A non-moral dilemma about cheating, but it brings up some points

I often give two versions of an exam and TELL THE STUDENTS I am doing this so that they don't even try to cheat. I've even had two different classes take the midterm at the same time, same room, every other seat, so the person next to you is in a different course. And I TELL THE STUDENTS that I am doing this.  A colleague of mine says I shouldn't TELL THE STUDENTS. Here are our arguments

1) Don't tell: students cheat a lot and this is a way to catch them.

2) Tell:  Dealing with cheating distracts from our mission of teaching so best to be preventative so it does not happen. Less noble- tell them so that you don't have to deal with the cheating issue.

I have heard of the following case at a diff school some years ago and want your take on it:
there was one question on the midterm that was different on the two exams- the prof changed the key number, but they were the same question really. The prof was in a hurry for some reason and FORGOT TO TELL THE STUDENTS. You can probably guess what happened next, but not what happened after that

One of the students exams had the solution to THE OTHER PROBLEM on it. Clearly cheating. When called in the student said:

Since you didn't tell us that they were different exams the cheating claim is unfair!

They DID admit their guilt, but they DID NOT have any contrition.

 Options for what penalty to go for:

1) A 0 on the exam itself

2) An F in the course

3) A notation on the transcript indicating Failed-because-cheated. I don't know what that notation was at the schol the story took place, but at UMCP its XF. (Side Note- not clear if someone outside of UMCP looks at a transcript and sees an XF they'll know what the means. But the F part makes it look bad.)

4) Expulsion from school. (This might not be the profs call- this may depend on if its a first offense.)

The lack of contrition bothers me, though the prof who told me the story said that the student may have said it out of shock- the first thing that came into their mind. I asked the prof how the student was doing in the class and the prof said, CORRECTLY, that that is irrelevant.

SO- what penalty would you go for?

The professor went for XF. The student, at the hearing, once again said


Since you didn't tell us that they were different exams the cheating claim is unfair!

The professor told me that he thinks the student was trying to claim it was entrapment, though he had a hard time expressing this coherently. If the student had been a coherent thinker, he probably wouldn't have needed to cheat.

He got the equivalent of an XF.

But here is my real question: Should we TELL THE STUDENTS that they are different exams (I think yes) or
should we NOT tell them so can catch them?

Limits of using the web for info- self-reference

(I wrote this a while back so when I say `I Googled BLAH' I meant back then. It is prob different now.)

While the web is a wonderful to find things out there are times when it doesn't quite work.

1. An old blog of Scott Aaronson's had as part of its title a Woitian Link. Wanting to find out what a Woitian Link is but not wanting to bother Scott (he's busy enough making comments on Shtetl-Optimized) I went to google and typed in "Woitian Link". The ONLY hits I got back were to Scotts blog. I finally had to email Scott. He told me that it was referring to the blog not even wrong by Peter Woit which often has links that... Well, Scott never told me quite what it was but I'll go there myself and try to figure it out.
   
2. An old blog of mine was the man who loved algorithms. Part of my blog said that I thought the man would be Knuth but it was not. (It was Thomas Kailath) One of the commenters said that it couldn't be Knuth since he was still alive. This made me want to check the original article to see if Thomas Kailath, is also still alive (he is). I didn't have the issue with me at the time so I typed "the man who loved algorithms" into google. The first page of hits all refered to my posting. Eventually I found one to verify that yes, indeed, he was still alive.
   
3. Donald Knuth VOLUME FOUR was originally published in a series of fascicile's. Whats a fascicle? Here the web was helpful- Wikipedia said it was a book that comes out in short pieces, the pieces of which are called `fascicle'. They gave only one example: Donald Knuth's Volume 4 will be coming out in Fascicle. Still, they DID tell me what I want to know. (Note- this was a while back, they have since removed that comment.) For most things the web is great. But for some more obscure things, better off asking someone who knows stuff.

Do you have experiences where you ask the web for a question and you end up in a circle?

Statistics to Scare

So how do you parse the following paragraph from Monday's NYT Evening Breifing.

A study in JAMA Pediatrics this year found that the average Halloween resulted in four additional pedestrian deaths compared with other nights. For 4- to 8-year-olds, the rate was 10 times as high.

The paragraph  means the percent increase for pedestrian deaths for 4-8 year olds was ten time the percent increase for people as a whole, a number you cannot determine from the information given. Using the fact that roughly 7% of Americans are in the 4-8 year range, that yields a little under three additional deaths for 4-8 year olds and about one for the other age ranges.

The paper unfortunately sits behind a firewall. But I found a press release.

Children in the United States celebrate Halloween by going door-to-door collecting candy. New research suggests the popular October 31 holiday is associated with increased pedestrian traffic fatalities, especially among children. Researchers used data from the National Highway Traffic Safety Administration to compare the number of pedestrian fatalities from 1975 to 2016 that happened on October 31 each year between 5 p.m. and 11:59 p.m. with those that happened during the same hours on a day one week earlier (on October 24) and a day one week later (on November 7). During the 42-year study period, 608 pedestrian fatalities happened on the 42 Halloween evenings, whereas 851 pedestrian fatalities happened on the 84 other evenings used for comparison. The relative risk (an expression of probability) of a pedestrian fatality was higher on Halloween than those other nights. Absolute mortality rates averaged 2.07 and 1.45 pedestrian fatalities per hour on Halloween nights and the other evenings, respectively, which is equivalent to the average Halloween resulting in four additional pedestrian deaths each year. The biggest risk was among children ages 4 to 8. Absolute risk of pedestrian fatality per 100 million Americans was small and declined from 4.9 to 2.5 between the first and final decades of the study interval. 

Doing the math, we see a 43% increase and a more than quintupling the number of pedestrian deaths for the youngsters. That sounds scary indeed. though it only adds up to a handful of deaths.  Moreover the authors didn't take into account the larger number of pedestrians on Halloween, particularly among 4-8 year olds.

A smaller fraction of people die as pedestrians on Halloween today then on a random day when I was a kid. I wonder if that's because there are fewer pedestrians today.

Also from the New York Times, a sociologist has found "no evidence that any child had been seriously injured, let alone killed, by strangers tampering with candy." I feel lied to as a kid.

So the upshot: Tell your kids to take the usual precautions but mostly let them dress up, have fun trick-or-treating and enjoy their candy.

Random non-partisan thoughts on the Prez Election

This post is non-partisan, but in the interest of full disclosure I disclose that I will almost surely be voting for the Democratic Nominee. And I say almost surely because very weird things could happen.I can imagine a republican saying, in 2015 I will almost surely be voting for the Republican Nominee and then later deciding to not vote for Trump.


My Past Predictions: Early on in 2007 I predicted it would be Obama vs McCain and that Obama would win. Was I smart or lucky? Early in 2011 I predicted Paul Ryan would be the Rep. Candidate. Early in 2015 and even into 2016 I predicted that Trump would not get the nomination. After he got the nomination I predicted he would not become president. So, in answer to my first question, I was lucky not smart. Having said all of this I predict that the Dem. candidate will be Warren. Note- this is an honest prediction, not one fueled by what I want to see happen. I predict Warren since she seems to be someone who can bridge the so-called establishment and the so-called left (I dislike the terms LEFT and RIGHT since issues and views change over time). Given my past record I would not take me too seriously. Also, since this prediction is not particularly unusual, if I am right this would NOT be impressive (My Obama prediction was impressive, and my Paul Ryan prediction would have been very impressive had I been right.)

Electability: My spell checker doesn't think its a word. Actually it shouldn't be a word. It's a stupid concept. Recall

JFK was unelectable since he was Catholic.

Ronald Reagan was unelectable because he was too conservative.

A draft dodging adulterer named Bill Clinton could not possible beat a sitting president who just won a popular war.

Nobody named Barack Hussein Obama, who is half-black, could possibly get the nomination, never mind the presidency. And Hillary had the nomination locked up in 2008--- she had no any serious challengers.

(An article in The New Republic in 2007 predicted a brokered convention for the Republicans where Fred Thompson, Mitt Romney, and Rudy Guilliani would split the vote, and at the same time a cake walk for Hillary Clinton with
Barak Obama winning Illinois in the primaries but not much else. Recall that 2008 was McCain vs Obama.)

Donald Trump will surely be stopped from getting the nomination because, in the end, The Party Decides.

Republican voters in 2016 will prefer Rubio to Trump since Marco is more electable AND more conservative. Hence, in the space of Rep. Candidates, Rubio dominates Trump. So, by simple game theory, Trump can't get the nomination. The more electable Rubio, in the 2016 primaries, won Minnesota, Wash DC, and Puerto Rico (Puerto Rico has a primary. Really!) One of my friends thought he also won Guam (Guam?) but I could not find evidence of that on the web. Okay, so why did Trump win? Because voters are not game theorists.

ANYWAY, my point is that how can anyone take the notion of electability seriously when unelectable people have gotten elected?

Primaries: Dem primary voters are torn between who they want to be president and who can beat Trump. Since its so hard to tell who can beat who, I would recommend voting for who you like and not say stupid things like

American would never elect a 76 year old socialist whose recently had a heart attack.

or

Trump beat a women in 2016 so we can't nominate a women

or

America is not ready to elect a gay president yet. (America is never ready to do X until after it does X and then the pundits ret-con their opinions.For example, of course America is ready for Gay-Marriage. Duh.)

Who won the debate?
Whoever didn't bother watching it :-). I think the question is stupid and has become who got out a clever sound bite. We need sound policy, not sound bites!

Differentiation and Integration

Recently there was an excellent xkcd about differentiation and integration, see here.

This brings up thoughts on diff and int:

1) For some students Integration is when math gets hard.

Diff (at least on the level of Calc I) is rote memorization. A computer program can EASILY do diff

Integration by humans requires more guesswork and thought, Computers can now do it very well but I think that it was  harder to get to work.

Someone who has worked on programs for both, please comment.

2) When I took Honors Calculus back in 1976 (from Jeff Cheeger at SUNY Stonybrook) he made a comment which really puzzled the class, and myself, but later I understood it:

             Integration is easier than Differentiation

The class thought this was very odd since the problem of, GIVEN a function, find its diff was easier than GIVEN a function, find its int.  And of course I am talking about the kinds of functions one is
given in Calc I and Calc II, so this is not meant to be a formal statement.

What he meant was that integration  has better mathematical properties than differentiation.  For example, differentiating the function f(x)=abs(x) (absolute value of x)  is problematic at 0, where it has no problem with integration anywhere (alas, if only our society was as relaxed about integration as f(x)=abs(x) is).

So I would say that the class and Dr. Cheeger were both right (someone else might say they were both wrong) we were just looking at different notions of easy and hard.

Are there other cases in math where `easy' and `hard' can mean very different things?

2019 Fall Jobs Post

Starting PhD students over time would always assume that the computer science academic job market would be a strong or as weak when they graduate as it is when they were starting, and they would always be wrong. That may have changed. We've had such a stretch of strong growth in computer science, starting as we pulled out of the financial crisis in 2012, that students who started in the strong market back then see only a much stronger market today.

Every fall I recap advice for students, and others, looking for academic jobs. Best source are the ads from the CRA and the ACM. For theoretical computer science specific postdoc and faculty positions check out TCS Jobs and Theory Announcements. If you have jobs to announce, please post to the above and/or feel free to leave a comment on this post. Even if you don't see an ad, almost surely your favorite university is looking to hire computer scientists. Check out their website or email someone at the department. The CRA just published a member book, a collection of one pagers for several departments, almost all of which are trying to grow.

Needless to say we're trying to greatly expand computing at Illinois Tech, come join us.

Something new this year, CATCS is collecting and disseminating profiles of junior theory researchers on the job market this year. Definitely take advantage whether to sign up as a job seeker or to reach out to theorists on the market once the profiles are posted. The CRA also maintains a CV database for candidates for academic, industrial and government research positions.

While this is a job-seekers market, you still need to put your best foot forward. Reach out to professors at conferences, such as the upcoming FOCS. Polish your CV and get your Google Scholar page in good shape. Practice your job talk, a bad one can kill your visit. Research the people you will see during the interview ahead of time, I like to write down one interesting discussion topic for each. You'll need to sell yourself to non-theorists. Data, cybersecurity and quantum are hot this year, highlight your work in those areas without making it look fake.

In any case have fun! You'll meet lots of interesting people in your job search and eat way too much.

The Sheldon Conjecture (too late for Problems with a Point)

Chapter 5 of Problems with a Point (by Gasarch and Kruskal) is about how mathematical objects get their names. If it was an e-book that I could edit and add to (is this a good idea or not? later on that) then I would have added the following.

The Sheldon Conjecture

Background: Nobel Laureate Sheldon Cooper has said that 73 is the best number because

a) 73 is prime.

b) 73 is the 21st prime and note that 7*3=21.

c) The mirror of 73, namely 37, is prime.

d) 37 is the 12th prime, and 12 is the mirror of 21.

Sheldon never quite said its the only such number; that was conjectured by Jessie Byrnes, Chris Spicer, and Alyssa Turnquist here. They called it Sheldon's Conjecture probably since Sheldon Cooper should have conjectured it

Why didn't Sheldon make Sheldon's conjecture? This kind of question has been asked before:



Could Euler have conjectured the prime number theorem

Why didn't Hilbert (or others) pursue Ramsey Theory?

(readers are encouraged to give other examples)

I doubt we'll be asking this about Sheldon Cooper since he is a fictional character.

I am delighted that

a) There is a Sheldon's Conjecture.

b) It has been solved by Pomerance and Spicer, see here

Actually (b) might not be so delightful--- once a conjecture is proven its stops being called by the name of the conjecturer. If you don't believe me just ask Vazsonyi or Baudet. If you don't know who they are then (1) see here and (2) that proves my point. So perhaps I wish it had not been solved so The Sheldon Conjecture would live on as a name.

Another issue this brings up: Lets say that Problems with a Point was an online book that I was able to edit easily. Then I might add material on The Sheldon Conjecture. And while I am at it, I would add The Monty Hall Paradox to the chapter on how theorems get there names. Plus, I would fix some typos and references. Perhaps update some reference. Now lets say that all books were online and the authors could modify them. Would this be good or bad?

1) Good- The book would get better and better as errors got removed.

2) Good- The book would get to include material that is appropriate but came out after it was published.

3) Good- The book would get to include material that is appropriate but the authors forgot to include the first time around.

4) Bad- For referencing the book or for book reviews of the book, you are looking at different objects. The current system has First Edition, Second Edition, etc, so you can point to which one you are looking at. The easily-edited books would have more of a continuous update process so harder to point to things.

5) Bad- When Clyde and I emailed the final version to the publisher we were almost done. When we got the galleys and commented on them we were DONE DONE! For typos and errors maybe I want to fix them online, but entire new sections--- when we're done we are DONE.

6) Bad- at what point is it (i) a corrected version of the old book, (ii) a new edition of the old book, (iii) an entirely new book? Life is complicated enough.

I would prob like a system where you can fix errors but can't add new material. Not sure if that's really a clean distinction.

William Kruskal's 100th birthday

Today, Oct 10, 2019 is William Kruskal's 100th birthday (he's dead, so no cake. Oh well.) William Kruskal was a great statistician. To honor him we have a guest post by his nephew Clyde Kruskal. We also note that the Kruskal Family is one of the top two math families of all time (see here). William is a reason why the other two Kruskal brothers went into mathematics: As a much older sibling (6 years older than Martin and 8 years older than Joseph), he encouraged their early mathematical development.

Here are some pictures of William Kruskal and of the Kruskal Family: here

Guest Post by Clyde Kruskal


I was asked to blog about my uncle, the statistician, William H. Kruskal, on the centennial of his birth. We called him Uncle Bill. He is best known for co-inventing the Kruskal-Wallis test.

There are two stories that I know about Bill's childhood, which must have been family lore:

(1) As a young child, Bill was a prolific reader. His reading comprehension outstripped his conversational English. One morning, having just read the word ``schedule'' in a book, and obviously having never heard it pronounced, he sat down to breakfast and asked:
"What is the ske·DU·le for today?"

(2) My grandparents once had Bill take an occupational assessment test. The tester said that Bill was a very bright child, and should become a traffic engineer to solve the problems with traffic congestion. (This would have been the 1920s!) As you probably know, Uncle Bill did not succeed in ending traffic congestion. Oh well.


Recently there has been a controversy over whether to ask about citizenship in the 2020 census. In the late 1900s there was a different controversy: whether to adjust the known undercount statistically. In general, Democrats wanted to adjust the count and Republicans did not (presumably because Democratic states tended to have a larger undercount). A national committee was set up to study the issue, with four statisticians in favor and four against. I was surprised to learn that Uncle Bill was on the commission as one of those against adjustment, since, I thought his political views were more closely aligned with those of the Democrats. He was very principled, basing his views only on statistical arguments. I saw him give a talk on the subject, which seemed quite convincing (but, then again, I did not see the other side). They ended up not adjusting.


For more on William Kruskal, in general, and his view on adjusting the census, in particular, see the pointers at the end of this post.


I have more to say. I just hope that I am on the ske·DU·le to blog about Uncle Bill at the bicentennial of his birth.


The William Kruskal Legacy: 1919-2005 by Fienberg, Stigler, and Tanur

A short biography of William Kruskal by J.J. O'Connor and E.F. Robertson

William Kruskal: Mentor and Friend by Judith Tanur

William Kruskal: My Scholarly and Scientific Model by Stephen Fienberg

A conversation with William Kruskal by Sandy Zabell

Testimony for house subcommittee on census and population for 1990 (see page 140)