When teaching the integration method of u-substitution, I like to emphasize its connection with the chain rule of integration. Likewise, the intimate conn...
Published: Aug 10, 2026
My teacher claims that when an equation in variables $x_1,x_2,\ldots,x_n$ has no solutions, you should denote this fact with $(x_1,x_2,\ldots,x_n)\in\varn...
Published: Aug 10, 2026
Probability of getting a head in coin flip is $1/2$. If the coin is flipped two times what is the probability of getting a head in either of those attempt...
Published: Aug 10, 2026
When solving linear nonhomogeneous equations, we deal with two types of solutions: particular homogeneous Why do we have these two types of solutions for ...
Published: Aug 10, 2026
While trying to find find a formula to calculate the length of the golden spiral I came across the sum of the Fibonacci numbers. I noticed that $$\text{Fi...
Published: Aug 10, 2026
Is $3x + 4x^2 + y$ a valid linear combination of $x$? I'm not sure if "a linear combination of $x$" allows for other terms than $x$ which would just ...
Published: Aug 10, 2026
Wordle is a viral web game where you have up to six attempts to guess a secret five-letter English word* using the letters A-Z. After each $5$-letter gues...
Published: Aug 10, 2026
Recently, I had a couple of students give me an interesting way of converting from vertex form to factored form that I've never seen before. One told...
Published: Aug 10, 2026
I'm trying to find the derivative of $x^2\sin x$ using only the limit definition of a derivative. I've tried two approaches, one using the diffe...
Published: Aug 10, 2026
My group theory is very rusty. If I want to just start with left inverses and left identities, must I link the axioms, or can I leave them independent? e....
Published: Aug 10, 2026