Mathstodon

0 posts0 participants0 posts today

David GraylessIn <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a>, a polynomial is a <a href="https://mastodon.social/tags/mathematicalExpression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematicalExpression</a> consisting of <a href="https://mastodon.social/tags/indeterminates" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#indeterminates</a> (also called <a href="https://mastodon.social/tags/variables" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#variables</a>) and <a href="https://mastodon.social/tags/coefficients" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#coefficients</a>, that involves only the operations of <a href="https://mastodon.social/tags/addition" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#addition</a>, <a href="https://mastodon.social/tags/subtraction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#subtraction</a>, <a href="https://mastodon.social/tags/multiplication" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#multiplication</a> and <a href="https://mastodon.social/tags/exponentiation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#exponentiation</a> to <a href="https://mastodon.social/tags/nonnegativeInteger" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nonnegativeInteger</a> powers, and has a finite number of <a href="https://mastodon.social/tags/terms" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#terms</a>. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1. <a href="https://mastodon.social/tags/Polynomials" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Polynomials</a> appear in many areas of mathematics and science.

Prof. Sally KeelyAttn Calc II students: This is a fun little integral. \( \int 2^{\ln(x)}dx \) A substitition \( u=\ln(x) \) won't work since there is no \( \frac{1}{x} \) to make the match. <a href="https://mathstodon.xyz/tags/integration" class="mention hashtag" rel="tag">#integration</a> <a href="https://mathstodon.xyz/tags/exponentiation" class="mention hashtag" rel="tag">#exponentiation</a>Think about before reading on.Nifty trick! Since \( 2=e^{\ln(2)} \), then \( 2^{\ln(x)} = (e^{\ln(2)})^{\ln(x)}=(e^{\ln(x)})^{\ln(2)}=x^{\ln(2)} \) Now the integral becomes \( \int x^{\ln(2)}dx = \frac{1}{1+ln(2)} x^{1+\ln(2)} + C \) Swapping from an constant-to-variable to a variable-to-constant made a world of difference. Sweet!

tc<a href="https://mathstodon.xyz/tags/functionalprogramming" class="mention hashtag" rel="tag">#functionalprogramming</a> Many people's vote for most <a href="https://mathstodon.xyz/tags/beautiful" class="mention hashtag" rel="tag">#beautiful</a> construct in <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="tag">#math</a> is \[ e^{i\pi}+1=0. \]Yeah, maybe. But I think a close contender (if you include the <a href="https://mathstodon.xyz/tags/CS" class="mention hashtag" rel="tag">#CS</a> realm) is \[ \lambda b.\lambda e.eb . \]This serves as the complete <a href="https://mathstodon.xyz/tags/Church" class="mention hashtag" rel="tag">#Church</a> encoding of <a href="https://mathstodon.xyz/tags/exponentiation" class="mention hashtag" rel="tag">#exponentiation</a> in <a href="https://mathstodon.xyz/tags/LambdaCalculus" class="mention hashtag" rel="tag">#LambdaCalculus</a>, driving home subtler points about <a href="https://mathstodon.xyz/tags/function" class="mention hashtag" rel="tag">#function</a> <a href="https://mathstodon.xyz/tags/mapping" class="mention hashtag" rel="tag">#mapping</a> and ordered pairs and the primacy of exponentiation over add/mult, both of which have uglier <a href="https://mathstodon.xyz/tags/LC" class="mention hashtag" rel="tag">#LC</a> representations.<a href="https://en.wikipedia.org/wiki/Lambda_calculus#Arithmetic_in_lambda_calculus" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://en.wikipedia.org/wiki/Lambda_calculus#Arithmetic_in_lambda_calculus</a>

tc<a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="tag">#math</a> <a href="https://mathstodon.xyz/tags/education" class="mention hashtag" rel="tag">#education</a> <a href="https://mathstodon.xyz/tags/school" class="mention hashtag" rel="tag">#school</a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="tag">#arithmetic</a> At risk of pointing out the obvious, here's something that didn't occur to me in these plain terms until last week:Everyone from little kids on up understands base-10 numbers to one degree or another, and yet decoding place-value <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="tag">#numbers</a> requires using <a href="https://mathstodon.xyz/tags/addition" class="mention hashtag" rel="tag">#addition</a>, <a href="https://mathstodon.xyz/tags/multiplication" class="mention hashtag" rel="tag">#multiplication</a>, and <a href="https://mathstodon.xyz/tags/exponentiation" class="mention hashtag" rel="tag">#exponentiation</a> in concert.

Recent searches

Search options

Administered by:

Server stats:

#exponentiation