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Site title: The Math Doctors – Continuing the Mentoring Tradition of Ask Dr. Math ™
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The start of a new year seems like a good time to take a look at the big picture. A question from September raises a big topic: What is mathematics, in general? What does all math – arithmetic, algebra, geometry, trigonometry, calculus, and beyond – have in common?
What does it mean to do math?Eh Doh Kue asked this:
I would like to know what all of math...
Last time, we looked at a problem that had a fairly easy solution, but I had to convince myself that the situation it assumed was actually possible, because the work did not imply its existence, but merely assumed it. Here I want to s...
Last time, we saw several problems where we were given remainders when an unknown polynomial was divided by two or three linear polynomials, and had to find the remainder on division by the product of those divisors. Here we’ll look a...
In searching for questions about polynomial division, I ran across several about problems where you are given the remainders when an unknown polynomial is divided by two or three different small polynomials, and have to find the remainder wh...
Last time, we saw how to divide polynomials using long division, which takes a lot of time and space. For the simplest cases, dividing by a monic linear polynomial \((x-c)\), there is a much more efficient method. We’ll again see both how to...
