The Math Doctors

Hyperbolic and Circular Functions and Complex Numbers

What Are Hyperbolic Functions?

Solving Polynomial and Rational Inequalities

Exploring Descartes’ Rule of Signs

Completing the Square for Quadratic Equations

Trig and u-Substitutions: Sign Problems

Another Tricky Integration by Substitution

When Integration by Substitution Goes Wrong

What is the Essence of Mathematics?

Vacuous Solutions: Correct, But Not Really

Polynomial Remainder Problems: Changing the Conditions

Finding a Polynomial Remainder, Given Other Remainders

How (and Why) Synthetic Division of Polynomials Works

How (and Why) Long Division of Polynomials Works

Searching for Rational Zeros of Polynomials

What’s the Difference? How the Meaning Gets Twisted

Is a Circle One-Dimensional or Two-Dimensional?

Pigeonhole Principle II: Sets, Subsets, and Sums

Pigeonhole Principle I: Paths, Penguins, and Points

Sample Standard Deviation as an Unbiased Estimator

Formulas for Standard Deviation: More Than Just One!

Standard Deviation and Its Rivals

Arranging Letters in Words, Revisited

Is There More Than One Standard Form for an Equation?

A Cubic Challenge