general
Number of intersections in a venn diagram with 8 circles
I am trying to calculate the number of intersections one would have in a Venn diagram with 8 overlapping circles but do not know where I would start. Any ...
Apr 08, 2026
Archive: General
general
First book on algebraic graph theory?
I really like abstract algebra and I have come to appreciate graph theory more and more. I would like to check out algebraic graph theory to see what it&#...
Apr 08, 2026
general
How is "n+n/2+n/4....1" equal to "2n-1" using the formula for geometric series?
I never knew not having good knowledge of basic maths will be so crippling!! So please help me out this time. I'll be working on my maths from today ...
Apr 08, 2026
general
Difference between convergence in measure and convergence almost everywhere
This question is an extension of a question asked earlier. Let $(X,\mathcal{M},\mu)$ be a measure space and let $f_{n}: X \to Y$, where $\{f_{n}\}$ is a s...
Apr 08, 2026
general
PDE initial value problem
Show that the solution of the initial value problem for $u_t+u_x=\cos ^2 u$ is given by $u(x,t)=\tan^{-1} \{ \tan [u_o(x-t)]+t\}$, where $u_0(x)$ is the i...
Apr 08, 2026
general
Meaning of Dot Products in Regards to Linear Algebra
I'm currently taking an intro to linear algebra course. We have reached the section on dot products and I fail to understand the meaning of it. What ...
Apr 08, 2026
general
Prove by the limit definition that the limit of a piecewise function is 1.
Prove by definition that: $$\begin{equation*} \lim_{x \rightarrow 1} f(x)=1 \end{equation*},$$ Where,$$\begin{equation*} f(x) = \left\{ \begin{array}{rl} ...
Apr 08, 2026
general
Find the eigenvalues of a 3 x 3 matrix
I have a question on determining eigenvalues for a given matrix A: $$ A= \begin{bmatrix} 2 & 1 & 2 \\ 0 & 2 & -1 \\ 0 & 1 & 0 \\ \...
Apr 08, 2026
general
Mr. Jones owns 4 pairs of pants, 7 shirts, and 3 sweaters.
In how many ways may he choose 2 of the pairs of pants, 3 of the shirt, and 1 of the sweaters to pack ?
Apr 08, 2026
general
Clairaut's Theorem And continuity of a multivariate function
Is showing that $f_{xy}$ is not equal to $f_{yx}$ at a given point sufficient/good to show that a function is discontinuous there? Can you also suggest a ...
Apr 08, 2026
