Everyone loves the “baby Gauss story” in which Gauss amazes his teacher by quickly summing the first 100 positive integers in a flash of brilliance—he adds the first to the 100th, the second to the 99th, and so on to get the sum of fifty 101s to obtain 5050. (Brian Hayes has a great article…
Tag: calculus
Calculus in politics
In his October 1996 editorial in the Notices of the American Mathematical Society, “Mathematics Is an Edifice, Not a Toolbox,” Hugo Rossi wrote: In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his…
E-Z Pass, speeding tickets, and the mean value theorem
On Monday I gave a lecture on the mean value theorem in my Calculus I class. The mean value theorem says that if is a differentiable function and , then there exists a value such that . That is, the average rate of change of the function over must be achieved (as an instantaneous rate…
Joke of the day
Two mathematicians walk into a bar. One is complaining about the state of mathematics education in America. “The average person just doesn’t know any math,” she exclaimed with disgust. The second mathematician said that he didn’t think things were so bad. After they placed their drink order with the server, the man excused himself to…
Wobbly tables and the intermediate value theorem
Tomorrow I’ll be introducing the intermediate value theorem (IVT) to my calculus class. Recall the statement of the IVT: if is a continuous function on the interval and is between and , then there exists a value such that . In other words, achieves all of the intermediate values between and . This is a very underappreciated theorem…
Line Rider Calculus
The first time I saw Line Rider in action, I knew I should use it for a calculus class, but I didn’t know how. Recently 360 wrote about using Line Rider in a calculus course, and so did Teaching College Math, who suggested creating a video of the action using the screen capture software Jing. This week’s topic in…
David Richeson: Division by Zero 