Mirrors, Means, and Logarithms

Image from Dalhousie University

We’re pleased to announce the first math talk of 2010.  Dr. Dragan Jankovic of Cameron University will be talking this

Wednesday, February 10th at 5 PM in PHSC 1105.

His title and abstract are:

Title: Mirrors, Means, and Logarithms

Abstract. I will talk about an intrinsic symmetry of the logarithmic curve involving the classical means(arithmetic, geometric, and harmonic). In this context two curves naturally arise: one old and famous (yielding pi and many other things), and the other new (to me) and interesting (yielding Apery’s constant). In other words: a little bit of geometry, calculus, and history.

To intrigue you just a bit, let’s talk for a minute about Apery’s constant.  As we discussed here (and you learned in Calc III), the series

You surely also learned that the series

also converges because it is a p-series with p=3.  The next question is: Which number does this series converge to?  The answer is Apery’s constant, , which is

Dr. Jankovic will no doubt have lots of interesting things to tell us, but we’ll mention two cool facts about :

1. In 1978 Apery proved that is irrational.  So, like , the above decimal goes on forever.  Nobody knows if it is transcendental (ie. a number like which is not the zero of any polynomial with integer coefficents).
2. Apery’s constant also has close connections to number theory.  For example, amazingly, if you pick three random natural numbers, the probability that the three are relatively prime (ie. no natural number bigger than 1 divides all three) is exactly .

P.S. To learn more about Apery’s constant and all your favorite other mathematical constants, you need to check out this webpage at Dalhousie University.  It is nothing less than a no-holds-barred cage match between mathematical constants!  Will Pi piledrive e?  Will Apery’s Constant put The First Surd in a headlock?  Check it out!

Math is taking all challengers who dare enter the Cage!

A Double Header

Update:  Due to the weather and the closing of the University on Jan. 28th, Frank Morgan’s talks are rescheduled for February 18th.

Here at OU Math Blog HQ we’re very excited about our third Math Club event of 2010.  On

Thursday, Febuary 18th

there is not one, but two talks by Dr. Frank Morgan of Williams College (and pizza, of course!).

Dr. Morgan in action! (Photo courtesy of Jeff Bauer of Citco)

Why are we so excited?  And, more importantly, why should you be excited?  Well, there’s a list for that!

1. Dr. Morgan does cool math.  He works in minimal surfaces (e.g. the shape soap bubbles on various wire shapes) and studies the behavior and structure of minimizers in various dimensions and settings.
   

   Photo by John M. Sullivan, Technical University of Berlin and University of Illinois at Urbana-Champaign

2. He is famous for his skills in talking about interesting math.  He’s even had a TV show called Math Chat!  Check out the book which came from his TV show is here.
3. His first talk (at 4 pm in PHSC 1105) is about the famous Poincare Conjecture, which we’ve talked about here.  The title and abstract is:

“From Soap Bubbles to the Poincaré Conjecture”

Abstract:  A single round soap bubble provides the least-area way to enclose a given volume. How does the solution change if space is given some symmetric positive density like r^2 or e^-r^2 that weights both area and volume? Such densities appear prominently in Perelman’s paper proving the Poincaré Conjecture. No prerequisites; undergraduates welcome.

4. His second talk (at 5 pm in PHSC 1105) is about math and baseball, which we’ve talked about here.  The title and abstract is:

“Baserunner’s Optimal Path”

Abstract:  When you hit that final long ball in the World Series of Baseball and know you need the home run, what is your optimal path around the bases?

5. Last, but not least, Dr. Morgan is a fellow math blogger!

Although talented, Frank Morgan is no wizard:

February’s Problem of the Month: Lilian’s Palooza

Hold on now, Lilian is very serious about her music.  She would totally get upset if you picked the wrong music for her party this Saturday.  So before we let you join the party-planning committee, you need to pass a little test.  It goes like this.  We’re going to give you a pile of records, and you need to put them in order from lamest to coolest (in your opinion).  We’ll then give the pile to Lilian, and she will thumb through them one by one.  Every time a cooler album is followed by a lamer album (in her opinion), she will let out a scream.  If she screams twice or more, you’re out!

Wait you don’t understand?  Okay, let’s say for example that we give you four records:  Abba,  Björk, Counting Crows, and Dances with Wolves: The Soundtrack.  Let’s abbreviate those as .  Now Lilian would order those as .  If you gave us , then she would scream at and scream at , and won’t be needing you.  Hey look, there are exactly possibilities for her to let out screams with albums:
,

That reminds me, you’re like a math champ aren’t you?  Why don’t you explain something to me while we’re getting those records?

• How many possibilities are there for screams with albums?
• How many are there for scream with albums?
• How many are there for screams with albums?

If you think Lilian would rank any two albums equally, we’re gonna dump you right now because she’s got her preferences on everything.

Hey, when you get all those figured out, you should like, submit them to the OU Math Department for a prize or something.
Hmmmm…on the other hand, maybe lots of other math hot-shots could work that out too.  They’d have to come up with a crazy-hard version to separate the top answers in that case…something like:

•  How many possibilities are there for screams with albums?

[See the rules for more information.]

Apery’s Constant, revisited

In a funny coincidence, Apery’s Constant came up in a discussion on mathoverflow.net about correct mathematical results which were dismissed by other mathematicians at first.  Quoting from Wikipedia:

However, in June 1978 Roger Apéry gave a talk entitled “Sur l’irrationalité de ζ(3).” During the course of the talk he outlined proofs that ζ(3) and ζ(2) were irrational, the latter using methods simplified from those used to tackle the former rather than relying on the expression in terms of π. Due to the wholly unexpected nature of the result and Apéry’s blasé and very sketchy approach to the subject many of the mathematicians in the audience dismissed the proof as flawed. Three of the audience members suspected Apéry was onto something, though, and set out to fill in the gaps in his proof.

– Wikipedia

It goes to show you that even in mathematics, things aren’t always black and white.  People outside of math think that when you answer a math question that either you’re right or you’re wrong.  But, in reality, sometimes even when you’re correct it takes a while before other people properly understand your results and why it’s correct.  Especially if you’re like Apery and don’t clearly explain your answer!

Moral:  Write your solutions clearly and completely!

P.S.  mathoverflow.net is a new website of questions and answers by and for researchers in mathematics.  Most of the questions and discussion are at the level of current math research (it’s definitely not the place for homework questions/answers), but there is also plenty of questions about suggestions for undergraduate books, math tricks for cocktail parties, and other relaxed topics.

Another Summer Program

We recently heard about yet another great math summer program:

Arizona Summer Program, 2010:  Undergraduate Research in Geometry.

http://math.arizona.edu/~asp/2010/

One of the instructors is OU postdoc Mike Jablonski!

Upcoming Career Events at OU

In honor of Adrienne Jablonski’s visit to the OU Math Club this evening, we thought we’d share some upcoming career events Adrienne recently gave us.  Check them out and/or ask Adrienne about them this evening!

Here are a few upcoming events and job opportunities to pass along to your students. The career fairs are also open for faculty and staff to attend to learn more about opportunities for students. This might be especially relevant to you if you supervise internships in your academic department.

Events

1.       OU Multicultural Career Fair, February 10, 12:30-4:30pm, OMU Ballroom

2.       Peace Corps Information Session, February 11, 3:00pm, OMU Beaird Lounge

3.       CIA Information Sessions, March 2, 12:00 and 5:00pm, OMU Regents Room

4.       Greater Grads Career Fair, March 2, 12:00-4:40 pm, Cox Convention Center

5.       Peace Corps Information Session, March 4, 3:00pm, OMU Beaird Lounge

Job Opportunities

1.       OPUBCO Communications Group (The Oklahoman, NewsOK.com, The Oklahoman Direct) is looking for a Database Marketing Analyst. Proficiency in Access and Excel are required, Experience with mapping software is preferred

2.       Crossroads Youth and Family Services, Social Services (see attached for available positions)

More Information about Greater Grads Career Fair:

Part of the Greater Oklahoma City Chamber’s Greater Grads program, the Greater Grads Career fair is designed to help keep Oklahoma’s college graduates from leaving the state in search of jobs. Hundreds of local college students will meet with employers about career and internship opportunities on Tuesday, March 2, from Noon to 4:30 p.m. at the Cox Business Convention Center, 1 Myriad Gardens in OKC. Shuttle transportation will be provided from the Coca Cola Bricktown Events Center on 425 E. California, where there will be free parking.

One of the fastest ways to get a job after graduation is an internship, which allows a college graduate to test drive their chosen career path and gain valuable experience. Another way is building a strong resume and then networking and making great contacts at career fairs.

If you or your students have any questions about any of the above opportunities, please let me know.

Best regards,
Adrienne Jablonski

P.S.  We may be wrong, but if you were hoping that Adrienne would explain Jablonski diagrams, then you’re probably out of luck.

You could try asking Mike Jablonski, but he'd probably just make up something .

Moneyball

Last semester John Paul Cook gave a talk about sabermetrics: the application of statistics to baseball.

There is an interesting book about sabermetrics called Moneyball by Michael Lewis.   Specifically it’s about how the Oakland A’s were able to use statistical analysis to get a big advantage in finding hidden gems when they recruited baseball players.  It’s a great read and well worth checking out.

Of course, once the book was published the Oakland A’s secret was out and now everybody uses similar techniques.  Has this had an effect on baseball?  At si.com the statistician Sky Andrecheck discusses this very question.  Check it out!

Arthur Benjamin on the Colbert Show

Dr. Stephen T. Colbert, DFA

Dr. Arthur Benjamin, PhD showed us some mathemagical tricks here, and we showed a video of him here.  Dr. Stephen T. Colbert, DFA showed us doughnut mathematics here.  In case you missed it, we were blessed with a meeting of these two great minds.  Check out the clip on colbertnation.com.

You call yourself a mathemagican.  What does that mean?  Were those two words by itself not nerdy enough?

– Stephen Colbert

Sunny REUs

Continuing in the theme of summer research projects, Dr. Shankar let us know about the following opportunity:

San Diego State University is pleased to invite applications to its Summer 2010 Mathematics Research Experiences for Undergraduates program.  The program dates this year will be June 21 — August 13 (final NSF approval pending), and the projects will be in number theory.

Please announce to any interested and qualified undergraduates, as well as to any graduate students interested in leading a project team.  The program will pay a stipend ($5000 for undergraduates) and provide housing.  The application deadline is March 8. For a detailed program description and application instructions/materials, please see the program website:

http://www.sci.sdsu.edu/math-reu/index.html

Thank you for your assistance in sharing this opportunity, as well as with writing letters of recommendation.

Best wishes,
Vadim Ponomarenko
Program Director

And to rouse your interest, here is the first photos from googling San Diego and San Diego State, respectively:

Sunny San Diego

Sunny San Diego State

And if San Diego doesn’t appeal to you, Dr. Shankar also let us know of this one in Sunny Michigan:

The Department of Mathematics at Central Michigan University will be hosting a Research Experience for Undergraduates (REU) Site funded by NSF during Summer 2010.  The program dates are June 7 – July 31, 2010.

Each student will receive a stipend of $3500, meal allowance of $840, and a room in an apartment for the summer.  Travel money to the REU site and for conference presentations will be provided.

The topics to be studied this summer will be in the areas of Differential Geometry, Graph Theory, Matrix theory, and Statistics.

Please inform any interested undergraduate students (who will be completing Calculus II and Linear Algebra before summer) about this program.  The application deadline is February 26, 2010.

For application information please visit the web site:

http://www.cst.cmich.edu/units/mth/REU2010/REU2010.htm

Thank you for your assistance in sharing this information with your students.

Sincerely,

Sivaram Narayan

Which also looks to be very nice in the summer:

Another Summer Opportunity

Dr. Cross let us know of another summer job opportunity.  If you’d rather work with young people rather than do research this summer, then this is the opportunity for you. It is the Duke University TIP (Talent Identification Program).  They are looking for undergraduate and graduate students who are interested in working as instructors or teaching assistants in their summer program for gifted students (7th – 10th graders).   A description of the summer program from their website reads:

Duke TIP Summer Studies Programs are superb academic opportunities and dynamic residential and social experiences for 7th through 10th graders. These three-week sessions are intense and demanding; students are challenged to think critically about themselves and their world.

Duke TIP Summer Studies offers:

• A community of motivated and engaged peers unlike any you have ever experienced.
• Course topics and learning experiences unavailable to most middle and high school students.
• Age-specific programs that are geared specifically toward gifted students.
• Expert instructors, 75% of whom hold or are working toward a terminal degree.
• A stimulating educational model that promotes higher-level thinking through interactive, inquiry-based learning.
• Engaging social and residential experiences to complement your academic endeavors.
• An intense, accelerated pace in the classroom. Students attend a single class for 7 hours each weekday and 3 hours on Saturdays.

– Duke TIP website

If you’re interested in applying, then you can look at the application here.  Also, one of our very own graduate students, Rebekah Smith, has participated in the Duke TIP program in the past.  If you have questions, no doubt she’d be happy to chat with you for a few minutes if you stop by her office.

If you go to Duke, be sure to pick up a DVD for Mike Jablonski!

Gettin’ a job!

Even if you aren’t graduating this year, you’ve probably been thinking about what you’d like to do when you graduate.  And if you are graduating this year, then you’ve probably been thinking about this a lot.  Most people who graduate with math and science degrees don’t end up becoming a teacher or a professor.  So what do they do?  How did they find their job?  What did they do to get that job?  What is a resume supposed to look like?  What happens at the University career fairs (like this one on Feb. 10th)?  Do people wear suits at interviews?   If you have questions about finding a post-OU career, then you’re in luck!  This

Wednesday, February 3rd at 5 pm in PHSC 1105

Adrienne Jablonski, Director of Student Career and Leadership Development for the College of Arts and Sciences, will be talking about the ins and outs of finding a career.  Among other things, she’ll be talking about:

• Why should Math students consider a career in industry?
• How to prepare for a Career Fair.
• What should a non-academic resume look like?

This event is for everyone! (undergrad and grad, math and non-math, seniors and non-seniors, …)  Bring friends and get your career search questions answered.

As always, Free Pizza!

The flyer is here.

Or you could file some TPS Reports: