided-by-10000-duplicate_720.jpg)
updates
Remainder when $5^{5555}$ is divided by $10000$. [duplicate]
Find the remainder when $5^{5555}$ is divided by $10000$. A step by step guide with explanation for a beginner student in modular arithmetic is needed.
Apr 22, 2026
updates
The expectation of absolute value of random variables
I need some help with the following problem: Let $X_1,...,X_n$ be a random sample from Normal$(0,1)$ population. Define $$Y_1=| {{1 \over n}\sum_{i=1}^{n}...
Apr 22, 2026
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Determine fraction of inch from decimal
I am working with data for the width and height of books. The data is in decimal form, such as 7.563, which I need to display as a fraction: 7 9/16 in. Th...
Apr 22, 2026
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Gershgorin circle theorem and similarity transformations
Consider the following problem, that was part of an old exam I am studying for: Let $$ A = \begin{pmatrix} 4 & 0 & 2\\ -2 & 8 & 2\\ 0 &...
Apr 22, 2026
updates
Importance of the Artin-Wedderburn theorem
I feel silly asking this, but what is the importance of the Artin-Wedderburn theorem in Algebra? In A First Course in Noncommutative Rings, T.Y. Lam calls...
Apr 22, 2026
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Evaluating differential entropies with Matlab: NaN issue
With Matlab I am trying to evaluate differential entropies. These are integrals like $$\int_\mathbb{R} p(x) \log (p(x)) \mathrm{d}x$$ where $p(x)$ is a pr...
Apr 22, 2026
updates
Examples to help understand discrete metric space.
I have been asked to provide examples (or proofs that none exist) regarding some points and subsets of discrete metric spaces. I believe I can set the int...
Apr 22, 2026
updates
Notation for partial derivatives
I thought that the meaning of $$ \frac{\partial f(x, y, z)}{\partial x} $$ is differentiation on $x$ with fixed $y$ and $z$. So $(x, y, z)$ in the numerat...
Apr 22, 2026
updates
How to find the derivative of $(2x+5)^3(3x-1)^4$
How to find a derivative of the following function? $$\ f(x)=(2x+5)^{3} (3x-1)^{4}$$ So I used: $$(fg)'= f'g + fg'$$ and $$(f(g(x)))'=...
Apr 22, 2026
