Help with Order of Magnitude Estimations and Dimensional Analysis

["pi"mp]

Greetings,

I'm attending a grad school in the fall whose Ph.D. comprehensive exams place a *huge* emphasis on order of magnitude estimations and dimensional analysis problems. I'm much better at problems that involve a little more mathematical playfulness and theory; I'm a little worried about these other kinds of problems.

Does anyone know of a good guide on the internet (or section of a book) that introduces techniques like these? I've tried looking but didn't find anything terribly promising.

Thanks in advance!

 

[HallsofIvy]

What?? A Ph.D. program that emphasizes "order of magnitude" and "dimensional analysis"? Those are ways of getting rough estimates and or typically taught in introductory courses.

 

["pi"mp]

"A DVD has an outer diameter of 12 cm and an inner diameter of 4 cm.
Holding the disk under white light you notice an iridescent rainbow of colors
reflecting off the disk. Based on this give an order-of-magnitude calculation of
the number of data bits encoded on the DVD.""In his dying breath, Julius Caesar reportedly said, “Et tu, Brute?” How
many air molecules from Caesar’s dying breath were contained in your last
breath?"

Yup. The above two questions are copied directly out of old comprehensive exams...and they both really bother me! I'm going in for theory and have never in my life worried about things like this. But I believe you when you say they are very introductory ideas.

 

[Vanadium 50]

Let me show you how you do this.

Light has a wavelength of about half a micron. The disk has an area of about 100 cm^2, or 10^10 square microns. 10^10/(.5)^2 = 40 billion bits, or 5 GB. (I think 4.7 GB is the actual number)

How many McDonald's are there in the US?
How many barbers?
Why does a tire last 10's of thousands of miles and not 10's or millions?

 

[analogdesign]

I'd look into business school primers as those types of questions are extremely popular for investment banks, hedge funds, and management consultancies.

They are fantastic Ph.D. comprehensive exam problems because the skills you acquire learning to solve problems like that are incredibly valuable in the working world. I can't tell you how important it is to be able to quickly evaluate ideas on an order-of-magnitude basis to help separate the wheat from the chaff.

 

["pi"mp]

Thanks a lot guys. Vanadium 50, do you have any resources you can think of to help with these skills? The three other problems you mentioned, I wouldn't know how to deal much with. Thanks!