Minipolymath4 Project Now Open!

As we talked about here, there was plans afoot to group-solve online an interesting and problem from the IMO.  The online discussion going on right now (unless, of course, you’re reading this later).  They decided to work on Question 3.  Here it is:

Problem 3.   The liar’s guessing game is a game played between two players and .  The rules of the game depend on two positive integers and which are known to both players.

At the start of the game, chooses two integers and with .  Player keeps secret, and truthfully tells to player .  Player now tries to obtain information about by asking player A questions as follows.  Each question consists of specifying an arbitrary set of positive integers (possibly one specified in a previous question), and asking whether belongs to .  Player may ask as many such questions as he wishes.  After each question, player must immediately answer it with yes or no, but is allowed to lie as many times as she wishes; the only restriction is that, among any consecutive answers, at least one answer must be truthful.

After has asked as many questions as he wants, he must specify a set of at most positive integers.  If belongs to , then wins; otherwise, he loses.  Prove that:

1. If , then can guarantee a win.
2. For all sufficiently large , there exists an integer such that cannot guarantee a win.

Check out (and join in on) the discussion here.

A Bonus Math Club!

This

Thursday, May 4th at 4 pm in PHSC 1105

there is going to be a talk in the OU Math department which everyone should be interested in.  Dwight Neuenschwander of Southern Nazarene University will be speaking on a mixture of math, physics, and history.  Best of all, it’s about one of our favorite mathematicians: Emmy Noether!

Here’s the details:

Title: Emmy Noether’s Elegant Theorem: Symmetry, Conservation Laws, and Unity in Physics

ABSTRACT: Mathematicians are well acquainted with Emmy Noether through her important work in abstract algebra, such as her major contributions to the study of rings and ideals. Regrettably, Noether is less well known among physicists, even though her theorem about transformations under Lie groups carries powerful applications to practically all of physics. The few physicists who do know of “Noether’s Theorem” by name typically recognize it in only the context of theories with gauge invariance,
which arise in elementary particle physics and general relativity. But these elite applications only scratch the surface of the Theorem’s scope, and present unnecessary barriers to its accessibility. Emmy Noether’s elegant theorem of 1918, which connects continuous symmetries to conservation laws, offers a unifying perspective for all of physics, from classical mechanics to geometrical optics, from quantum theory to relativity.
In this pedagogical presentation, the Theorem’s definitions, strategies, and results
will be introduced and illustrated with elementary physics examples. Extensions of these concepts to field theory will be indicated briefly. Biographical notes about Emmy Noether will be emphasized.

Undergraduate and graduate students studying mathematics and physics are especially invited to attend.

Sadly, there’s no Pizza this time, but tea and cookies will be served at 3:30 PM in PHSC 424.

Also, it’s worth noting that Dwight Neuenschwander won the David Halliday and Robert Resnick Award for Excellence in Undergraduate Physics Teaching in 2000.  He also wrote the well reviewed book entitled “Emmy Noether’s Wonderful Theorem”.

From amazon.com’s reviews:

I am a lifelong student of Physics. I have been a student long beforeI got my PhD in Physics. I am currently a Distinguished Scientist at a Government Lab. This is first review (and possibly the last) I’ve written for an Amazon book, but I felt compelled to write this after reading this book. It is an excellent example of a ‘true’ teacher at work who understands how to relate information. This is an art form.

– from Charles W. Glover’s amazon.com review

How to Toss a Coin Over the Phone

This

Wednesday, April 18th at 5 pm in PHSC 1105

our own Dr. Ravi Shankar will be talking in the Math Club.  He answer the puzzling problem of telling someone something without telling them and related conundrums:

Your favorite uncle Mo who lived in Alaska has recently gifted you his zamboni. But he left it to you and his other favorite niece, Eva, who lives in Arizona. You give Eva a call and neither of you wants to share the zamboni. You decide to flip a coin for it. So Eva flips and you call, “Heads!” and she says, “Oops, sorry, no. You lose.” To which you reply, “I don’t believe you!” An argument ensues until you realize you went to a math club talk at OU, where you were shown how to flip a coin over the phone and both be reasonably sure that the other person could not have cheated.

In this talk we will explore how to solve this problem and other similar “authentication” and “signature” problems (how do you convince a bank teller on the phone that you know the secret pin number for your account without actually revealing the pin number?)

– Dr. Shankar’s abstract

There's more than one way to find out what somebody knows!

As always, Free Pizza!

P.S.  Come and quiz Dr. Shankar on Weierstrass gap sequences!

Andy Magid in Math Club!

Dr. Magid in 1980

On

Wednesday, April 11th, at 5 pm in PHSC 1105

our own Andy Magid will be talking in the Math Club about Boolean Algebra.  That’s the mathematics of zeros and ones.  Well, it’s a bit more than that!  It shows up in abstract algebra, and is at the center of computers (binary anyone?) and mathematical logic (True vs. False).

It should be a very interesting talk.  Here’s the title and abstract if you want to know more:

Title:  Boolean Algebra, Operations, and Rings

Abstract:  Z/2Z valued functions on a set correspond to subsets of the set, and vice versa: the support of a function is a subset and the characteristic function of a subset is a function. From this correspondence can be derived ring operations (addition and multiplication) on subsets and subset operations (intersecti0on and union) on functions. And new operations on both.

And of course there’ll be the usual Free Pizza!

George Boole doesn't take maybe for an answer!

Random Walks with Erin Pearse

This

Wednesday, March 28th at 5 pm in PHSC 1105

will be a Math Club talk by our own Erin Pearse.  He’ll be talking about random walks:

Erin Pearse on a more colorful day.

Title: Exploring networks with random walks

Abstract: I will give a brief introduction to the theory of random walks on networks, including mixing times and convergence to stationarity. I’ll give a brief description of Monte Carlo techniques and explain the application of random walks in this context. Next, we’ll look at diffusion mapping, a framework for dimensionality, clustering, dataset parametrization, and inferencing that is constructed using random walks. I’ll show how this technique applies to machine learning and give an example of that forecasts the success rate of students at OU. This talk will be accessible to anyone who can multiply matrices and has a vague idea of what a discrete probability distribution is.

And, of course, there’ll be the usual Free Pizza!

No word on if the Ministry of Silly Walks will be involved.

Fun with Physics, A Personal Odyssey

As part of the Focas on Arts and Sciences week, on Thursday, Feb. 23, our distinguished alumni will make public presentations.

Dr. Stair

One of the speakers, A.T. Stair, has an MS in Math from OU (’56) and a PhD from OU in Physics.

The lecture is titled “Fun with Physics, A Personal Odyssey” and will be held on

Thursday, February 23 at 4:00pm in Nielson Hall, 170. 

A full calendar of events for the week of February 20-24 is available at http://cas.ou.edu/focus-on-arts-and-sciences-week

============================================

A.T. Stair’s Bio:

Stair grew up on a dairy farm near Canton, Okla. before heading to OU. While at OU, he was active in Delta Tau Delta fraternity, the Air Force ROTC and he developed his life-long interest in skiing and table tennis.

After graduating Phi Beta Kappa from OU, Stair served in the United States Air Force as a 1st Lieutenant to the Air Force Cambridge Research Laboratory in Boston. After two years of active duty, he resigned to become a civilian scientist at the lab. He also lectured in applied physics at the Lowell Technological Institute in Massachusetts. In 1962, he and Doran Baker established the Space Dynamics Lab at Utah State University.

Stair continued to study the non-local thermodynamic equilibrium in the upper atmosphere and became a branch chief within the laboratory and the scientific director for NLTE research. This research continued through his career with the U.S. Air Force. Following his retirement, he became a consultant with the U.S. government, developing further studies of the atmosphere and creating joint programs for missile defense. He currently works as the president of Visidyne, Inc. and is involved with a new sensor called Sun and Aureole Measurements, used for measuring the optical properties of cirrus and their effects on radiation balance of the earth and solar energy.

Getting Excellent Recommendations!

If you are applying for jobs, internships, REUs, graduate school, scholarships, etc., then you need letters of recommendation. The not-so-secret secret is that letters of recommendation make all the difference. Bad or even so-so letters will kill your chances.

This

Wednesday, February 22nd at 5 pm in PHSC 1105

Adrienne Jablonski, the OU College of A & S Director of Student Career and Leadership Development, will tell you everything you need to know to get excellent letters of recommendation.

As always, there will be Free Pizza!

Upcoming Career Events

Adrienne Jablonski has let us know of some upcoming career related events at OU:

Here are a few other career events coming up. Please pass along to your students.

• February 23, OU Multicultural Fair, Kerr McGee Stadium Club, 12;30-4:00 p.m.
• The College of Arts and Sciences will host a Professional Networking Reception for A&S students on Wednesday, February 29 from 4:30-6:00 p.m. at Beaird Lounge, OMU. This free event is a great opportunity for students who are looking for an internship or are graduating and job seeking to connect with employers who are hiring. Light refreshments will be served.
• For other career workshops and events: http://cas.ou.edu/career-development 

Best regards,
Adrienne Jablonski

Adrienne also asked us to let you know that Chesapeake Energy will be at the networking reception on February 29th and they specifically said they wanted to meet with math majors!

If you’re thinking about getting a job or summer internship, you should contact Adrienne about going to these events.  She can also help you get your resume and interviewing skills in good shape.

“Newtonianism for the ladies”

Intrepid OU math professor Ralf Schmidt and OU grad student Lynn Greenleaf took ten OU undergrads to the University of Nebraska’s 14th annual Nebraska Conference for Undergraduate Women in Mathematics (NCUWM).

Blog HQ asked the women who went to answer a few questions about their experiences and here is some of what they had to say.

Blog HQ: Why did you decide to go to NCUWM?

Dana:  I decided to go to NCUWM because I went the previous year and enjoyed myself so much that I want to go again.

Michelle:  I decided to go to NCUWM because I attended last year and it was the single most enriching experience of my undergraduate career.  This year did not disappoint.

Wen:  I’d like to able to meet more women in math, and to see how is their life and study. I’m more interested in the graduate panel which discussed about almost every aspect of graduate study.

Katlin:  Dr. Miller told me about this conference my freshman year. I went last year and it was a great experience.

Find the Sooners! (click to make bigger)

Blog HQ:  What happens at this conference? What did you do there?

Edwina:  The conference showcases research done usually through REU’s, holds panels for graduate school and careers in mathematics, and has breakout sessions which are specialized for issues students tend to encounter during school or the application process.

Dana:  At the conference, there are so many things that happen.  There are plenary talks from respected women mathematicians; this year they were given by Dr. Ingrid Daubechies and Dr. Sara Billey.  There are several 15 minute talks about research in mathematics that undergraduate women have done, either through an REU or in coursework.  There are also panel discussions about career opportunities for people with math degrees, graduate school in math, summer research opportunities.  There’s also a banquet on Friday evening where I got to meet students from other universities as well as Juan Franco who is the Vice Chancellor for Student Affairs for University of Nebraska–Lincoln.

Michelle:  At the conference, you meet other undergraduate women sharing your interests and discuss your research, interests, and possible graduate opportunities you might share.  You listen to two phenomenal plenary talks from the foremost mathematicians in the field, then you go into smaller groups and discuss a predetermined topic which each participant signed up for earlier.  You have the chance to listen to presentations from other undergraduate women detailing their research, which is one of my favorite parts.  They also have a pizza party and a formal dinner where you are strongly encouraged to branch out and meet those outside of your group.  I met other analysts and we were able to discuss our research projects.

Blog HQ:  Give 5 words that describe the NCUWM conference.

Blog HQ:  What was your expectation for the conference?  What did it actually turn out to be like?

Wen:  I was expecting to hear lots of math research classes or presentation, and I thought the conference is all about math, all about the research, but it turned out to be fun and very useful. It is not only concerning about the study side, also discuss about how to balance life and math. I learned a lot about how other women deal with their problem and challenges. Especially how marriage and children affect to women in different ways. It’s very helpful to hear from different women how they deal with marriage and children.

Dana:  Since I had gone to the conference, I knew what to expect in terms of the scheduling but I didn’t expect to have even more fun going this year than I did last year.

Teresa:   I thought I would hear a lot about math at the conference and different career paths open to mathematicians.  I did all that and made lasting friendships!

Michelle:  My expectations were largely built on my experience from the 2011 conference, where I had an amazing time.  The 2012 conference was just as good and I got to explore more of UNL than I had been able to the previous year.

Blog HQ:  What was the coolest math thing you heard?

Teresa:  The coolest thing was learning that mathematics underlies recent Pixar animation.

Dana:  A student gave a talk entitled “Stem detection of strawberries utilizing the medial axis transform” and the cool part was is that, using math, she was able to create a bounding rectangle for where the stem of a strawberry would most likely be in a photo in only about 20 seconds.  The even cooler part was that this type of technology could have future applications in the spread of wildfires, dance choreography, and identification of what tree a certain leaf came from.

Edwina:  There was an interesting talk about Lenny Jones’ article ” When Does Appending the Same digit Repeatedly on the Right of a Positive Integer Generate a Sequence of Composite Integers?”

Blog HQ:  What’s the best piece of information you received at the conference?  The thing you will be sure to remember?

Edwina and Michelle:  “Math will never love you back, but that shouldn’t stop you from pouring yourself into it”

Katlin:  There are a lot of opportunities in mathematics. It is important to be prepared.

Dana:  The best piece of advice I received at the conference was from an invited guest at the conference.  She said that even though she has her Ph.D. in math, there are still days where she feels stupid so we should not get discouraged during those times when math is most frustrating.

Wen:  One lady quotes:  “Do not worry about your difficulties in Mathematics; I can assure you that mine are still greater.” –Einstein, which is the same quote I like the most.

Teresa:   The best piece of information I received at the conference was that any job description with the word “analyst” is a job that can be done with a math degree.  I will always remember the nine hour drive there and back.

Blog HQ:  What would you say to someone thinking about going to next year’s conference?

Katlin:  You should absolutely go. Even if you’re not interested in pursuing a career in mathematics, you should go. Last year, this conference encouraged me to start doing research and seriously consider graduate programs.

Dana:  I would definitely encourage them to go.  It definitely is a great way to make new friends within OU’s math community as well as with other women across the country.  You also see a lot of different ways to think about math and use math.  It’s also a really awesome experience to be around other women who have the same interests and the same struggles that you do, whether it comes from gender discrimination from classmates or from doing your analysis homework.  It makes me feel encouraged to know that I’m not the only one out there.

Wen:  You should definitely go the conference where you’ll meet other women interested in math, and you’ll learn about the career and graduates school whichever you interested most. And also, you’ll make new friends in the same school since there were 10 of us.

Teresa:  You should do it!

About the title:

One of us from Blog HQ was at the OU History of Science collection last week and was shown one of the best sellers of the 18th century.  It is described by Massimo Mazzotti at UC of Berkeley thusly:

Francesco Algarotti’s “Newtonianism for the ladies, or dialogues on light and colours” (1737) was an eighteenth- century best seller. It was also one of the main channels through which Newtonian ideas reached the general public in continental Europe. The book offered a description of some of Newton’s experiments on the nature of light and colours in the form of a genteel dialogue between a chevalier (cavaliere) and a marchioness (la marchesa di E***). Through an enjoyable, mundane, and apparently light-hearted conversation, past doctrines about the nature of matter and light were sketched, considered, and proved mistaken. Along the way, Algarotti gracefully disposed of contemporary anti-Newtonian philosophers as well. At the end of her initiation into the true philosophy the marchioness couldn’t but agree that Newton’s theory of light, and indeed his entire philosophical system, provided a veritable description of the functioning of the machine of the world.

This OU history of science library has a first edition.  You can even find a digital photo of the front page on their website. Here it is:

The title is in Italian, but there's no mistaking it!

And here’s the facing page:

Movie Night!

The first Math Club of 2012 is this

Wednesday, February 1st at 5pm in SCI 324.

Notice that we’re in the Film and Media Studies Lounge in Old Science Hall 324.  That’s right next door to PHSC.  Here it is on the campus map:

Click on the map to make it bigger.

We’ll be watching the Best Picture nominated film Moneyball.  We learned from John Paul Cook last semester that there is lots of interesting math in the Moneyball story.  Plus there’s Brad Pitt (An Okie!), Jonah Hill, and baseball.  Something for everyone!

Here’s the trailer:

And, as always, Free Pizza!