 Nov 2020

betterexplained.com betterexplained.com

We say i (lowercase) is 1.0 in the imaginary dimension Multiplying by i is a 90degree counterclockwise turn, to face “up” (here’s why). Multiplying by i points us South It’s true that starting at 1.0 and taking 4 turns puts us at our starting point: And two turns points us negative: which simplifies to: so
Great explanation of why \(i=\sqrt1\)

Imaginary numbers seem to point North, and we can get to them with a single clockwise turn. Oh! I guess they can point South too, by turning the other way. 4 turns gets us pointing in the positive direction again It seems like two turns points us backwards
Imaginary numbers explained in plainenglish

Imaginary numbers let us rotate around the number line, not just move sidetoside.
Imaginary numbers Another graph:
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 Oct 2020

www.its.caltech.edu www.its.caltech.edu
 Sep 2020

pitt.edu pitt.edu

Abby's favorite subject in high school
Math

 Jul 2020

en.wikipedia.org en.wikipedia.org

In logic, functions or relations A and B are considered dual if A(¬x) = ¬B(x), where ¬ is logical negation. The basic duality of this type is the duality of the ∃ and ∀ quantifiers in classical logic. These are dual because ∃x.¬P(x) and ¬∀x.P(x) are equivalent for all predicates P in classical logic


en.wikipedia.org en.wikipedia.org
 Jan 2020

en.wikipedia.org en.wikipedia.org

en.wikipedia.org en.wikipedia.org

stackoverflow.com stackoverflow.com

en.wiktionary.org en.wiktionary.org

en.wiktionary.org en.wiktionary.org
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 Aug 2019

tutorial.math.lamar.edu tutorial.math.lamar.edu

We won’t need these facts much over the next couple of sections but they will be required on occasion
Nonetheless, they should be thought as an important method of mathematics.


tutorial.math.lamar.edu tutorial.math.lamar.edu

Last, we were after something that was happening at x=1x=1x = 1 and we couldn’t actually plug x=1x=1x = 1 into our formula for the slope. Despite this limitation we were able to determine some information about what was happening at x=1x=1x = 1 simply by looking at what was happening around x=1x=1x = 1. This is more important than you might at first realize and we will be discussing this point in detail in later sections.
This reminds me of the exercise we had this morning in class.

Likewise, at the second point shown, the line does just touch the graph at that point, but it is not “parallel” to the graph at that point and so it’s not a tangent line to the graph at that point.
A visual representation of a Tangent Line is very useful, I honestly wasn’t visualizing what a Tangent Line was, in my head.


tutorial.math.lamar.edu tutorial.math.lamar.edu

We will be seeing limits in a variety of places once we move out of this chapter.
Will the L’Hospital method be explained in this chapter?

 Apr 2019

www.irrodl.org www.irrodl.org

On the Efficacy of Open Educational Resources: Parametric and Nonparametric Analyses of a University Calculus Class

 Aug 2018

www.nytimes.com www.nytimes.com

Facebook’s chief concern, he said, was a feature of the proposal called a “private right of action.” Unlike the Obama bill, which left most enforcement to the F.T.C., Mactaggart proposed letting consumers sue companies that violated the law. (Illinois had included such a right in its biometrics law, allowing Licata to sue Facebook.) Facebook feared that if interpretation of the new rules was left to juries, rather than regulators, it would take years just to determine what the company’s compliance obligations were. “We support more disclosure in principle,” Castleberry explained to me. “But the stakes are just much higher with the private right of action.”
aka, we could bleed too much here because of the small deltas... Here's a good example of where, if you can aggregate things, the total seems much larger from afar compared with smaller injustices which are all appropriately accounted and then tallied. Think calculus...

 Apr 2018

www.tandfonline.com www.tandfonline.com

So I started thinking, Where can I do this [kind of math] all the time? … I started talking to my dad and he was like, “Well engineering is somewhere where you could do this … if you want to do the math all the time, then go into engineering.”
It's curious that the Calculus teacher didn't recognize Katie's excitement about the problem or that different types of careers using Calculus were not part of the classroom discussions.

 Feb 2018

www.insidehighered.com www.insidehighered.com

Integrating Technology, Homework Help and Calculus

 Feb 2014

www.tweaktown.com www.tweaktown.com

The Backblaze environment is the exact opposite. I do not believe I could dream up worse conditions to study and compare drive reliability. It's hard to believe they plotted this out and convened a meeting to outline a process to buy the cheapest drives imaginable, from all manner of ridiculous sources, install them into varying (and sometimes flawed) chassis, then stack them up and subject them to entirely different workloads and environmental conditions... all with the purpose of determining drive reliability.
The conditions and process described here mirrors the process many organizations go through in an attempt to cut costs by trying to cut through what is perceived as marketinghype. The cost differences are compelling enough to continually tempt people down a path to considerably reduce costs while believing that they've done enough duediligence to avoid raising the risk to an unacceptable level.
