The Chalkboard

How to Learn by Lewis Carroll

2012-01-26T16:02:00.004-05:00

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!

Employment Op: Business Intel and Math

2012-01-12T14:17:00.002-05:00

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 30^th, 2012. We will be conducting on-campus interviews at JHU on February 7^th, 2012. Any questions can be sent to USRecruitment@thorogood.com.

Check them out at: www.thorogood.com

Math in the Media: Eating Mathematics?

2012-01-12T10:56:00.005-05:00

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!

NPR on the JMM

2012-01-11T12:52:00.004-05:00

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!!

I'll be on Cogito.org next week....

2011-10-28T16:17:00.003-05:00

I will be hosting a discussion forum on the website www.cogito.org for the next couple of weeks. Cogito is a math and science website and online community for talented youth, and part of the Center for Talented Youth (CTY) family here at Hopkins. I'll be taking questions and offering advice on whatever I can (involving mathematics, I suspect).

It sounds like it will be a lot of fun. I'll post my thoughts here in the interim.

My response to the NYT Op-Ed on Math Ed

2011-10-25T15:01:00.006-05:00

Well, it has been a while since I commented here on the New York Times Op-Ed on Math Education and its ills. My rebuttal here in this blog caught the interest of a talk show in California, though I did not reply in time to attend the discussion. I did write a rebuttal to the article and submitted it to the NYT. Alas, it was ignored. Oh, well.

Here it is, though. At least I accept my own submission. Enjoy:

Why Not Teach Math for Math’s Sake?

It is quite conventional wisdom, with lots of supporting evidence, to believe that the way we teach primary and secondary mathematics here in the US is generally failing our young students. This was detailed in the recent article in this forum “How to Fix our Math Education”, by Sol Garfunkel and David Mumford, and I see the general effects of pre-university education in students daily from my perspective as the director of an undergraduate program in mathematics at an American university. I believe the problems discussed in that article are real and demand action, and I applaud the authors for writing the piece. I disagree, however, with the conclusions of Professors Garfunkel and Mumford.

From my perspective, students come to university with a view of mathematics as a giant tool box they carry around with them, the tools being techniques useful to solve many kinds of diverse math-based problems. Pre-university education seems to be filled with disparate situations where a new concept is introduced (abstract or applied) to solve a certain kind of numerical problem, a technique is drawn up and the student receives a worksheet containing 40 or so variations of the same type of problem. Once completed, the class moves on to the next idea. While this assessment of pre-university education is simplistic, the outcome is that students never really learn how to think analytically, reason deductively, understand why these tools exist in the first place, or see just how each idea fits into the whole. Context via applications to real world phenomena (the kernel of the above authors’ proposed solution) may help in this regard, but there is a deeper problem with simply embedding math into applications to prove its usefulness.

The idea that mathematics lives only to serve its applications and functions only as the language of the sciences is absurd on many levels. More like music and poetry than physics or engineering, mathematics is an art, the art of pure reason. One could say that mathematics is the distillation of pure rational thought. When we teach math, we are not teaching how to solve problems. Instead, we are teaching how to think analytically; how to analyze any given complex situation, discover and understand its underlying logical structure, and figure out how to abuse that underlying logical structure to say something useful or conclusive about that situation. Numerical problem solving is solely one manifestation of this process. In the general sense math has very little to do with actual numbers at all. It is just that the use of a number system as one of our basic building blocks allows for a natural logically consistent system. Instead of giving students tools for solving problems, we should be teaching them the very nature of how and why these tools exist and were developed. Questions like why there is a quadratic formula, and why does the sine function exist at all are much more thought provoking and fundamental than how they work. We should be engaging students to actually design and redesign the tools themselves, a process of self-discovery which enables them to own the math they create. We should be giving them the confidence and experience to be able to see a problem as an opportunity for creativity and ingenuity, rather than an obstacle to overcome. And we should be teaching them that mathematical constructions have an innate aesthetic quality. They exist simply for what they are: beautiful constructions, often useful, whose existence lies entirely in the imagination, but whose manifestations in the real world are everywhere.

Math, like music and poetry, has a few constituent parts (notes and keys in music, words with contextual meanings and rhyming schemes in poetry) and a few logical rules which they follow. But with these few rules and parts, no one questions the infinite beauty and variance of musical creations or the fact that a few well-placed and possibly rhyming words can draw such emotion (think Shakespeare). And no one questions the value of teaching primary and secondary students music for music’s sake. Why not teach math for math’s sake? View it as a ground up endeavor where applications can serve as motivations for new mathematical ideas, but where the math lives outside of any application; where the beauty of self-exploration and discovery of fascinating concepts arises simply out of the aesthetic appeal of the constructions; and where the process of developing the skills of analysis and deduction in abstract logical systems becomes the goal of mathematics at the primary and secondary level. The application-based problem-solving skills could come along for the ride, and be reinforced in the other science-based classes. But the math would exist on its own.

Someone once said to me, “When are we going to stop getting students to solve problems and start getting them to POSE problems?” At the research level in math, we design and use the tools we need to pose and solve questions and problems as we need them. Teaching children the rudimentary process of doing this would go a long way to curing our math education woes.

What is that old saying “Teach a student a technique, and she will be able to solve some problems. Teach a student how to develop techniques, and she will be able to solve any problems.” I just made that up. But if we can teach our children to think analytically (read mathematically) before they reach university, imagine what we can do with them in university and beyond.

Thinking of graduate school?? Think NSF first!

2011-10-20T16:24:00.004-05:00

Hey graduating seniors!

Thinking of graduate school in mathematics or some math-centric science? How about a Fellowship as a good credential? The National Science Foundation is one place to look. I just got this announcement form a colleague here:

To senior math majors:

NSF will again be awarding Graduate Research Fellowships in math and science. Last year, 2000 fellowships were awarded, including 80 in mathematics. The fellowships are for 3 years and provide an annual stipend of $30,000. The deadline for applications is November 15. (Reference letters are due on November 29.) Information and online applications are available at http://www.nsfgrfp.org/.

Check into it: What is it they always say? "You can't win one if you don't apply" (okay, maybe not they. Maybe only I say that.

Competative Math: Time for the Putnam

2011-09-28T12:57:00.002-05:00

Welcome back to everyone who has been here at Hopkins, and welcome to those who are new. Yes, it is that time of the year again.... to start getting in shape for a little competitive mathematics.

Early December again brings the

William Lowell Putnam Mathematical Competition,

a locally held, national competition in undergraduate-level mathematics. Highly competitive and highly prestigious, the Putnam offers cash prizes as well as a very strong resume/CV credential to those who master the 6-hour two part exam. In fact, the Math Department recognizes the best from JHU in the exam each year with an award and cash prize. Recent JHU best-performers have included students who achieved recognition from the Putnam Committee. And our best school ranking in the last few years was 21st (out of upwards of 500 institutions that take part).

Registration for the 72nd national Putnam exam closes sometime around mid October, and the exam will be held on Saturday, December 3, from 10am-1pm and 3pm-6pm.

If you are interested in participating (and as a math major, I highly recommend that you consider these exams part of your training as a mathematician), please contact me in any way you can.

We are setting up training sessions for this exam on Wednesday evenings from 5-7pm. We will get a room once we have a head count and start a week from today.

Keep looking here for more announcements and news as the schedule develops.

Math Play: Every Natural Number is Interesting.

2011-09-15T15:14:00.003-05:00

I just read this in the first chapter of the text we use for our senior class Advanced Algebra. The book is Introduction to Advanced Algebra by W. Keith Nicholson. I like it, so I will pass it on.

If you study math, you have probably heard of the Well-Ordering Axiom, a property of the integers which is equivalent to the Principle of Induction. The Axiom states: Every non-empty set of non-negative integers has a smallest member.

Intuitively clear, no? Here's how it works in practice:

I claim that every positive integer is interesting. To show this, let's assume it is false (this is a proof technique known as proof by contradiction, in which one assumes the claim is false, then works by deduction until something absurd follows, a clear contradiction. If the logic is solid, only the assumption can be flawed. Thus your original statement must be true. )

Since the statement is assumed false, there must be a non-empty set of uninteresting positive numbers. But by the Well-Ordering Principle, there then must be a smallest uninteresting number. But an extreme element of any ordered set is automatically interesting (in that it is special)! Hence we arrive at the contradiction, making our assumption false and the original statement true.

Silly, yes?

How to (what?) Our Math Education?!!?

2011-09-08T13:26:00.003-05:00

Having concern for the state of mathematics education here in America is such a common thing among the population that there are probably almost as many ideas for a solution as there are people with concern. And while the issue is unsettled, it is great to have voices loud enough to keep the discussion lively and vogue. A recent (August 25) addition to the discussion is the New York Times Op-Ed piece

How to Fix Our Math Education

by Sol Garfunkel and David Mumford. I guess it is a hit piece on the No Child Left Behind initiative, but more it is an indictment on the standard idea of teaching math for math's sake at the elementary and secondary level. Their view seems to be that since mathematics was developed in tandem with science and applications, it should be taught that way. Bringing in the deep conceptual beauty of mathematical relationships in a class focusing on engineering or finance would better serve the students' educational needs rather than teaching the pure elements of, say, algebra in their own right.

I will let you read the article and form your own conclusion. My take? Little can be farther from the truth! The applications of mathematics are many, varied and beautiful. But the essence of mathematics is the study and development of pure rational thought. It is precisely the abstract nature of pure mathematics that should be taught to young students in our schools. And it should be taught as an art at every level, with applications only to serve as neat ways to display its innate beauty. The lack of a cohesive story about abstract mathematical relationships and patterns in our math class sequences is what fails our educational systems today. And not the fact that we do not apply math correctly. This is just my opinion.

I found the letters in rebuttal to this article of most interest to me: Read here for some of them:

Math = The Practical and the Beautiful

One real money quote that gives away my take on this whole business? From the Computer Scientist Jonathan David Farley's letter at the end:

You do not study mathematics because it helps you build a bridge. You study mathematics because it is the poetry of the universe. Its beauty transcends mere things.

Pure candy, that quote is!!

JHU Mathematics #1 in the world in research citational impact!!!

2011-07-15T13:20:00.003-05:00

The Times Higher Education, a London-based publication that focuses on higher education issues, puts out a series of university rankings each year. JHU does okay, IMHO, with a ranking of 13th in the world, based on a multitude of criteria, and 14th based solely on teaching and research reputation.

But to measure the influence that a research-oriented faculty has on the general research community, it is proper to measure the citational impact of a department's publications; how often papers are cited by other papers. The times measured this citational impact in mathematics. And who came out on top in a survey covering this last decade? Funny you should ask....

Congratulations to our active research faculty here in Hopkins Mathematics! A job very well done.

Advice for an independently-learning pre-college student.

2011-07-15T12:41:00.012-05:00

Back again, I am....

Here was a question I received recently:

Hello, ... I recently finished my sophomore [year in high school].... I have, for the past year, learned mathematics independently, taking trig, pre-calculus, calculus BC, and multi-variable calculus on my own. For the first two courses, I used an online provider. The third, I took an AP test to demonstrate that I have sufficiently learned the material so that I might receive credit for it when I go to college.

For the last course, multi-variable calculus, I would like to find a way to gain either recognition (such that I would not have to take the class in college) or credit for the course before I enter college. This is not the only class that I will have taken independently for which I cannot take an AP exam to be granted recognition. Also, I plan on starting other math courses independently (Linear algebra, differential calculus, etc.), so there will be multiple classes which I will have learned, but nothing to show for them.

Is there a way, through Johns Hopkins, I could acquire either credit for having learned college-level courses independently? If not through Johns Hopkins, do you know of a way to do this using different means?

A good question, as there are many pre-college out there struggling to quench their thirst for mathematical knowledge amidst a dry, arid environment void of opportunity. My reply:

While I like your initiative, and value your capabilities, I am wondering why you are trying to burn through all of this material at such a high speed. The AP exams, while a nice system for providing advanced training in mathematics to pre-university students, do not really measure proficiency in calculus. Rather, they measure your ability to apply proper techniques to appropriate problem types. While this is helpful, it is not really what mathematics is all about.

In your case, looking for opportunities outside high school for advanced training (as you are doing through self-study) is a good idea. But simply relying on an online course or a book and a standard exam may wind up giving you a false indication of your true knowledge base in these subjects. And if you foundation is not strong in basic subjects, you may find yourself faltering later on at the higher levels.

Some questions: (1) Do you have a mentor at your high school, or nearby, a math instructor, or mathematician to help guide you through your self studies? Someone who can see your "path" from above while you walk it is very important to your training. (2) Is there a goal in your life, which provides the reason for going from trigonometry to vector-calculus and beyond in a single year? These are beautiful subjects full of amazing insight and deep conceptual meaning. Burning through them at top speed is really selling the individual topics short. This is like driving through a safari park at 80 miles an hour. You have done the park, but have you really spent time learning about the animals. (3) Have you looked at simply taking courses on these topics at your local university, one at a time, and with live instruction? Even at the community college level, there are very good instructors whose lectures in class and conversations outside of class can be extremely helpful in seeing more then the techniques.

Yes, we here at Hopkins have many ways of evaluating the proper level for students to start at their first semester here. And we are committed to ensuring that students are not taking courses they are clearly too advanced to take. Acknowledging a students proficiency in a mathematics course may not always involves credits for the course (maybe just a waiver), but most of our evaluation involves some sort of comprehensive documentation of prior training, and not just an exam. Exams are not usually very good indicators of real understanding.

I hope this helps. Good luck in your training.

Spirit, initiative and resourcefulness are primary qualities of the budding scholar. Having and/or finding a mentor or guide is absolutely fundamental (even Harry Potter wouldn't have made it on his own!) And taking your time to digest what you are learning always leads to "better nutrition", no?

Math in the Media - Jump Math

2011-04-19T11:04:00.003-05:00

A neat article appears in the Opinionator column of the New York Times by David Bornstein;

A Better Way to Teach Math

The article details a new attitude and focus in the education of mathematics at the primary school level. The organization, Jump Math, is based in England and is the project of John Mighton, a playwright and author, and seems to already be showing results.

Really, it sounds like Jump Math (as I write this, the link above to the organization is down) is not a new set of concepts to teach. Rather, it is simply an idea that the best way to teach mathematics (at any level) is to instill the idea that high level math is not just for those who have "the ability" to get it, but for everyone. Many of us who teach math really do understand that anyone can understand high level math. The problem is that many students have already concluded that they are not able to get math, so they do not have the confidence to really try to understand what is going on. Couple that with a sense that many teachers of mathematics do not really get the art and beauty of mathematics. So they teach a technique-based, problem-centric type of math that loses the deeper meaning. Without proper motivation, much mathematics loses its context, and hence much of its meaning.

From the article:

Imagine if someone at a dinner party casually announced, “I’m illiterate.” It would never happen, of course; the shame would be too great. But it’s not unusual to hear a successful adult say, “I can’t do math.” That’s because we think of math ability as something we’re born with, as if there’s a “math gene” that you either inherit or you don’t.

I have heard this ALOT, and my response is always something like "probably because you were taught by people who didn't get it. Anyone can do math...."

The article is nicely written, and quite pleasing to hear for someone like me. I will be probing this new set of ideas called Jump Math over the near future and report my finding here. To me, at least on the surface, something like this is exactly what I think pre-university teaching of mathematics needs.

The article promises more at the end of the week. We will await the continuance. For now, a good ending quote:

"Even deeper, for children, math looms large; there’s something about doing well in math that makes kids feel they are smart in everything. In that sense, math can be a powerful tool to promote social justice."

One has to love quotes like that....

Math in the Media - Algebra a leading indicator of success in life??

2011-04-05T16:05:00.003-05:00

Whoddathunkkit? Well, except for most of us that do math for a living, you mean?

This article in the Washington Post:

Requiring Algebra II in high school gains momentum nationwide

by Peter Whoriskey, seems to be really an article on the debate of the merits of teaching high level mathematics as part of the core curriculum in high school.

Peter discusses a study that shows a correlation between successfully taking mathematics through Algebra II, where properties of functions like exponentials and logarithms are analyzed (along, I guess with complex numbers) in high school and continued success in college and through a career. Whether learning algebra is the reason people are more likely to succeed, or those more likely to succeed usually wind up taking the challenge of Algebra II, is not apparent.

But the study is interesting and should keep up the discussion.

My personal take. Forcing middle schoolers and high schoolers to master problem solving strategies using highly abstract models in mathematics is a way to wire their brains for the complexities of real life events that will present themselves in any and every career path choice, no?

One can teach strategy and problem solving in any specific discipline using the techniques of that discipline, and you get people well versed in that discipline. But mathematics is a 100% in-the-head discipline. Mastering the abstract complexities of mathematical structure and analysis means learning not just how to problem-solve, but it is like learning the actual art of problem solving. It becomes adaptable to any future discipline one winds up in.

Good sound mathematical training is like producing problem-solving stem cells. Later in life, when you need those stem cells to morph into good problem solving skills in some job, you will have them ready for use.

I also believe that Algebra II is attainable for every high school student. Some of the quotes in this article come from students who do not get the subject. It looks like they were/are not well-taught the subject. Perhaps THAT is the real problem? Non-uniformly good teaching.

STEM Over Spring Break....

2011-04-05T15:28:00.002-05:00

Here is an interesting activity; a way to give back to those yearning for the kind of "fun" of mathematics that you feel and felt back then....

Christine Newman, the Assistant Dean for Educational Outreach and Dr. Meg Bentley, Program Manager at the Center for Educational Outreach in the Whiting School of Engineering at JHU, are organizing a day of fun math-centric informal activities for Baltimore City School kids during their upcoming Spring break next week. It's called STEM over Spring Break (the STEM part means, I believe, Science, Technology , Engineering and Mathematics) and is meant to be lighthearted and playful. if you are interested in taking part by working with city students on fun math-ish activities, or if you just have some bright ideas for playful math or interested math activities you would like to share, contact Dr. Bentley directly at meg(dot)bentley(at)jhu(dot)edu. Or click on the link to the Center above for more information.

It is always good to stop once in a while along your own path and give a hand to those struggling along the same one, no?

A career with the NSA...?

2011-03-01T15:00:00.001-05:00

The National Security Agency has just announced their upcoming Intelligence Community Virtual Career Fair on Tuesday, March 8, 2011. A chance to talk directly to NSA Recruiters about career opportunities. And a place that hires LOTS of mathematicians for careers doing pure mathematics (imagine that!). The posting, in its entirety is below. Check'em out.

Join the National Security Agency at the Intelligence Community Virtual Career Fair Tuesday, March 8, 2011 from 2 p.m. - 8 p.m. (Eastern)

Let’s talk about your future at the National Security Agency. Please join NSA March 8th at the IC Virtual Career Fair to explore exciting opportunities for your future. Reserve your spot today: http://www.aftercollege.com/op/op.asp?id=5307

Who: We are looking for technical career professionals (computer network operations, software/hardware design developer, software engineer, global network exploitation and vulnerability analyst, computer scientist, computer/electrical engineer, computer systems analyst, computer systems architect)

Language analysts and instructors (Chinese Mandarin, Dari, Farsi, Pashto, Punjabi, Somali and Swahili)

What: The Intelligence Community Virtual Career Fair

Where: The nearest Internet connection.

When: Tuesday, March 8, 2011, from 2 p.m. to 8 p.m. (Eastern)

Why: To discover the incredible benefits of working with the National Security Agency. You’ll be able to chat with recruiters. Explore exciting career fields. Enjoy live presentations. Mingle with like-minded folks. And just have an all around positive career-oriented event … all from the comfort of your own computer.

Register today: http://www.aftercollege.com/op/op.asp?id=5307

U.S.citizenship is required. NSA is an Equal Opportunity Employer.

All applicants for employment are considered without regard to race, color, religion, sex, national origin, age, marital status, disability, sexual orientation, or status as a parent.

Playful Math: Doodling to Aleph_null

2011-01-25T13:53:00.005-05:00

I believe most people who really get mathematics are the ones who see the frivolity in much mathematical construction not as a flaw, but as a strength ( I am teasing my profession here). And sometimes presenting mathematics in playful ways is precisely the best way to expose deep meaning.

With a hat-tip to Engineering Innovation (@JHU_EI), a high school summer program in the Whiting School of Engineering here at Hopkins, I am reposting a video from one of their recent tweets.

Doodling in Math Class: Infinite Elephants

Have fun!

Oh, and BTW, we mathematicians tend to associate letters from other alphabets to important constants and concepts in our work. Aleph (the first Hebrew letter) is commonly used for measures of infinity. Aleph_null, or Aleph with the subscript zero, is used to denote a kind of infinity called countable infinity, and denotes the size of a set of objects that can be placed in a one-to-one correspondence with the natural numbers 1,2,3,... Jus'sayin'....

Math (not quite) in the Media... College not producing?

2011-01-20T09:54:00.004-05:00

A new study has come out which seems to conclude that a college education may not be worth the many hundreds of thousands of dollars it is costing these days. Here is an article from the Huffington Post detailing some of the points coming from the data. I have not read the study. The article, I have, and am less than impressed.

My take: While there may be quite an important trend uncovered by this survey, I believe (from my position) that some of the assumptions may not be fully vetted.

45% of Students Don't Learn Much in College

The article starts off well enough (emphasis mine):

A new study provides disturbing answers to questions about how much students actually learn in college – for many, not much – and has inflamed a debate about the value of an American higher education.

The research of more than 2,300 undergraduates found 45 percent of students show no significant improvement in the key measures of critical thinking, complex reasoning and writing by the end of their sophomore years.

However, this part bothers me:

One problem is that students just aren't asked to do much, according to findings in a new book, "Academically Adrift: Limited Learning on College Campuses." Half of students did not take a single course requiring 20 pages of writing during their prior semester, and one-third did not take a single course requiring even 40 pages of reading per week.

Where is the metric measuring critical thinking and complex reasoning OUTSIDE of a writing class? Mathematics and physical science-based courses are prime venues for the development of rational and analytic reasoning, no? How come no mention of non-writing-based courses in the ENTIRE article? Perhaps no data from these courses is in the study?

More from the article:

Three of the five classes [Julia Rheinecker, a freshman at the University of Missouri,] took... were in massive lecture halls with several hundred students. And Rheinecker said she was required to complete at least 20 pages of writing in only one of those classes.

I am very dubious about any direct link between college class size and either the difficulty of a course or its perceived lack of rigor. Large-lecture courses can be quite challenging and yet every bit as personal and interactive as small seminar-type classes. I doubt this study had any focus on class size at all. So this part is not relevant, IMHO.

And finally, some additional conclusions in the study:

_Students who studied alone, read and wrote more, attended more selective schools and majored in traditional arts and sciences majors posted greater learning gains.

_Social engagement generally does not help student performance. Students who spent more time studying with peers showed diminishing growth and students who spent more time in the Greek system had decreased rates of learning, while activities such as working off campus, participating in campus clubs and volunteering did not impact learning.

Knowing something about how math is taught and learned at the university level, I am hard-pressed to believe any data showing that studying alone is better than studying with peers. On this point, I can write volumes! And there are data and programs (Think PLTL, for example) to support the opposite conclusion. In fact, we have a local PLTL program here at Hopkins, and our data do not support this study's conclusion in this point.

Overall, I see this study as being a bit alarmist. Critical studies on the effectiveness of college education are absolutely necessary. I will read this study. But I am already biased due to this article. Oh well....

Undergraduate Research Opportunity!

2011-01-11T14:21:00.002-05:00

I just got a solicitation for a great summer program in research for undergraduates. Click on the flier to see the details. It is the Research in Industrial Projects for Students (RIPS) program at the Institute for Pure and Applied Mathematics (IPAM) at UCLA. Top-notch, IPAM is, and I am sure the opportunity is quite competitive. But the program is a good one, and will make for a great credential (not to mention the experience!). Check it out and let me know if you plan to apply: The deadline is February 10. Plenty of time to get your act together, no?

Mathematics Study Tips - Finals Time!!!

2010-12-01T14:59:00.002-05:00

I have posted many of my own tips on studying in mathematics classes here in this blog (see the tag for Study Tips). So when I happened on this article on the online newsroom Huffington Post, I clicked through.... What I saw sounds remarkably familiar, and ALL good advice. Give it a read:

12 Ways to Ace Your Finals

Pay attention to the study groups part, the adding stress to your studying to reduce stress in the exams, and such. Good luck all!

Math in the Media - Me??

2010-11-09T09:52:00.004-05:00

I received a request recently to do an interview for the student-run newspaper here at Hopkins, called the Newsletter. It came as part of a series they do called "Things I have learned" and features short interviews here with professors to learn more about who they are, why they do what they do and where they see their future taking them.

I got contacted by a student Emily Nadelmann. Here is the article. It was fun, and gave me a chance to talk a bit about how I see my profession, my study and my interacitons with it. Give it a read. The title is

Professor discusses the artistic aspect of mathematics and teaching

Math in the Media - Shock Therapy as a study technique??

2010-11-04T15:26:00.002-05:00

Just ran across this report:

Electric brain stimulation can improve math skills

Read the article. An Oxford study has found that low levels of electrical stimulation of the brain (read: shock therapy?!!?) can improve math assessment skills. And these skills last for at least for a long time (at least half a year??).

I can already see the ill-advised do-it-yourself home implementations of this kind of study technique. Geez....

I can already see this giving other study aids a run for their money, no?

Mathematics Study Tips - Pre- (and post??) pare for lectures

2010-10-28T10:59:00.003-05:00

Hey again all. Some time ago, I started writing down what I consider are good tips and practices for studying and getting through mathematics courses at the university level. Click on the "Study Tips" tag to see those. here is another I find myself often saying to struggling students:

To make most of the lectures (the backbone of the course, no?), why not prepare for them. To really make them an integral part of your course experience, why not post-pare for them also!? What do I mean...?

It is commonly accepted that it is easier to remember something when you hear it more than once. Maybe then it is placed in more than one position in your brain, with different associations triggering its location. Maybe it still sits in one location but is better interconnected with other triggers. Maybe I have no idea.

But it would certainly help greatly to not only know what is coming up in the next lecture (check the syllabus online before the meeting), but also to have spent some time in the book on the material before the show. No ?

Preparing for the Lecture

If you know the next lecture is on ( a hypothetical) Section 4.6, say, why not spend 10-15 minutes before the lecture reading through that section? You don't have to understand completely what you are reading. Some of it will make sense, some not. But at least you will be exposed to terms, concepts, boxed items, examples, BEFORE you enter the class to actually see the lecture develop the ideas. This way, the stuff you did understand on first reading will be cemented by the lecture development. You can even relax a bit on this part of the lecture.

When you get to the part of the lecture that comes from material in the book that mystified you, you can then spend some precious attention time focused. Pretty efficient, huh? We, as instructors, really do like to follow the book in many of our courses. Books are written in an organized fashion. We may embellish the material, but the core usually comes from the book.

Your notes in a lecture are an important facet of your eventual understanding. See here for some tips on taking notes.

Post-paring for the lecture

After the lecture is where the fun really starts! Here is my idea for good practice....

Grab a small block of time (another 15 minutes), in a quiet place and free from distractions, somewhere between an hour and three hours after the lecture. It won't take long. Go over your notes slowly and carefully an in your mind, relive the lecture, re-listening to the instructor and imagining the lecture hour unfold. As you f0llow your notes, you will remember things that were said that you did not write down (or finish writing down). Write them down now. You will see examples half-finished. Finish them now. You will references to the book. check them and make a mental note of them, You will make connections that you did not make before. Note them in your notes. You will see thing in your notes that STILL mystify you. Mark them (in red?) with a big question mark. Make a note to yourself to go to your TA or the instructor and ask specifically about these question marks (much of this part is also talked about in my installment of this series on Notes. Take a look there also).

All of this is called "completing the experience". It is a way to make your notes of the lectures a complete and central account of the course, as they should be. And it is a form of studying that WILL pay big dividends as the course progresses.

Try this for a few weeks. It really is a minimal effort for the benefit it offers. You will see improvement.

In bocca al lupo!

Course Pre-req changes....

2010-10-14T09:48:00.002-05:00

Here is a heads-up on some course pre-requisite changes that we will be implementing immediately. We will be forcing anyone considering 110.211 Honors Multivariable Calculus to either take 110.201 Linear Algebra or 110.212 Honors Linear Algebra as a co-requisite (at the same time), or to have one of them (or equivalent) as a pre-requisite. If either of our versions of Linear Algebra are to be used as a pre-requisite, then the final grade must be a B+ or better.

The reasons are simple: A good, solid working knowledge of linear algebra is absolutely necessary to fully understand the theoretical underpinning of multivariable calculus. One can say that multivariable calculus IS the non-linear generalization of linear algebra (or that linear algebra is simply the linearization of multivariable calculus). This allows us to concentrate on the calculus nature of the topic without having to focus on leveling the background deficiencies of some of our students. It also will dampen the urge of some of our students to jump into a course they only later realize they are not qualified for. Our version of honors Calculus III is deeply theoretical by design. And we want to focus this level of training on those who definitely will be seeking a major in mathematics, or have a real interest in and dedication to the formal development of the mathematical topic.

As for the co-requisite option, it turns out that how linear algebra is used and developed within vector calculus lends itself well to a side-by-side learning experience.

We will continue to monitor this course (along with its text choice). But for the short term, you must have linear algebra in your back pocket (or promise to attain it) prior to jumping into the deep end of the multivariable calculus pool.

Happy swimming.

Summer Internship Oppo!

2010-10-08T11:40:00.002-05:00

Hey, just got word from the Mathematics Research Group over at the National Security Agency (NSA: You know those guys, right?). The Director's Summer Program is a research-based 12 weeks in the summer where one works on issues involving pure mathematics, cryptology and communications technology. It is a paid position, prestigious, and of course highly competitive. It would also be a great career booster, even if you really have no intention of working at the NSA in the future.

The application process is all online, and the deadline is October 15. Give it a look.

Get Funded for Studying....

2010-09-28T17:17:00.002-05:00

Hey all,

Thought I would send along a note about upcoming scholarship and fellowship opportunities open to Math and science majors: Two of note are:

The SMART Scholarship: A scholarship-for-service opportunity for U.S. graduate and undergraduate students. The acronym stands for Science, Mathematics, And Research for Transformation, and fully funds either undergraduate or graduate studies in most of the natural sciences, engineering, and mathematics. Fully funded means tuition, health care, a stipend, etc. The term scholarship-for-service means that you will be required to work summers as an intern (tough gig, no?) at a government agency. See here for details . (Incidentally, the self-launching web-ad on this site rocks, IMHO..., at least the first time you see it. But it cycles through, which can get annoying.) The deadline in in December.
For senior intending to study mathematics in graduate school and first year graduate students in mathematics, the National Science Foundation offers the Graduate Research Fellowship Program, a 40K a year fellowship with few strings attached, as long as you study. Here is the brochure (as a PDF). The deadline for this is mid-November

We will be strongly encouraging our majors to apply for these, and think we have good chances. We will also hold a meeting to discuss how to apply and help you through the process. Look for the details to come soon.

We are a Top 50 Freshmen Advisor!

2010-09-22T15:44:00.004-05:00

Well, I'll be.... It seems that I've been noticed.

A website devoted to online resources for the college-age and college-focused among us, eCollegefinder.org has showcased websites devoted to education innovation and advice, and career advice and advocacy, among other things. Their just concluded their latest top 50 list, for Freshmen Advisors. I made it. It is quite the complement and very nice to be noticed.

I thank them for their endorsement, and hope I can live up to the their (and your) expectations.

Nice.

Jobs Opps for seniors...?

2010-09-21T17:17:00.009-05:00

Hey Majors (and especially you seniors....),

What are you thinking of doing after your stint here at Hopkins is done? While this question is rhetorical (for now), time flies when graduation approaches. I get many bits of information about opportunities at times. here are a few for you:

The JHU Fall Career fair is next Wednesday. I haven't stopped in to one of these yet, but the list of participants has over a hundred companies and organizations. They wouldn't be there if they weren't interested in what you have to offer them. Give it a try.
The National Bureau of Economic Research, in Cambridge, MA, has a need for full-time Research Assistants, one year positions starting in the summer, for students interested in a bit of research experience before starting graduate school in a quantitative field (not necessarily economics, mind you). Click on the image for a flyer. Nice place, the NBER. Seriously good place to stay for a year.
The Quantitative Trading and Analysis program at Citigroup is looking for Almost Bachelors and Masters students in Mathematics who have an interest in Wall Street-type analysis. Here is a flyer for this one also. And Okay Kayaoglu, who graduated here last year, specifically mentioned that he is looking for Hopkins students.
Campus Coordinator and Senior Hopkins student Nicholas Gilson has put out the call for Teach for America, a non-profit that places graduating seniors and graduate students in low-income classrooms for a two year stint to learn the art of teaching and give a bit to the world. It's a wonderful opportunity to take some time to adjust to life outside of college, and to enrich your life and credentials with valuable teaching experience. The next application deadline is in October. Give the website a look, and Nicholas an email if you are interested. Here is an article on the program.

I'll have others, I am sure. But these look like interesting leads, no? Happy life-getting! And talk to me if you want or need further information. if you are interested in the last item, I have Okay's email address.

2010 Putnam training sessions

2010-09-17T13:07:00.003-05:00

Hey everyone. For those interested (and I have just contacted many of you who are), the Putnam training sessions will be held on Wednesdays, from 5pm - 7pm in Krieger 304. All are invited to participate, and I believe the format will be an interactive discussion on techniques and strategies for attacking Putnam-type questions using previous exam questions as a guide.

Out very own Duncan Sinclair, a veteran graduate student here, will run the sessions.

Have fun getting in shape (?) for December!

Surviving university-level Math?

2010-09-16T13:11:00.003-05:00

I gave a orientation talk this fall to incoming freshmen. It was part of a set of Academic Interest Panels, designed to facilitate the transition from a student's previous life to university life. My contribution was to make them aware of a problem I see with incoming freshmen in their first math class here at Hopkins: That what they expect for math at this level, in terms of workload, focus, level of rigor, expectations of the student's as well as that of the instructors is really very different from the reality. And the transition shock that sometimes results can doom a student's chances in that first class. The talk was entitled

Thriving in University-level Mathematics

It became more than just a warning, however. I wound up giving lots of advice on how to study, how to treat the course and its components, the role of the lectures, recitations, homework, the instructor the TA, etc.

The step from secondary school math to what we offer is quite large.... easy to trip on, so to speak.

Click on the title link to see a PDF of the slides. It's worth a look, I believe. Enjoy.

AP credits tightening??

2010-09-14T11:52:00.003-05:00

Here is a heads-up on a policy change coming down the pipeline....

Recently, in a post entitled AP Preparation Adequate?, I posted on a concern we have with the way we award credits for exam scores under the AP system. The questions is: How well is the AP system prepping our students for college-level math?

There has always been a concern that many HS programs tend to teach for the exam, devoting much time on problem types and techniques and sacrificing some of the deeper theoretical material development in the process. Here at the university level, where we do not sacrifice the theoretical material, we find the transition for some students to be quite difficult. Anecdotal and personal evidence abounds (my interactions with individual students, for example). Systemic evidence (searching for evidence throughout our service courses) is more difficult to uncover.

The previous post presented an attack to uncover some systemic evidence. This evidence is now leading to a decision by the department to change the policy regarding credit awards.

Namely,

instead of offering Calculus I credits for a 4 or a 5 on the AB exam, we will restrict the credit awards to those receiving full marks, or a 5 on the AB exam.
Instead of offering Calculus II credits for a 4 or a 5 on the BC exam, we will restrict the credit awards to those receiving full marks, or a 5 on the BC exam.
The award of credits for Calculus I by receiving a 3 or a 4 on teh BC exam will remain in place.

Putting this new policy in place will take some time, but the wheels are now turning. Comments?

Putnam Training

2010-09-14T11:40:00.004-05:00

Ever try playing a competitive sport without a good training regimen already in place and in action for months before the game? Running a fun run without prepping for it for weeks beforehand? Take an exam without paying any attention to the material until the night before?

The Putnam Exam will arrive this December. If you are interested, now is the time to start prepping for it. The Mathematics Department, as well as the Mathematics Club here on campus, provides Putnam Training sessions designed to help you develop strategy and practice, getting you in shape for the "Big Game".

Sessions are currently scheduled for Wednesday evenings from 5pm-to-7pm. The will be run by Duncan Sinclair, an advanced PhD candidate here in our department. Training will focus on questions from old exams and the strategies for attacking them, as well as interactive discussions and scrimmaging. All are invited, whether you will take the exam or not, and all are encouraged to participate actively.

Contact me or Duncan directly (find our email addresses on the Mathematics Department website, or reply in this thread) if you are interested. if you are but cannot make the time slot for the sessions, Duncan will poll the interested group for alternative time slots and/or dates.

On to the games...!

Competitive Math: The Putnam

2010-09-14T11:22:00.004-05:00

William Lowell Putnam Mathematical Competition,

a locally held, national competition in undergraduate-level mathematics. Highly competitive and highly prestigious, the Putnam offers cash prizes as well as a very strong resume/CV credential to those who master the 6-hour two part exam. In fact, the Math Department recognizes the best from JHU in the exam each year with an award and cash prize. Recent JHU best-performers have included students who achieved recognition from the Putnam Committee. And our best school ranking in the last few years was 21st (out of upwards of 500 institutions that take part).

Registration for the 69th national Putnam exam closes sometime around mid October, and the exam will be held on Saturday, December 4, from 10am-1pm and 3pm-6pm.

If you are interested in either of these competitions (and as a math major, I highly recommend that you consider these exams part of your training as a mathematician), please contact me in any way you can. We train for this exam during the fall semester, and will be setting up session shortly.

Keep looking here for more announcements and news as the schedule develops.

A disappearing number?

2010-07-15T10:08:00.003-05:00

A new math-centric play opens tonight at the Lincoln center in New York for a brief run: A Disappearing Number, by Simon McBurney. Said of the performance:

This groundbreaking work embraces the universal relevance of math..., [and] revolves around the mathematical and spiritual nature of infinity, which becomes the link between two mathematicians: one an established Cambridge professor, G. H. Hardy, the other a young, autodidactic genius from India, Srinivasa Ramanujan.

Folks on the inside (of the research mathematics profession, that is) will instantly recognize Ramanujan, one of the more fascinating geniuses we have in math, both in his ability as well as his story. You should google each of these two mathematicians, though.

But really, back on task, making the beauty and mystery of real mathematics appealing by interweaving it into a drama is still rare these days, and very welcome.

The story at one point links itself to A Mathematicians Apology, a 1940 essay by Hardy on the aesthetics of mathematics. He compares mathematics to art and poetry, much like A Mathematician's Lament, which I highlighted recently. A great quote from the new play (which I can only paraphrase at this point):

"Like poetry and art, mathematics is the discovery and design of patterns. Beauty is the prime feature of good mathematics.... There is no place in this world for ugly mathematics."

You gotta admire statements like that.

It is said that one of these performances (there are only 5 of them) will be taped and released in theaters as a HD film in October.

I'll be looking for it.

RIP Martin Gardner: 1914-2010

2010-05-28T14:43:00.002-05:00

Here are some tributes from some of our profession to one who arguably advanced our field more than most of us combined have. As Martin Gardner digested high level mathematics to a point easily attainable and entertaining to a lay audience, he exposed the art, the beauty and the fun of mathematical study to a whole generation of readers. He is one of the minds that inspired me. It is truly sad to hear of his passing.

From the pages of the Magazine that carried his articles for more than 25 years: Scientific American.

New Advice for Incoming Freshmen....

2010-05-21T10:21:00.004-05:00

A new item under the category of Incoming Freshmen advice has been worked out, and an announcement here is worth the post. In short,

Who should be taking the honors versions of our mathematics courses?

A lot of questions have come up among individuals about the role of the honors versions of our service courses, and who is really qualified to take them. We have updated our advice page:

http://www.mathematics.jhu.edu/new/undergrad/placement/

Before the change, the advice page recommended the honors version of multivariable calculus, 110.211 Honors Multivariable Calculus, to anyone with a score of 5 on the Advanced Placement BC-level exam. While this score certainly opens up access to the course, really the focus and intent of the course is different from that of the regular version 110.202 Calculus III.

The honors version, like all of our honors versions, is really a course in "mathematics taught the way mathematicians would really like to teach mathematics" (my quote). It is a highly theoretic versions of the standard curriculum, focusing to a large extent, on the underlying theory of a topic and focusing less on the applications and techniques. It is a great course for budding mathematics majors and those who aspire to learn mathematics in a more formal way. In fact, it is a great course to use as a bridge to higher level mathematics, and we encourage our mathematics majors to take the honors versions of all of the courses where we offer such a version.

On the other hand, the honors versions of our courses are not really for someone who simply wants to have the title "honors" on their transcript. Nor are they for students who are not interested in gaining a deep understanding of why topics like calculus are so foundational to higher level understanding of all mathematical modeling.

We have found that many students were jumping directly into this course (and the other honors courses) and having to reassess their choice after a couple of weeks into the semester. Many of these students found themselves switching "down" to the regular version of the course. Not a good way to start one's career here at Hopkins, no?

With this new advice page, we hope to better inform students of our intent, as well our offerings in courses. We always welcome any and ALL commentary of our curriculum, and strongly encourage questions about our programs.

And for ALL of the incoming freshmen out there, welcome to Hopkins. My door is always open!

Why I teach....

2010-05-13T10:00:00.003-05:00

There are many reasons why we do the things we do. The choice of one's career is typically not an actual choice more than an evolution of minor choices and mixed opportunities that lead one to where one winds up. I teach mathematics (among the many things I do here at Hopkins) because I really like it! It provides a sense of career fulfillment one usually has when one is markedly satisfied with their job choice. But why it brings this sense of fulfillment is a bit deeper. Just to try, I will throw an occasional post on this blog detailing why I love my job. Here is the first:

They say war is composed of seemingly endless hours of boredom and drudgery interspersed with occasional moments of pure and abject terror. A full appreciation as to why some people choose to fight wars (choose to reenlist during an active campaign and get back into the theater) can only come from an understanding of just what that adrenaline rush during the terror moments actually feels like.

When one is "doing" math research, one tends to struggle for long periods in an imagined world trying desperately to understand how the complicated parts of a seemingly beautiful structure work in a way that combines the imaginations of other mathematicians and the possibilities that are consistent with all other imagined structures. In this sense it is the purest of arts, as it only exists within the constructs of one's mind.

This usually leads to long periods of confusion and frustration interspersed with moments of total clarity. It is in these moments when something works out that one has a sense for something so much bigger than reality that the adrenaline rush hits and euphoria sets in. These moments and their constructions are filled with so much beauty to us, that we "know" exactly what Mozart or Monet must have felt. We live for these moments, and cannot wait to tell everyone else about them. (It is such a pity that these constructions are not so easily accessible outside of our small worlds!).

When I am teaching, I am describing, narrating, and constructing bits and pieces of an abstract (we say "formal") world that I see quite clearly to people who are trying to understand. I have many tools to help other people see more clearly. I use as many different perspectives as I can think of, look for visual clues in the looks of others to see if they are slowly comprehending, dig into details to find the keys to understanding. The act of teaching is just like the act of doing math research. How to give someone a fully see-able abstract object is not an easy task. But it is a puzzle that requires mathematics to solve (read: more abstract imaginative thinking).

However...,

every so often there is that moment; that single instant when after all of the description and frustration and time spent in trying to understand, the moment when full comprehension dawns. That moment when I have successfully handed over a fully developed complicated imagined object to someone else. There is that look the other person (a student, or a colleague) gets when they "see" it, when they get it, when they sense that they have grasped exactly what you are trying to hand to them. They see the beauty of it, and appreciate both the object itself as well as their accomplishment in being able to "see" it....

I teach for that moment. It does not matter how often it comes (although I strive for moments like that to come as often as possible), because when it does, nothing can top the sense of fulfillment it brings.

That sense of connection between student and teacher is totally 100% ethereal. And not only can it not be matched by ANY physical bond, it also leave a mark, which lingers in both parties for a long time.

This is why I teach....

The 2010 J.J. Sylvester Awards!

2010-05-06T13:40:00.005-05:00

I am proud to announce this year's winners of our J.J. Sylvester Award for Outstanding Performance by a graduating senior (we will fix this link problem shortly). This year's winners are:

Adam Saltz
Xinlu Huang

These two overachievers quite well-represent two of the three types of students we find here at Hopkins.

Adam is a math major intent on seeking a graduate degree in mathematics, although he will take an academic sabbatical this next year before attending graduate school. He will graduate with department honors with a perfect GPA in math, and receive a master's as well as a bachelor's degree in mathematics as part of our BA/MA program. He has also worked in the department as a Teaching Assistant, acting as a recitation instructor for our freshman classes. In this capacity, he is one of our best.

Xinlu, instead, is a combination Mathematics and Physics major who is also a student of the Peabody Institute. She averages about twice the normal number of credit hours per semester here (I am convinced that she owns a time-turner like the one Hermione uses at Hogwarts!), and carries an almost perfect GPA also. She will stay here at Hopkins for another year, however, to achieve her Master's at Peabody.

Congratulations to both of them. With credentials like these, many doors now stand open for each of them.

Incidentally, these two students represent the "I have always and only wanted to do math and view Hopkins as a stepping stone to graduate school" type and the "math is a great outlet for my creative side and I want the math degree to compliment my other interests and add a good credential to my resume/CV" type. The third type of student we see here at Hopkins is the Pre-Med, a wholly different yet equally as complex and interesting species. ;-)

EVERY Mathematician's lament....

2010-04-30T15:38:00.005-05:00

The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such.

So starts a 25 page essay called A Mathematician's Lament, written in 2002 by Peter Lockhart. Certainly, most all mathematicians know this, and it really is this belief that leads us to the obsession with the beauty and general aesthetic quality of mathematics and mathematical research.

Now an expanded version of this essay has been published by Lockhart and Kieth Devlin. I have not read either the original essay or the book yet (I will be shortly). But I am so struck with this early quote and how I often find myself at social situations saying precisely this sort of thing:

"Math is an art. You know, like painting or music...."

Sometimes, some things just speak to you, no? I'll have more when I have read the works.

AP preparation adequate?

2010-04-22T16:40:00.004-05:00

We here at Hopkins give Advanced Placement credits for our calculus courses depending on the score one receives on the AP exams, offered in May of each year. The results come out in July. We give 8 total credits for Calculus I and Calculus II (a full year's worth) for a score on the BC-level exam of 4 or 5 (out of 5), and 4 total credits for Calculus I for a BC-level score of 3, or an AB-level score of 4 or 5 (again, out of 5).

Roughly speaking, the AB-level coincides with Calculus I and BC with Calculus II.

Well.... One of our own, Professor Stephen Wilson, performed a AP score verses grade in the next level course analysis which wound up being quite insightful. It turns out that getting a BC score of 5 is a good indication that the student is prepared to go directly to Calculus III. However, a BC score of 4 may not be. Almost no student who took Calculus III and brought in a BC score of 4 got an A in the class. Likewise, almost no student who brought in an AB score of 4 got an A in Calculus II (the logical next step).

It may be the case that not getting full marks on the AP exams means it is better to step back and re-evaluate the idea that you are really ready for the next level. We will certainly be keeping an eye on this over the next year or so. I thought I would put this out there now.

Advising must be a careful business, no?

Mathsputin??

2010-03-25T14:49:00.002-05:00

In 2002, the Russian mathematician Grigori Perelman solved one of the most fascinating mathematics problems of our time; The Poincare Conjecture: a hypothesis, which is now a theorem, that states (very roughly) that anything that locally looks enough like a three sphere must actually be a three sphere. Originally posed in 1904 by Henri Poincare, Perelman proved the result in 2002. Due to its beautiful simplicity in statement and extreme difficulty in establishment, this problem was one of those on the list of Millennium Prize Problems. Successfully solving one of the problems highlighted on this list earns the work a $1000000 prize. Nice reward for nice work, no?

It turns out that Dr. Perelman is not one for fanfare, or notoriety. He has been nicknamed "Mathsputin" due to his efforts to live simply and remotely. In character with these efforts, he has refused the gift.

Beautiful mathematics is its own reward. I get that.

But perhaps one should take the money and donate it?

Math and the Media: A Mathemagician?

2010-01-27T10:15:00.003-05:00

To some, possibly any and all math is simply magic. It seems to work and who knows what is really going on behind the math doers back. Then you learn the "trick" and it all seems perfectly natural. Until the next "trick", that is....

On the late night satirical news program "The Colbert Report" tonight (January 27, 2010, 11:30pm EST on Comedy Central) is Arthur Benjamin, a Hopkins bred mathematician (PhD in 1989) currently at Harvey Mudd College. A self-styled "mathemagician", he combines mathematics and magic to explore the power of mathematics through stunts and feats of mental agility.

You can visit the Hopkins Alumni page for this announcement (there is a neat video of one of his talks). Better yet, stop by Stephen's place for the show.

Summer Research Op....

2010-01-15T11:44:00.005-05:00

This just came in across my desk.

A summer research opportunity for math majors, called the The Research in Industrial Projects (RIPS) Program, a venture of the Institute for Pure and Applied Mathematics (IPAM) at the University of California Los Angeles (UCLA). The RIPS Program "provides an opportunity for exceptional students in math and related disciplines to work in teams on real world research projects by a sponsor from [either] industry or a national lab." From the website:

Projects are selected to have a major mathematical component and to be something that will pose an interesting challenge to talented undergraduates. Recent projects have included how to do a physics-based animation of a lava lamp, how to stitch together two images, how to analyze cancer data using microarrays, statistical data assimilation methods for weather data, modeling particle transport phenomena in reactors, and designing missions to the moons of Jupiter.

Recent projects have included organizations like Pixar, Microsoft, Symantec, Los Alamos National Laboratory, and the Jet Propulsion Laboratory, among others.

Details can be found at www.ipam.ucla.edu/rips, and the deadline for applying in February 15, 2010. Happy op hunting!

So you want to teach?

2010-01-13T14:25:00.002-05:00

Hey soon-to-be-math-major grads.....

Any interest in teaching? Building a career with good time off (think summers!), a relatively stress-free environment, stable career, and that good feeling one gets when you realize you are making a difference in someone else's life?

Math for America (MfA), an organization whose mission is "to improve math education in US public secondary schools by recruiting, training and retaining outstanding mathematics teachers", is offering five-year Fellowships to earn a Master's Degree in Mathematics Education and a teaching position. They are seeking 60 new fellows in the New York City area alone (with other opportunities in DC, Los Angeles and San Diego).

The New York City fellows will get their degree from MfA NY partner universities Bard College, NYU or the Teacher's College at Columbia.

The fellowship includes all tuition for the degree, a total five year stipend of 100K and a regular teacher's salary for the last four years of the fellowship. An excellent opportunity to be trained the right way. All of the contact information and application stuff is on the website. I have additional contact info with me, should you be interested.

They are actively looking for new fellows. Be a part of it?

Math in the Media - Teaching a Supreme...

2010-01-12T15:07:00.002-05:00

Many common concepts and terms in mathematics are of general use outside of math. Think of adjectives like "tangental" and "functional". The mathematical definition and the non-mathematical meanings are usually quite similar.

Today in the Washington Post, Robert Blake writes of a recent exchange within the confines of a Supreme Court session. Supreme Court Justice Anthony M. Kennedy asked a question to University of Michigan law professor Richard D. Friedman. Friedman answered the question,

"but added that it was "entirely orthogonal" to the argument he was making in Briscoe v. Virginia.

Friedman attempted to move on, but Chief Justice John G. Roberts Jr. stopped him.

"I'm sorry," Roberts said. "Entirely what?"

"Orthogonal," Friedman repeated, and then defined the word: "Right angle. Unrelated. Irrelevant."
"Oh," Roberts replied.

A nice answer, as almost every first-year student here at Hopkins in engineering or the natural sciences can attest. No dot-product needed. It goes on:

Friedman again tried to continue, but he had caught the interest of Justice Antonin Scalia, who considers himself the court's wordsmith. Scalia recently criticized a lawyer for using "choate" to mean the opposite of "inchoate," a word that has created a debate in the dictionary world.

"What was that adjective?" Scalia asked Monday. "I liked that."

"Orthogonal," Friedman said.

"Orthogonal," Roberts said.

"Orthogonal," Scalia said. "Ooh."

Friedman seemed to start to regret the whole thing, saying the use of the word was "a bit of professorship creeping in, I suppose," but Scalia was happy.

"I think we should use that in the opinion," he said.

"Or the dissent," added Roberts, who in this case was in rare disagreement with Scalia.

See what Hopkins Math can offer you? Something to teach even a Supreme Court Justice.

Math Blog from the Other Coast

2009-11-05T15:30:00.004-05:00

An excellent mathematics-based blog has come across my (virtual) desk:

What's new

The diarist, Terence Tao, a professor in the Mathematics Department at UCLA, explores mostly his research and related issues, so some of the posts may be stratospheric and out of the reach of many math enthusiasts. But there are also posts with good air-pressure, and some excellent advice on math-related careers and writing techniques, as well as mathematical constructs and such. For instance, his latest post on the nature of "proof-by-contradiction" makes for excellent reading. Give it a try!

Mathematics Study Tips - Banking practice problems

2009-11-05T14:53:00.004-05:00

In the recent post Mathematics Study Tips - Scrimmaging, I talked about a method for studying for a mathematics exam by mimicking, as best as you can, the exam environment. Sounds obvious, right? One doesn't create a soldier by watching war movies. The idea of practicing for an exam by doing new problems in a timed environment works to gauge your understanding of the material while reducing the stress of an exam by acclimating yourself to the climate within the exam. Here is another idea, mentioned in that last post:

In an actual exam, there usually will NOT be a marker on each problem telling you, for example, that "this problem is from Section 3.2 on the Mean Value Theorem". Instead, all you will see is the statement of the problem (and an implicit promise by the Instructor that the problem falls within the scope of the course). Without the context of which section the problem came from, can you still manage to do the problem? One way to help you to be sure is to take your problems out of the context they are in. Try this:

After each section of a text has been discussed in lecture and you have completed the homework problems for submission, take some time to re-write some of the other section exercises (ones that are "like" the ones in your homework set) in a common place later in your notebook. Add other problems when other sections are completed. Rewrite these problems verbatim from the text, but do not write the section or problem number. Don't DO these problems, just bank them for later.

Now when the exam approaches, and you are looking for items to focus on, go to this section of your notebook, grab 5 or 6 of these "banked" problems, go to a quiet, distraction-less place, and time yourself doing these problems without notes, text, or any other aid. If you can do the problems with ease, you are ready for these types of problems on the exam. If you cannot, however, or if some of them prove difficult, then simply re-orient these problem problems with their original sections and note these sections as ones you still need to focus on. Out of context, these problems are much closer to what you will see on an exam.

Another way to do this is to work with someone else, who can grab a problem from the text without telling you which section it comes from. While this is easier and requires little prior planning, it does involve more than one person. But then again, talking mathematics with others is really how one learns, right?

Again, in bocca al lupo!

Math in the Media - The Professional Take

2009-09-10T11:34:00.005-05:00

Got an interesting email blast on a service offered by one of the professional organizations for mathematicians, the American Mathematical Society (AMS). The heads-up comes from Dr. Ellen Maycock, the Associate Executive Director of the AMS. An excerpt:

The American Mathematical Society would like to remind you of a special service we offer, Headlines & Deadlines for Students, providing email notification of mathematics news and of upcoming deadlines that are of special interest to both graduate and undergraduate students. These email notifications will be issued about once a month, and when there's special news. Imminent deadlines will be included in these emails, which will link to a web page that's a centralized source for information relevant to students and faculty advisors, at
http://www.ams.org/news-for-students/.

We hope that you will share this email with the appropriate individuals in your department. It's not necessary to be a member of the AMS to sign up for this email service, at
http://www.ams.org/news-for-students/signup.

I will add that the news items highlighted on this website may also be of interest to pure enthusiasts of this discipline (and not just students of the field). It's good stuff, and I will be highlighting at times some articles mentioned here. But for now, take a look and sign up if you want the email service.

Beyond Calculus II: Honors Vector Calculus or not...

2009-07-21T13:36:00.005-05:00

A common question I often get from our very ambitious undergraduates focuses on a choice of vector calculus classes we offer. Vector Calculus, Calculus III, and Multivariable Calculus are all names for the same basic study of the properties of functions of more than one independent variable. This material is required for most engineering disciplines, as well as mathematics, and most of the natural science majors here at Hopkins. Since the techniques and material makes a lot more sense once students have studied most of the properties of functions of one independent variable, this course naturally follows the Calculus I and II sequence.

We have two flavors of vector calculus here at Hopkins:

110.202 Calculus III and 110.211 Honors Multivariable Calculus

The basic question is; Which should I take?

The basic answer is: depends....

Both of these courses fulfill the same requirements for all majors and minors that require multivariable calculus. Both can serve as prerequisite courses for any higher level course that requires multivariable calculus. Both cover the same basic material over the length of one semester, and run from the basic notions of vectors, matrices and the real space R^n through notions of continuous and differentiable functions of more than one independent variable, ending the basic material with the final major theorems tying together major aspects of the course: Green's, Stokes' and Gauss' Theorems.

The major difference between these two courses is one of focus. 110.202 Calculus III is more of a standard Calculus course, developing a blend of theoretical background on the nature of functions of more than one independent variable and the actual calculations involved in solving problems pertaining to this material. 110.211 Honors Multivariable Calculus, on the other hand, spend much more time on the theoretical nature of the material, digging deeper into the "why" aspects of calculus instead of "how things work". Students in the latter will develop a better understanding of content like the Inverse and the Implicit Function Theorems, and learn better how to analyze functions and problems that are not so straightforward. Furthermore, the honors version goes a bit beyond Gauss' Theorem and 110.202, with an introduction to differential forms, and a basic development of a generalized unified theory of the latter three theorems entitled "generalized Stokes'". Both courses are a challenge, but the latter is more so.

Students getting a BC score of 5 (or a 110.109 grade of B+ or better) can be encouraged to take this version if they are so inclined. Students with less strong scores should stay in 110.202, or at least should inquire further with the Math Department before registering for the honors version. In either case, while 110.211 is indeed a great course in vector calculus, taught the way mathematicians really want to teach a math course, it should be understood that the course will be quite a serious challenge.

Course sizes typically run over 100 easily for each lecture of 110.202, with about 4 recitation sections of 25 each. In contrast, 110.211 runs with about 40 students in 2 recitation sections.

Though always self-selected, students are usually quite enthusiastic about the honors version. it is also great fun to teach!

Hope this helps....

Chicken or Egg or ...: Which comes first? CalcIII, LinAlg, or DiffEq?

2009-07-01T09:37:00.006-05:00

If I can point to a set of questions that are asked most often of the Math Department, one definitely on the list is the following:

Is it better to take Calculus III or Linear Algebra first?

Throw Differential Equations into the mix, and you get a branching of one's math career into three distinct paths. All three of these courses, at least here at Hopkins, have a full year of single variable calculus as a prerequisite; necessary for technique as well as theory in the case of multivariable calculus (Calculus III) and Differential Equations, and necessary for a sufficient level of "mathematical maturity" in the case of Linear Algebra.

But for many majors, and interests, one must take courses in and well understand two, if not all three, of these topics. So what order makes the most sense?

Its a good question. It turns out, it is not really important....

I am starting a new series about these and other courses under the tag and title "Beyond Calculus II". In this series, I will explain better the idea and focus of these three (and other) courses taken after a full year of calculus is achieved. Here at Hopkins, a large population of our students start their tenure here at this level.

For now, though, let's stick with the topic above. To start:

There is neither multivariable calculus nor differential equations in linear algebra, yet there is a bit of linear algebra in both of the others. In contrast, linear algebra is a more mature course, sometimes requiring more in the way of expanding one's frame of reference mathematically than the other two.

That said, we actually took a look at performance among students who took the two courses 110.202 Calculus III and 110.201 Linear Algebra back to back over a two year period (there are quite a few of them). I will pass on the details of this study, but we found that there was no real preferred order to these two, at least as far as ultimate grades go.

Couple this with the fact that any linear algebra found in either calculus III or differential equations is essentially covered within the courses, and any of the three may be taken in any real order. Hence preference for time slots, professors, and/or friends in the course may be of higher priority in your choice than content.

And one last note, our course 110.302 Differential Equations, fairly standard in content with most sophomore-level courses at American universities, is a course in ordinary differential equations (involving functions of one independent variable, in contrast with partial differential equations). One can easily describe this course as Calculus II.5 (weird notation, hih?). It can be viewed as the proper successor to Calculus II, rather than Calculus III. Just sayin....

Math in the Media: Math and the City?!?

2009-06-15T13:05:00.004-05:00

Drawing a crowd in close enough to hear what you have to say is what a headline is all about. A guest columnist for the New York Times' The Wild Side, Steven Strogatz, filling in for Olivia Judson, pulled me in easily with his headline in the column on May 19th:

Math and the City

Though not quite similar to Sarah Jessica Parker (et.al.)'s work, it is a good title.

Here, instead, Mr. Strogatz discusses a couple examples of the mathematics of life that mathematicians tend to see everywhere via their training; patterns, proportions and logical structure that show up again and again in disparate contexts. In this case, Zipf's Law on the frequency of word usage in a language, patterns in economies of scale, similarities in the energy needs of a city based on its size to the energy needs of mammals based on their size all share a remarkable one-ness in their structure. "Spooky" is Steven's word fo it.

Its a good read....

One personal note, though (said with tongue firmly planted in cheek): Steven leads the article with

"One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden."

Right, he is. Sometimes is seems kinda like what Neo sees at the end of The Matrix (although in our case there is no trace of any sort of messianic behavior, no doubt).

And it is quite a pleasure. That is, when it isn't a curse.

Sleeping; a good study tip?

2009-06-10T14:02:00.003-05:00

Want to do better on your next math exam? Try sleeping well the night before. Easy right?

Apparently, cramming may not be the right approach to optimizing performance. This article in the Daily Telegraph today by Science Corrrespondent Richard Alleyne,

Good night's sleep adds up to better exam results - especially in maths

announces the results of a University of Pittsburgh study that says

a night of "high quality sleep" helps schoolchildren get better exam results - especially in maths.

Arguably, the study is small (56 students) and the article quotes another article from the Daily Telegraph who quotes the study. But the results make sense, at least from my perspective.

One caveat: The type of sleep most effective is not long in time, but restful in nature, with few if any awakenings or disturbances. However, knowing one has an exam the next day may be cause enough to make the sleep not so restful, no?

Still.... There is good advice in these results.

Mathematics Study Tips - Scrimmaging

2009-06-10T11:37:00.003-05:00

Here is a thought experiment: Choose a competitive team sport that requires special skills and one that you have not really played on a regular basis. Then imagine yourself watching 40 hours of instructional videos (about the semester-length of the lecture portion of a standard Hopkins math class) while seated on the couch. Or, if you like, imagine going into the back yard or to a court and practicing a set of drills designed to skill-up your ability to play.

Now imagine jumping into the middle of a real game filled with people who really know how to play. How will you do in that first game? Not so hot, huh?

Building a skill set in a way in which one can play effectively in a sport such as soccer, tennis, basketball, etc. requires many techniques. But one of the absolutely necessary ones is to scrimmage; practice playing in mock games to get a feel for the competition, put drill skills into practice, adapt technique, and learn to think amidst all the action.

Duh, right?

So how come almost no students study for an exam by actually trying to do never-before-seen problems out of the context of which section they are in and in a timed environment? SCRIMMAGE FOR AN EXAM!?!? Well, why the heck not?

Examinations can be extremely stressful and frustrating. "I know this stuff! I've done problems just like these hundreds of times! But with only an hour to do 6-7-9 problems, I just blank! I must be a terrible test-taker."

I doubt it. Most of us can easily pass a walking test, I believe. But then again, we have been practicing that for a while now, right?

Try this next time: After each section is covered and HW problems done, grab a set of problems from that section which are of the same type as those in the HW assignment. Bank them (write them down without reference to the section they came from). As an exam approaches, take some out and under a specific time limit (10 minutes per problem in a calculus course, maybe?) do the problems without regard to notes, book, or any other source (be smart: do this in a place without ANY distractions).

If you can easily do the problems, then those types of problems are yours to jam on in the exam.

If you cannot, then you know what to study a bit more. In this case, study, wait some time, and then try again on a couple more.

Give it a shot. It's better than re-doing HW problems, or re-reading chapters five times over.

In bocca al lupo!

More Virtual Math!

2009-06-09T14:49:00.004-05:00

Here is a current update of an earlier post here:

For the last few years, the Mathematics Department have been running online versions some of our freshman and sophomore level service courses (110.108-9 Calculus I-II, 110.201 Linear Algebra, 110.202 Calculus III and 110.302 Differential Equations). Designed and implemented inhouse, these course run for seven weeks in the summer, co-instructed by two of our graduate students each, and are identical in every other way to the in-class versions we run during the regular semesters. This year's version start this next week, on June 15th.

The design philosophies of these courses center around two fundamental principles:

The courses sacrifice nothing, both in content and in implementation, from the standard in-class, lecture-based version of the course (which ran concurrently in the summer).

The courses feature live, online lecturing, as well as live recitation sessions, as a core part of the instruction (currently we are the only implementation of online education using fully interactive and live lecturing, I believe; Tell me if I am mistaken. It's hard to keep up).

The implementation of this endeavor is facilitated by a software package called Elluminate Live! (ELive!), a virtual classroom environment that features (screen shot at right):

an online virtual whiteboard which acts like a chalkboard.

streaming audio,

Powerpoint-style slides that can be superimposed on the whiteboard and written over,

Classroom attendance moderation,

full student interaction including notification of a "raised hand", side chatroom (fully monitored by the instructor, voice and/or whiteboard enabling for each students or students,

full recording of live sessions for asynchronous reviewing later, with time stamps for accompanying notes.

Course document management is handled via the WebCT course management software. Homework is done the old fashioned way, but submitted via fax and/or email and graded electronically, and exams are proctored locally. For more details, see the Math Department's webpage.

Past results have been excellent, and this summer we are offering four of our courses in this format (all of the above with the exception of 110.108 Calculus I). I can provide tons more information is anyone is interested.

Thought I would throw this out there again. Cheers....

2009-06-02T11:07:00.011-05:00

Something from the "who'dda thunkit?" category:

Apparently, "mathematician is the best career in America right now", with a median income of over 90K. But really, don't take the word of a monk about how great the monastery is. Take it from the Karl Fendelander. In an article on Yahoo! hotjobs entitled

"The Hottest $40-an-Hour Careers"

Mathematician rates up there with Art Director, Geoscientist, Computer Software Engineer and Pharmacist. Go figure!!

Here is the relevant entry:

Mathematician
This career has numbers on its side. In their sweeping study of jobs in America, CareerCast [a job search portal] found that mathematicians are at the very top -- that's right, mathematician is the best career in America right now. Mathematicians are extremely satisfied with their jobs, happy with their lives, and, of course, don't mind that $40+ an hour.
A bachelor's degree get you started, but getting any further usually requires a post-graduate degree. From finance to physics, mathematicians find careers in any industry that deals with numbers.
Median Hourly Wage for Mathematicians in 2007: $43.72 ($90,930 yearly)

From an insider, to be honest, the career can cause awkward silences at cocktail parties ;-) .

But its an excellent lifestyle, rated as one of the lowest in stress, and we are in demand.

New Text....

2009-05-19T11:19:00.007-05:00

We will be changing the text for the fall 2009 and beyond semesters for the courses 110.108-9 Calculus I-II (Phys. Sci. & Eng.). The old text was the red book at left: "Single Variable Essential Calculus" by James Stewart (ISBN-13: 9780495109556).

The new text comes from the same author, and is really simply the expanded version of the same material. It is "Single Variable Calculus: Early Transcendentals" (ISBN-13: 9780495011699).

The summer courses will continue to use the old text. Sorry for the inconvenience. This new choice will be stable for a while, we believe.

Back again, eh?

2009-05-07T15:40:00.006-05:00

Hello all again.

After a long hiatus, I decided to begin posting here again. There were reasons for the gap in attendance on my part. But I do notice that some posts are read long after their birthdate, and people do find their content useful. So I will start up again and continue to post on current events, mathematics issues, and department-related matters. For instance, we have started a Facebook group devoted to matters concerning the department. To see it, you will need FB access. Just do a search on our data.

Also new, we will again be changing the textbook for our course sequence 110.108-9 Calculus I-II (Eng. & Phys. Sci.). The author will be the same as the previous book (James Stewart), but we will be using the expanded version. When I get the ISBN, I will pass it along.

Talk to you soon.

2008 Competitions

2008-10-06T14:41:00.003-05:00

Hello again to the mathematical community here at Hopkins.

It is again the fall, and it is again the time for competition. The two upcoming fall events are:

(a special note: The Putnam link above is to the page that should be shortly updated to reflect the 2008 exam information.)

As last year's post stated, both are distributed exam competitions, offered locally here at Hopkins, at the undergraduate-level. Both offer cash prizes and all the prestige your time can buy. Read last year's post for more details.

For this year, we are already registered for VTech, whic is given November 1 in the morning. Again, there is no need to individually register for this until the day of the competition. I will post more about this in a couple of week. Also, I wil broadcast via email to all math majors and Math Club members.

Registration for the 69th national Putnam exam closes sometime around October 12, and the exam is held on Saturday, December 6, from 10am-1pm and 3pm-6pm.

Again, we will be offering training sessions, organized with the Math Club here at Hopkins, which will again be weekly seminars, hosted by the same graduate student we used last year. Details to come.

Low Stress Job?!!?

2008-09-23T10:02:00.003-05:00

Very interesting quick view from the outside on the life of a mathematician, from the world out-there: According to Laurence Shatkin, author of "150 Best Low-Stress Jobs," as detailed in the Yahoo! hotjobs section, a mathematician with a Ph.D. can earn a starting salary in the 80s while enjoying a relatively stress-free life: The money quote:

"[T]he most stressful aspects of the job are the importance of being exact and a level of competition, in essence it's all good."

I have to admit that there may be a bit more stress in one's life than simply the overpowering compulsion to be exact. And the competition among mathematicians can be quite fierce in its own way (although in truth we have nothing on the social scientists: Our theories (theorems) are usually not judged on the matter of being correct. We cannot have competing theorems like in economics and sometimes in physics. What is right is right, after all. Our competition is more a matter of who proves something first, or in the most beautiful way, or just how "interesting" our results are).

And while some of my mathematician friends over at the National Security Agency and NASA, or some of the securities specialists on Wall Street (you would be surprised on how many mathematicians work in lower Manhattan) may quibble with Shatkin's quote that "[m]athematicians are not under pressure as this isn't life and death; they're dealing with theoretical realms," I have to admit it is a good life.

Something to consider, anyway....

The Putnam Results!

2008-03-19T09:38:00.003-05:00

The William Lowell Putnam Mathematical Competition for 2007 results have just been announced. And we have good news to announce: Two of our participants have received special recognition for their performance. The recognition comes in the form of a set of special categories marking the top performers and based on their ranking given by their overall exam score. Our two top finishers placed in the top 100 out of the 3753 participants of this year's competition:

Kihyuk Hong, a senior, received the title of "Honorable Mention", given to those whose score ranks them between 27.5 and 74, out of the 3753 contestants who participated.

Sunny Kam, a freshman, placed in the next category (oddly titled only category "I"), for rankings between 78 and 94.

These two contestants will have their names published as top performers on this examination in the American Mathematical Monthly in the near future. The results of the exam this year, and the distribution of scores, can be found at the Mathematical Association of America's American Mathematics Competitions website for the Putnam at:

http://www.unl.edu/amc/a-activities/a7-problems/putnamindex.shtml

Also, three registrants can act as a team for the competition. Hopkins was one of the 413 institutions to enter a team, and we placed 22 this year.

Altogether, this was an excellent performance by our students. Congratulations to all who participated.

Math in the Media - Pi Day

2008-03-14T10:41:00.006-05:00

Kind of a weird thing to me, but weird can be fun also, eh?

Happy Pi Day, 3-14, that is....

But what about the actual Pi Moment? Maybe 3-14 at 59 minutes, 26.54 seconds...? Close, anyway, what?

Research Opportunity

2008-03-14T10:21:00.006-05:00

Here is an interesting internship that may run for a while: Acting as a resident Math Expert for a series on fairly low-level mathematics-based puzzles set to air on public television here in Maryland. Can you think of a better way to enter an interesting career path as an Expert right out of the box?

I am filing this as a research opportunity, although I think it is more of a fun thing to do and a good resume builder, especially for those of you who want to fill out your resume with serious activities of a more unusual flavor.

The only less-than-ideal thing about this internship is that it is unpaid. But I believe the bragging rights and networking (please excuse the pun) possibilities make a strong alternative form of payment. I will stay in contact with the person over there who sent me this. I definitely think this is quite interesting and wonder what else we could do for Maryland Public Television.... Ideas?

Math in the Media - The Price of Higher Ed 2

2008-02-08T09:43:00.001-05:00

As a follow up to the last post, the Washington Post this morning contained an article detailing current legislation pending in Congress (passed by the House actually) that addresses many of the costs associated with higher education. While the main thrust of the College Opportunity and Affordability Act is to provide more aid for students of need to attend college, there are provisions in the bill designed to dampen textbook prices.

For instance, forcing publishers to state the price of a textbook up front when promoting a book to a professor for possible use in the classroom (this is not often done currently). And ending the practice of packaging textbooks with tons of rather useless addons which are typically not used in the course and are almost always of little or no value (think of that CD you never touched attached to the inside back cover of your calculus text (well, at least not our book for 108-109)).

A similar bill has also passed the Senate, and now the reconciliation between the two must begin. It is also said in the article that the White House opposes the bill. No threat of a veto, but Bush wuill seek changes before he signs.

I believe it is a good thing that Congress is paying attention. Let's also hope the publishers are....

Math in the Media - The Price of Higher Ed

2008-02-08T09:43:00.000-05:00

Interesting editorial in the Washington Post yesterday. Well, interesting to those who aren't constantly confronted with the soaring costs of a university education. The world outside of the Ivory Tower sees clearly the number of zeros in the tuition bill. What those on the inside also face is textbook prices; sometimes over $1000 a year (a stat from the University of Maryland, mentioned in the article).

The article, "Required Reading", correctly details many points that frustrate professors as well as students. One is the extraneous material of little or no value packaged in with the book: CDs with "helpful" software, solutions manuals, study guides, etc. which are then valued greatly by publishers. We don;t use them and do not need them.

Also, when "new editions" come out every two or three years, the "old edition" becomes worthless, both for students retaking a course and for any possible resale of the book. This again keeps prices high. The editorial staff at the Post are correct that at the level of Calculus, there are really no new innovations that would possibly lead to a maor overhaul of the subject. In fact, many of the calculus texts are so overevolved that there is movement in the textbook business to actually pare down the content.

Our choice, seen at right, is a bioled down version of a calculus text. It retains the basic core of the subject while relegating the extra stuff to a publicly accessible website. The result is that the price is at a level of somewhere around 10 years ago. Not great, but there is a recognition amongst publishers that their customers are not happy.

And professors aren't happy either. Some years back at American University, I chose a book for a PDEs class that was $12.95 (it was a reprint of an out-of-print book). I chose it because 1) it was quite adequate for the class, and 2) it was 12 bucks.

Boy, did that get noticed....

Math in the media - Killing Fractions?!?

2008-01-31T10:37:00.000-05:00

We all know making a seemingly outrageous statement to gather attention, and then expounding on your point once the audience is yours, is a sure-fire way to start a conversation. I am not sure it is always the best way to bring the topic to the floor, however.

Dennis DeTurk, a professor in the Mathematics Department at the University of Pennsylvania, Dean of the College of Arts and Sciences there, and Evan C Thompson Endowed Term Professorship for Excellence in Teaching, advocates the abolishment of fractions as a mathematical tool, and to simply use decimal representations of real numbers (there.... how's that for an outrageous statement to start the conversation?).

The USA Today article by Maureen Milford is here:

Professor: Fractions should be scrapped

Needless to say, he has attracted attention, some quite critical.

Well, to be fair, he doesn't really hate fractions at all, and isn't leading the charge to erase their existence. I will let you read the short USA Today article fully, but all he really seems to be saying is that it would be better to teach kids decimals when it is time for them to learn about parts of numbers and their arithmetic. Then later, when they are a bit more mature mathematically, teachers can introduce the ratio format of a fraction. True or not, his quote in the article is well-reasoned, IMHO:

"Mathematicians are always questioning the axioms. Everybody knows that questioning those often results in the most substantial gains in terms of progress."

I not sure whether it would matter, personally. I have kids that recently went through the first fraction stage in school. It can be troublesome, but I have always found that complicated abstract mathematical structures are not a hindrance to kids generally. They tend to eventually master almost anything you throw at them. So what if it takes a little while. I always viewed it a a "good wiring" technique for learning future, even more complicated abstract structures.

Summer Research Opportunities

2007-12-13T09:57:00.000-05:00

The Institute for Pure and Applied Mathematics at UCLA anounces their Research in Industrial Projects (RIPS) Program for 2008. Click on the flyer to see the details (or follow the links above), but programs like this run throughout the nation and provide excellent research opportunities at the undergraduate level for math majors and students of other majors interested in research involving applications of pure and applied mathematics.

Applications can be submitted online, the deadline is in February, and many FAQS are noted here....

Feel free to contact me with any questions you may have concerning this and/or other opportunities. I will post any other calls for applications of this type under the same tag.

Essential Calculus Environment

2007-11-01T16:25:00.000-05:00

To all interested: We changed our textbook for our Calculus Series for Physical Scientists and Engineers. The new text is called Single Variable Essential Calculus by James Stewart.

It is a boiled down version of the standard Stewart Calculus text and also published by Thomson Brooks/Cole. It is smaller, lighter, cheaper and not so filled with the extraneous information that fills most every text on the subject these days. I am doing Calculus II at the moment, and I find it quite concise and well developed. Any embellishments that I would like to see, I am happy to do on my own in lecture.

In fact, most of the stuff excised from the regular version of Stewart Calculus has been offloaded to the author's website http://www.stewartcalculus.com/.

I am interested in the student's reactions to the book. Please comment below on your reaction to the text. The more detail you can give, the better. If in the eyes of the students, it is a terrible book, we need to know that.

Thanx....

Putnam Training Sessions, Fall 2007

2007-11-01T16:13:00.000-05:00

The William Lowell Putnam Mathematical Competition takes place on December 1 this year.

This note is just a reminder that the Mathematics Department is conducting weekly training and proactice sessions designed for students to prepare for the competition. These session are headed by one of the graduate students here in the Math Department: Hamid Hezari.

The sessions are held on Thursday evenings, from 6pm to 8pm in Krieger 308. Pizza and drinks will be present.

Cheers....

The German Abitur

2007-11-01T15:52:00.001-05:00

With the ever increasing number of students coming in to JHU with advanced placement credits in calculus under their arms, we are now getting a larger and larger number of students who have studied abroad prior to attending Hopkins. Many of these students also have some sort of advanced training.

As a means to recognize this international form of advanced placement, we look at the exam curricula, both in content and level, and compare it to what we offer as coursework here. The Advanced Placement AB and BC exams correspond roughly to what we offer as Calculus I and II, respectively.

We have been looking at the German Abitur lately, and have come to the conclusion that the Mathematics Department will accept a score of 10 or above (out of 15) for 4 credits of either 110.106 or 110.108 Calculus I. This is fairly consistent with that of MIT, and Duke as well as others.

So far, other international exams will have to be examined on a case by case basis.

Come talk to me if this conclusion is of interest to you. Also, as I learn more I will append this post or add others under the Advanced Placement tag.

The Hunt!

2007-09-19T12:51:00.000-05:00

Well, rumors come to pass at times.

The Math Club here at Hopkins has successfully organized and caried out a puzzle hunt, whereby student teams compete to solve a series of logical puzzles that carry them accross campus over the course of a day to find a hidden object (The Notorious Field's Medallion; The Field's Medal is a high award offered to outstanding accomplishments in research mathematics, and is treated much like the Nobel Prizes are in the sciences. The award is named after a mathematician who spent time here at Hopkins. Hecen we name our object after him also.)

I will talk more about the hunt in time. But suffice it to say that there will be a 2nd Hunt next Fall in September.

Congratulations both to the organizers of the Hunt, and to the winners.

Competitive Mathematics

2007-09-19T12:26:00.001-05:00

Welcome back to everyone who has been here at Hopkins, and welcome to those who are new.

A word about some fall events. Mathematics is many things to many people, but to some it is actually a competitive sport. Here at Hopkins, we have two upcoming competitions that we register teams for and participate in:

Both are distributed exam competitions, which means they are offered locally at a university who has students registered to take the exam. Both offer undergraduate-level mathematics problems that require cleverness to solve well, and both offer cash prizes as well as the prestige of doing well in the competition. In fact, doing well on the Putnam is an accomplishment that should be placed prominantly on a resume or curriculum vitae (an academic resume, so to speak). And the Math Department offers a cash prize to the best performer from JHU. Last year, our two top Putnam performers ranked at 140th and 154th out of some 3640 participants.

Registration for the VTech competition is basically a matter for the Math Dept. here, and we will be registered. The exam is on Saturday, October 27, from 9am-11:30am.

Registration for the 68th national Putnam exam closes sometime around October 12, and the exam is held on Saturday, December 1, from 10am-1pm and 3pm-6pm.

If you are interested in either of these competitions (and as a math major, I highly recommend that you consider these exams part of your training as a mathematician), please come in to talk to me. The Department also offers training sessions, organized with the Math Club here at Hopkins, which are weekly seminars. But more on that later....

Math in the Media - First Do the Math

2007-07-31T10:26:00.000-05:00

So, is extra high school math actually "good" for you? There is some evidence here....

An article in the Washington Post by Health and Science writer Rick Weiss (July 30, 2007), entitled "First, Do the Math" details the results of a study performed by researchers at Harvard and the University of Virginia. Basically, taking an extra biology, physics or chemistry course in high school provides a boost in grade values for the college versions of these courses. But only in the respective field of the course. And no boost is seen in the other fields.

However, taking an extra math course in high school provides a boost in all three areas plus mathematics. More bang for your buck in that plan. The money quote from the article:

"The one thing that helped students do well in all college science was having taken an advanced high school math class. That undermines a commonly held belief that math training is not particularly important or helpful for the study of biology."

I venture the same can be said for an extra college math course, or even a math minor. But, then again, I am biased....

We're Back...!

2007-07-30T11:26:00.000-05:00

Sorry for the lack of input during these last two months. With the changeover from Spring semester to Summer break, so many other things have overtaken my ability to write on current events and department happenings. And with my vacation looming, there will be another break soon. However, check back every once in a while for new posts here. And certainly check back often once the Fall semester arrives.

Mathematics Study Tips - Notes

2007-05-09T10:55:00.000-05:00

From time to time, I will post some tips for undergraduates in helping to master Mathematics classes both here at JHU and anywhere else. These tips are mine only, and reflect what I see from my view as a professor. They may be directly contradicted by the tips of others in the academic community. So be it. This is my blog.

Taking notes in a math class is one of the most basic ways to record the information given in a lecture for use later when trying to piece together the subject matter of a course in a comprehensive way. When working on homework problems, or studying for exams, a good set of notes allows for the information from the lecture to be reviewed and placed in a context where one can reflect on difficult concepts over time. The professor may cover material not directly in the text, provide alternative techniques or insight to understanding material in the text, or offer particularly good exmaples not found in the written material.

But how to take notes effectively is difficult to teach and even more difficult to figure out on ones own.

Some tips I find useful (since I am male, I will refer to the professor as a "he"):

Try to record what the professor is saying and not just what he may write on the board.
It is difficult to listen and write at the same time. Be terse in your note taking, so that you do not spend too much listening time simply writing.
Don't work so hard at being neat, but do work hard on being clear.
Leave space in your notes to fill in obvious gaps after the lecture. This goes back to the point that you cannot listem and write at the same time. Why waste time writing something obvious when you can listen instead and fill in the gap later.
Provide space to fill in the details of examples or proofs "left to the audience". When a professor says "this is a good exercise", he almost always means it. You should leave space in your notes at that point to do the exercise later.
Directly after a lecture (meaning sometime soon afterwards), go through your notes and fill in any gaps, thinking about what the professor said, what you remember of questions from other students, and other thoughts you have and still have fresh in your mind. Do this in another color pen or pencil (these extra markings may become critical to understanding a concept clearly).
Add your own insight ot your notes. Even if it seems obvious at the time, if you make a connection not mentioned by the professor, write it down.
As you go through your notes, you will find places which don't make sense, even after some thought. In yet another color, mark these places with a big question mark. Talk to other students, the TA, or the professor and get these question marks resolved as soon as you are able. Write in the resolution into your notes.
Don't worry about rewriting notes, or trying to prepare them for publishing. The purpose of the notes is not to impress. The purpose is to use them to gain understanding.
Compare your notes with a friend or an acquaintance in the class, and add to your notes things the other student recorded but you did not.

Lectures are a critical part of the course experience. The purpose of a professor is to, in some sense, organize the material into a logical story line, allowing you to make much progress by taking steps that follow each other naturally, and partially digest the material, making it edible brain food for you. Since it is a live interaction, he can gauge your (as a class) understanding of the material and alter his presentation to fit the needs of the class. or at least he should....

All of this winds up sitting in your notes. And winds up being the backbone of the course information structure.

I hope this helps.

Future Scholars Orientation

2007-05-09T10:41:00.000-05:00

Sorry for the gap in posting.... Now that the semester is winding down, there is a little more time to breathe.

For all of you interested in the Future Scholars Program, we have seven winners this year. Again, these winners are Baltimore area high school juniors to whom we have awarded the opportunity to take two of our classes here in the Mathematics Department this next academic year tuition free during their senior year in high school. Congratulations to them, and I look forward to meeting and working with them this next fall.

We will schedule an orientation session this June, to meet the new scholars and provide them the necessary information to take advantage of the program. Tentatively (and we are in the process of notifying the scholars now), we are setting the meeting for

Tuesday, June 26, 2007 at 6pm in Krieger Hall Room 211

Parking vouchers will be provided (visitor parking will be plentiful in the evening hours), and we encourage strongly that parents also attend this session.

Please let us know if, as a scholar, you cannot attend. We can always reschedule the meeting if most of you cannot make it, and make time for you outside the general session if simply one or two of you cannot attend at the above time.

Awards 2007 - The Best of Us

2007-04-19T11:37:00.000-05:00

As this academic year draws to a close, the Mathematics Department yesterday had its Spring Picnic. Among the festivities was a recognition of the service and achievements of our best performers over this last year and before. The awards this year went to:

J.J. Sylvester Award for Outstanding Achievement as an Undergraduate:

David Sher - will start graduate study in mathematics at Stanford University next fall.
Matthew Sedlock - will start graduate study in Applied Mathematics here at JHU next fall.

Excellence in Teaching for Junior Faculty

Michael Ching - J.J. Sylvester Assistant Professor

Excellence in Teaching for Teaching Assistants

William Kelso Morrill Award for Excellence in the Teaching of Mathematics

Michael Limarzi

These people are being honored as our best and brightest. As a department, we thank them for their service and dedication to mathematics education here at JHU.

Virtual Mathematics - Online JHU Summer Courses

2007-04-13T14:45:00.000-05:00

Last year, the Mathematics Department designed and implemented an online version of our first semester freshman Calculus course (110.108 Calculus I). This was a collaborative effort of a group of us in the department, and funded in part by a mini-grant from the Center for Educational Resources here on campus. Administered by two of our graduate students, Siddique Khan and Brian MacDonald, the course ran for 8 weeks to 10 students.

The philosophy of the course offering centered around two fundamental principles:

The course shall sacrifice nothing, both in content and in implementation, from the standard in-class, lecture-based version of the course (which ran concurrently).

The course will feature live, online lecturing, as well as live recitation sessions, as a core part of the instruction.

The implementation of such an endeavor was facilitated by a software package called Elluminate Live! (ELive!), a virtual classroom environment that features (screen shot at right):

an online virtual whiteboard which acts like a chalkboard.

streamin audio,

powerpoint-style slides that can be superimposed on the shiteboard and written over,

Classroom attendence moderation,

full student interaction including notification of a "raised hand", side chatroom (fully monitored by the instructor, voice and/or whiteboard enabling for each students or students,

full recording of live sessions for post lecture viewing/reviewing, with time stamps for accompanying notes.

The results were excellent, and this summer we are offering four of our courses in this format (as well as accompanying in-class versions). I can provide tons more information is anyone is interested.

Thought I would throw this out there. Cheers....

Math in the Media - The Mozart of Mathematics

2007-04-09T09:17:00.000-05:00

Again, the Washington Post grabs the mathematics bull by the horns to post a good quick biography on one of the Masters of the Mathematics Universe (he is what some call a "universalist"; a mathematician trained and competent across many if not all fields of mathematics).

Leonhard Euler.... Enjoy!

Also, the author of this article, David Brown, as well as the author of an upcoming biography of Euler, Ronald S. Calinger of Catholic University, will be online live tomorrow morning (April 10) at 11am here. If you are inclined, tune in....

Future Scholar Results announced....

2007-04-03T16:01:00.000-05:00

We have made decisions regarding the Future Scholars for the next academic year, and will be mailing out notices to winners this next week.

For those of you who are curious, the Future Scholars Program invites local area high school Juniors to take a locally proctored exam to compete for the chance to take Hopkins University Matheamtics courses here in campus during your senior year in high school. Tuition is fully paid for (though fees and books are not) for a course in each of the two semesters of that year. The exam was administered this last month, and we are in the process of notifying the winners.

Congratulations to the winners, and good luck to all who entered.

Putnam Results are in...!

2007-04-03T15:52:00.000-05:00

Well, Putnam results have been announced. And our two top scorers have been ranked at 140th and 154th, out of a total of 3640 contestants. Congratulations to these two on excellent performances.

If you played the game, and want to know how you did, drop me a line.

Math in the Media - E8!

2007-03-19T16:27:00.000-05:00

And finally some constructive news from MathWorld: The structure of E8 is now understood? Well, at least it is now understandable, at least in theory. For another (and better) perspective, look here....

Actually, it is more advisable to look here, and here....

And congrats to the Atlas team (I knew Jeffrey Adams (on the left, in shorts) from my grad student days at Maryland)!

And by the way, if you think math is anything but cool, stare for a while at the following "picture" of E8 :

Math Club News - Putnam Training

2007-03-05T11:05:00.000-05:00

The first workout for next year's Putnam exam in December is tonight, March 5, 7pm in Krieger 308. Bring pencil, paper, and a full stomach for this up-to-a-2-hour session. The topic: The Pigeonhole Principle.

See this post below for more information on these workouts in general, and who to talk to about them.

Putnam Training Sessions

2007-03-01T17:04:00.000-05:00

Heard of the Putnam Exam?

Want to try but feel you don't want to enter a race without training? The Mathematics Club here at Hopkins is setting up training sessions to help potential Putnam contestants prepare for the exam.

The first workout is titled "The Pigeonhole Principle": The idea that if you need to put more than n objects into n holes, then at least one hole will have more than one object in it. Simple, eh? This general counting principle sits behind many clever proofs to many simply stated but tricky problems.

The Math Club will be hosting many of these workouts, and will base these on mathematical principles and techniques, rather than grabbing random problems to address.

Talk to the Math Club President, Kihyuk Hong at the JHU email address khong4, for the times, places, future training topics, and indeed anything else pertaining to the Putnam.

Incidentally, the Math Department offers a course in Putnam training every fall. Talk to me if you are interested.

There is a rumor...

2007-02-28T14:23:00.000-05:00

that hunting season starts sometime in the fall. Hmmmmm.........

Definition - Dynamical Systems

2007-02-28T14:05:00.000-05:00

This post will be a part of a series, marked by the tag "Dynamical Systems", in which I will offer thoughts on the nature of Dynamical Systems as a mathematical discipline.

Today I will briefly give my definition of the study, and stop there.

Definition: Dynamical Systems is the formal study of the properties of mathematical objects by studying how those objects behave under transformations.

Usually the types of transformations involved are defined in one of two ways:

By a continuous variable (like differential equations, where time is viewed as an action by the real numbers on the space of solutions of the ODEs, and the dynamical systems in this category are called flows), or
by a discrete variable (think of the behavior of points of a space under the repeated application of a single map from the space to itself. This is viewed as an integer action on the domain of the function, where each integer n is associated to the map given by the n-times composition of the function with itself).

This definition encompasses a very broad interpretation of DS, and reflects its use in so many areas of mathematics, from algebra and analysis, to probability and statistics, to topology and geometry, to number theory.

It is also my favorite....

Teaching Awards

2007-02-26T14:20:00.000-05:00

Vote Now! Mathematics Teaching Awards

Nominations are now being accepted from all undergraduate students. Let your voice be heard! Vote for your favorite junior mathematics professor and your favorite teaching assistant (see lists below) . Simply send your vote to award@math.jhu.edu by March 9th. The winner will be announced in May on the Mathematics web page at www.math.jhu.edu.

Thank you for your participation and we look forward to hearing from you,
The Department of Mathematics

Eligible faculty include:

Matthew Blair
Rich Brown
Michael Ching
Daniela DeSilva
Michael Goldberg
Eugene Ha
Jian Song
Florin Spinu
Graeme Wilkin
Qiao Zhang

Eligible teaching assistants include:

Agarwala, Susama
Baber, John
Banerjee, Abhishek
Banerjee, Romie
Breiner, Christine
Chen, Yifei
Choi, Sung Rak
Cutrone, Joseph
Dahl, Jonathan
Hezari, Hamid
Hussey, Caleb
Jiang, Jin-Cheng
Khan, Siddique
Kleene, Stephen
Kramer, Joel
Limarzi, Michael
Lin, Longzhi
Lyzinski, Vince
MacDonald, Brian
Marshburn, Nicholas
McGowan, Michael
Seyyedali, Reza
Sinclair Duncan
Tavakol, Mehdi
Tucker, Matthew
Wang, Shuai
Wright, Thomas
Zhong, Qi
Zrebiec, Scott
Zulkowski, Patrick

The Future Scholars Competition starts now.

2007-02-23T12:50:00.000-05:00

The exam is now out and for the next three weeks, Baltimore area high school juniors will have the opportunity to compete for 10 slots as JHU Mathematics Future Scholars. The program allows recipients to take up to three math classes here at JHU tuition free for full university credit during their senior year in high school. Look here for the details.

Good luck to all!

Math in the Media - Anxiety

2007-02-21T16:16:00.000-05:00

Funny how when math intersects with popular media (MSM is one of the nice names for main stream media in the blogosphere), it is usual to hear stories that describe some negative aspect of it or of its unpopularity in general or just how darn hard it is to achieve good test scores at the primary and secondary level.

Well, on that note, here is another one.

Signing on....

2007-02-21T10:31:00.000-05:00

Hello to all. This post marks the beginning of a conversation I want to have with the mathematics community both here at Johns Hopkins University and there wherever you are. Primarily, this blog will manifest my thoughts, recommendations, announcements, and rants (occasionally) pertaining to mathematics in general and the department in particular as it impacts the community here at JHU.

I have not decided yet how I want to run this blog, whether I want to allow general posting or restricted, whether I want to keep this as a bulletin board or actually run it as a forum for active discussion. At this point, it is barely even public. We will see what I want to do with it in time. For now, if you have comments about this blog or need to contact me for any other reason, feel free to use my email at the university.

See you in class.