Wednesday, September 12, 2012

Math in the Media - Cowlicks and Hurricane Eyes

Ever wonder why babies have cowlicks (that spot on their head where the hair just doesn't want to follow any particular direction)?  If the time of the day depends on your time zone, then how does one determine the time at the North Pole?  How come hurricanes have "eyes"?

The answer, unfortunately (or fortunately, depending on your perspective) is mathematical in nature.  More specifically topology.  For a glimpse of why, read today's New York Times article:

Singular Sensations

by Steven Strogatz.  A fun article, with the promise of a lot more in the future.  Give it a read.

One thing you will start to find.  We as mathematicians see our craft everywhere, in basically ALL places.  Math really is the exposure of logical structure, regardless of the context.  But it takes talent to expose that math in an engaging way to someone not trained to see it.  Mr. Strogatz has talent.

Happy reading.   

Wednesday, August 22, 2012

Rest in Peace, Bill Thurston....

A great mathematician, and my professional grandfather (he was the thesis advisor of my thesis advisor), died some days ago.  William Thurston, a pioneering mathematician is many areas, whose contributions not only spanned many areas of mathematics but tied disparate topics together through geometry, fell to cancer at the age of 65.

I only met him and saw him speak a few times, but all of my work is to be considered "thurston-esque" in that it plays on the tools and ideas he exposed and developed.  I remember distinctly early on in my thesis research struggling to understand what was going on in one of his papers, yet feeling the fascination and joy in the slow but steady comprehension.  Every mathematician, like every writer and artist, has a style about them.  Not just a style in the way they write but a style in the way they think, perceive, and present.  I see that style in the "children" of Bill Thurston, people like Benson Farb, Richard Canany, Lee Mosher, Yair Minsky, Martin Bridgeman, and my advisor Bill Goldman.  They seem to see mathematics the way a child views a carnival: full of wonder and joy, fasinated with each new discovery, and simply happy to be a part of the whole scene.

Of course, this is a huge loss for the mathematics world.  But his contributions even up to now will continue to percolate through the outer edges of what is known and what is yet to be discovered.  And his attitude, his style, as seen through his descendents, will certainly live on.

Rest in Peace, Bill Thurston.  The community will miss you.  And we thank you dearly for your thoughts.

Wednesday, June 27, 2012

Math in the Media: Math Food?

One of the more basic and interesting shapes (spaces) in mathematics is the torus.  We typically describe is as the surface of a doughnut or bagel.  That it is mathematically different from the surface of a ball is a good entry point for a lay explanation of some fun higher mathematics. 

Speaking of a bagel, here is an interesting video on a way to mathematically play with your food:
A Mathematically Correct Breakfast
Buon appetito!!!

Thursday, May 31, 2012

A Find: In Praise of Lectures

Currently vogue in internal university discussions involving education is the idea that the standard lecture format for a course is not the most effective means to educate students.  We here at Hopkins are quite interested in understanding better how serve our entering students in the large-lecture courses we call Gateway Science courses (Our study of this issue here at Hopkins is appropriately called the Gateway Science Initiative.  Also, you can read a JHU-centric white paper on this issue).  I am on the Steering Committee studying this issue.  There is a lot of talk about active learning, and other alternatives to inspire students who do not benefit from the simple instructor-led lectures.

I definitely agree with the idea that the classroom experience could benefit from a purposeful study of how our students acquire knowledge and an active design approach to how we teach.  However, I was always a bit troubled by some of the criticism leveled at the standard lecture format.  I love lecturing, feel comfortable in leading a classroom this way, and see great value in the experience.

It turns out I am not alone.  Thomas Korner, a mathematician in Trinity College at Cambridge University, has written a defense of the lecture format:
 I find this essay particularly inspiring.  Give it a read.  It definitely says things that I strongly agree with.

Monday, April 23, 2012

Math in the Media: To save this math class, we must destroy it!

Words failed me (mostly) when I read this article today in the Washington Post:
At Virginia Tech,  Computers Help Solve a Math Class Problem
It is a common problem that the transition from high school mathematics courses to those at university can be quite difficult to make.  Even in courses whose content is basically the same, like Calculus AB in the AP system and what most universities call Calculus I, the treatment of that content is much different here at the university.  Of course, students sometimes do not do well.  And I am sure that sub-standard teaching from some of us up here may be a part of it.  We need very much to analyze how we teach and learn to do a better job!  And many of us are.  IN fact, here at Hopkins, we are devoting a LOT of resources precisely to this problem of how to better and more comprehensively educate our incoming students.

But to help cure the "problem" of not-high-enough passing rates by essentially removing instructor face-time from teaching!?!  That is patently absurd in my book.

Mathematics is absolutely NOT about learning a few techniques to apply to standard problems set up to test those techniques, which is exactly what many unit-based, worksheet driven, math courses seem to be like pre-college level.  Porting that type of course to the university level may in fact raise passing rates.  But without the ability to study nuanced mathematical ideas and relationships via discussion and debate (think Socrates), one never learns how to THINK mathematically.  Only to calculate.

Maybe that is what VTech is looking for.  I, for one, am not.  

Tuesday, March 27, 2012

Math in the Media: The Scale of the UNiverse 2.

A stunningly beautiful illustration of the scale of the universe, from its largest (it's estimated size) to its smallest (the size of the strings that make up our matter, according to string theory), all in a striking sliding scale video, set to music.

ABC News found this. You must take a look!

'The Scale of the Universe,' by Two Teenage Brothers

Simply amazing!!!

Monday, March 26, 2012

Thursday, March 1, 2012

Math in the Media: Flipping a Lecture???

Here at Hopkins, we are engaging in a project to better understand the general purpose and success of how the large-lecture, so-called, Gateway Science classes (the calculus, chemistry, physics, biology, etc.) in preparing students for the higher-level, specialized study of their future majors. It is a huge affair, and taken as a holistic, university-wide endeavor, has the potential to transform the general curriculum here at JHU in far reaching ways.

But more on that later. There is an interesting article in the Chronicle of Higher Education on turning the standard lecture-type model for university instruction into a much more interactive and enriching experience. The article

How 'Flipping' the Classroom Can Improve the Traditional Lecture

is a very good read. Eric Mazur, a physicist from Harvard, gave a talk here at Hopkins recently on his efforts to enliven the classroom experience. Engaging, he was, and his notion of peer-instruction, whereby students learn by active discussion with their peers while under the direction of the instructor, is just one aspect of the search for new models to engage students and promote a better, deeper sense of learning.

If you are here at Hopkins, you WILL see more of this in the years ahead. For now, give the article a good read.

Wednesday, February 8, 2012

Study tip for the day: Quality vs. Quantity

People often ask me how many hours one must spend outside of class per hour inside of class to succeed in a university-level math course. I hesitate to answer. The reason is that the question is ill-posed. To really understand the logical structure of mathematical ideas, how they work and fit together, why they exist and work the way they do, one must really spend the time to dig into every nuance of the idea. To do this on a research level, a mathematician understands that she must isolate herself from outside distractions for sufficient periods of time to fully explore the structure of a new idea. The isolation-booth manner is as vital to the process as deep, dreamless sleep is to the health of a person. I call the process of getting to the level where one can focus exclusively on the task at hand without distraction as "going deep". It is kind of a meditation-type thing, and only really works when one practices it regularly. It can be dangerous, though, as the day-to-day tasks tend to get neglected. But it is quality time for understanding complicated mathematics, and easily outdoes simple quantity time when the latter is filled with noise and attention-taking "shiny objects" (distractions).

It's loads more productive to spend an hour in an isolation booth environment focusing solely on your mathematics work instead of 3, 4, or 6+ hours poring over books and notes while checking your phone, listening to music or chatting with friends (or potential friends). Distractions keep you from "going deep" and really digging into the conceptual and logical structure of the math you are doing. And if you do not allow yourself to go deep to really get a concept or idea, you wind up simply memorizing facts and patterns. While this may work for problems just like the ones you have seen, the minute a problem of a different form comes up, you will be lost.

Hence, there are no good guidelines in the form of "6 hours of study per hour in lecture". Studying is a personal thing, and the studying environment matters. If you refuse to allow yourself NOT to fully understand a new concept, then any and all time spent in the pursuit of full understanding is worth the effort. To do it right, allow yourself the ability to "go deep". Then you minimize the time spent to only the quality time.

Some people brag about their ability to multi-task. To me, the ability to mono-task is the lost art in society.

Thursday, January 26, 2012

How to Learn by Lewis Carroll

I have recently been talking to a student about the whole idea of how one learns, especially at the university level. This student is thinking of starting a club of Hopkins students dedicated to discussing the theory and practice behind how one learns. Really a great idea. I will advise and keep you posted. For now, I give you Lewis Carroll's (Of Alice in Wonderland fame) ideas for learning. Enjoy! What is that old saying: Much truth is said in jest....

How to Learn by Lewis Carroll

1. Begin at the beginning, and do not allow yourself to gratify mere idle curiosity by dipping into the book, here and there. This would very likely lead to your throwing it aside, with the remark `This is much too hard for me!’, and thus losing the chance of adding a very large item to your stock of mental delights . . .

2. Don’t begin any fresh Chapter, or Section, until you are certain that you thoroughly understand the whole book up to that point and that you have worked, correctly, most if not all of the examples which have been set . . . Otherwise, you will find your state of puzzlement get worse and worse as you proceed till you give up the whole thing in utter disgust.

3. When you come to a passage you don’t understand, read it again: if you still don’t understand it, read it again: if you fail, even after three readings, very likely your brain is getting a little tired In that case, put the book away, and take to other occupations, and next day, when you come to it fresh, you will very likely find that it is quite easy.

4. If possible, find some genial friend, who will read the book along with you, and will talk over the difficulties with you. Talking is a wonderful smoother-over of difficulties. When I come upon anything—in Logic or in any other hard subject—that entirely puzzles me, I find it a capital plan to talk it over, aloud, even when I am all alone. One can explain things so clearly to one’s self! And then you know, one is so patient with one’s self: one never gets irritated at one’s own stupidity!

If, dear Reader, you will faithfully observe these Rules, and give my little book a really fair trial, I promise you, most confidently, that you will find Symbolic Logic to be one of the most, not the most, fascinating of mental recreations! …

Mental recreation is a thing that we all of us need for our mental health. Symbolic Logic will give you clearness of thought—the ability to see your way through a puzzle—the habit of arranging your ideas in an orderly and get-at-able form—and, more valuable than all, the power to detect fallacies, and to tear to pieces the flimsy illogical arguments, which you will continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating Art. Try it. That is all I ask of you!

Thursday, January 12, 2012

Employment Op: Business Intel and Math

People often ask me what kinds of jobs math majors can get other than science applications or as an actuary. Really, the answer is: All Kinds. Usually, one needs a good hook in an outside area to get into the interview. But then the analytical skill set of a mathematician can shine. However, sometimes recruiters simply understand well that someone skilled in mathematical analysis possesses the ability to learn most skills very quickly. These recruiters are willing to take a math major who can learn on the job, quickly and efficiently.

I just got this request from a recruiter. Read it and go for it. Sounds like an interesting career:

Thorogood Associates is currently recruiting college seniors for full time business intelligence consulting positions. We are contacting you, as the [Director of Undergraduate Studies] of the Mathematics Department, because we think you may know students that would be good candidates for this position.

As a business information consultancy, Thorogood helps its clients use their data to make better business decisions. Our work has both a business and technology aspect. We don’t necessarily look for education or experience in both of these areas but rather an interest and an aptitude that will allow a candidate to be successful in this type of work.

We are seeking candidates that have excellent problem solving skills, leadership qualities, and initiative. Candidates must be willing to take responsibility for the achievement of results, have self-confidence, and be energetic and friendly.

If you know of any students that have the qualities that would allow them to be successful in this position, please let them know about this opportunity. They can apply for this position via J-Connect. Applications are due on January 30th, 2012. We will be conducting on-campus interviews at JHU on February 7th, 2012. Any questions can be sent to

Check them out at:

Math in the Media: Eating Mathematics?

Alright..., just for fun.

If you are not yet convinced that mathematics is not a subject to study as much as it is the underlying logical framework for all that exists both in reality and in imagination, I give you another example.

The New York Times' Kenneth Chang has written a piece on the mathematics of pasta:
Pasta Graduates From Alphabet Soup to Advanced Geometry.
Those seemingly random and crazy shapes, designed specifically for texture, even cooking, and the ability to meld well with sauces and such, can be quite beautiful and subtle. This article exposes those who look for the mathematical structure behind the designs and the playful aspects of the shapes.

Take a look. But beware. You may never view a plate of spaghetti in the same way again!

Wednesday, January 11, 2012

NPR on the JMM

Well, here is something you do not hear every day: A human interest story on a national radio news program focusing on the joys and wonders of a national meetings of 6000+ mathematicians!

Go figure!!!!

National Public Radio decided to attend the Joint Mathematics Meetings of the American Mathematical Society and the Mathematical Association of America, the national gathering place for the year of all stripes of mathematicians, to see just what was happening there. The result was a report by Ari Daniel Shapiro entitled

A Unique Expression Of Love For Math

detailing the huge diversity of expression and study, both in the art and the science of mathematics, that mathematicians bring to their profession. The transcript and the audio of the piece is at the link.

What a nice way to view the world of mathematics that we see every day, but which most people never get a glimpse of.

Thank you, Ari and NPR!!