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Blog Profile / The Endeavour

Filed Under:Academics
Posts on Regator:989
Posts / Week:5.4
Archived Since:April 26, 2011

Blog Post Archive

How well does sample range estimate range?

15 hours agoAcademics : The Endeavour

I’ve been doing some work with Focused Objective lately, and today the following question came up in our discussion. If you’re sampling from a uniform distribution, how many samples do you need before your sample range has an even chance of covering 90% of the population range? This is a variation on a problem I’ve […]

Integration trick

Here’s a clever example from Paul Nahin’s new book Inside Interesting Integrals. Suppose you want to evaluate Since the range of integration is symmetric around zero, you might think to see whether the integrand is an odd function, in which case the integral would be zero. (More on such symmetry tricks here.) Unfortunately, the integrand […]

Experts vs Professionals

Working with professionals can be a joy. Not only can they solve your problem, they may help you see what problem you should solve. I’ve had several instances lately when I hired a pro to do something I’d attempted myself. In each case I was very pleased and wondered why I hadn’t done this sooner. […]

What do you mean by can’t?

You can’t subtract 4 from 3 (and stay inside the natural numbers, but you can inside the integers) You can’t divide 3 by 4 (inside the ring of integers, but you can inside its field of fractions, the rational numbers). You can’t take the square root of a negative number (in the real numbers, but […]

Optimism can be discouraging

Here’s an internal dialog I’ve had several times. “What will happen when you’re done with this project?” “I don’t know. Maybe not much. Maybe great things.” “How great? What’s the best outcome you could reasonably expect?” “Hmm …  Not that great. Maybe I should be doing something else.” It’s a little paradoxical to think that […]

Titles better than their books

What got you here won’t get you there. I’ve been thinking about that title lately. Some things that used to be the best use of my time no longer are. I bought Marshall Goldsmith’s book by that title shortly after it came out in 2007. As much as I liked the title, I was disappointed […]

Public reaction to Ebola

Ebola elicits two kinds of reactions in the US. Some think we are in imminent danger of an Ebola epidemic. Others think Ebola poses absolutely zero danger and that those who think otherwise are kooks. Nothing can be discussed rationally. Even narrow scientific questions lead to emotionally-charged political arguments. Those who have a different opinion […]

John Napier

Julian Havil has written a new book John Napier: Life, Logarithms, and Legacy. I haven’t read more than the introduction yet — a review copy arrived just yesterday — but I imagine it’s good judging by who wrote it. Havil’s book Gamma is my favorite popular math book. (Maybe I should say “semi-popular.” Havil’s books […]

Taking responsibility for the mistakes of others

The version of Windows following 8.1 will be Windows 10, not Windows 9. Apparently this is because Microsoft knows that a lot of software naively looks at the first digit of the version number, concluding that it must be Windows 95 or Windows 98 if it starts with 9. Many think this is stupid. They […]

Wouldn’t trade places

Last week at the Heidelberg Laureate Forum, I was surrounded by the most successful researchers in math and computer science. The laureates had all won the Fields Medal, Abel Prize, Nevanlinna Prize, or Turing Award. Some had even won two of these awards. I thought about my short academic career [1]. If I had been […]

The great reformulation of algebraic geometry

“Tate helped shape the great reformulation of arithmetic and geometry which has taken place since the 1950?s.” — Andrew Wiles At the Heidelberg Laureate Forum I has a chance to interview John Tate. In his remarks below, Tate briefly comments on his early work on number theory and cohomology. Most of the post consists of […]

Mental crypto footnotes

I spoke with Manuel Blum this afternoon about his password scheme described here. This post is a few footnotes based on that conversation. When I mentioned that some people had reacted to the original post saying the scheme was too hard, Blum said that he has taught the scheme to a couple children, 6 and […]

Posts from HLF

Here are the blog posts I’ve written so far for the Heidelberg Laureate Form blog: Mathematics and art restoration Mental cryptography What is smoothed analysis? Studying algorithms to study problems Cheap transistors, expensive wires An xkcd-style poster

Proof maintenance

Leslie Lamport coined the phrase “proof maintenance” to describe the process of producing variations of a proof over time. It’s well known that software needs to be maintained; most of the work on a program occurs after it is “finished.” Proof maintenance is common as well, but it is usually very informal. Proofs of any […]

Uses for orthogonal polynomials

When I interviewed Daniel Spielman at this year’s Heidelberg Laureate Forum, we began our conversation by looking for common mathematical ground. The first thing that came up was orthogonal polynomials. (If you’re wondering what it means for two polynomials to be orthogonal, see here.) JC: Orthogonal polynomials are kind of a lost art, a topic […]

Mathematical beauty

Michael Atiyah quoted Hermann Weyl in the opening talk at the second Heidelberg Laureate Forum: I believe there is, in mathematics, in contrast to the experimental disciplines, a character which is nearer to that of free creative art. There is evidence that the relation of artistic beauty and mathematical beauty is more than an analogy. […]

Love locks

If you walk across the Seine in Paris on the Pont des Arts you’ll see thousands and thousands of love locks. I saw this morning that Heidelberg has its own modest collection of love locks on the Old Bridge across the Neckar. These may be new. If they were here last year, I didn’t notice […]

In Heidelberg

I’m in Heidelberg again for the Heidelberg Laureate Forum. Next week I will be writing about the forum on the HLF blog and posting on Twitter with hash tag #hlf14.    

Common sense and statistics

College courses often begin by trying to weaken your confidence in common sense. For example, a psychology course might start by presenting optical illusions to show that there are limits to your ability to perceive the world accurately. I’ve seen at least one physics textbook that also starts with optical illusions to emphasize the need […]

Prevent errors or fix errors

The other day I was driving by our veterinarian’s office and saw that the marquee said something like “Prevention is less expensive than treatment.” That’s often true, but certainly not always. This evening I ran across a couple lines from Ed Catmull that are more accurate than the vet’s quote. Do not fall for the […]

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