Wednesday, December 1, 2010
Tuesday, November 9, 2010
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
Thursday, November 4, 2010
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?
Thursday, October 28, 2010
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.
Thursday, October 14, 2010
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.
Friday, October 8, 2010
The application process is all online, and the deadline is October 15. Give it a look.
Tuesday, September 28, 2010
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
Wednesday, September 22, 2010
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.
Tuesday, September 21, 2010
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.
Friday, September 17, 2010
Out very own Duncan Sinclair, a veteran graduate student here, will run the sessions.
Have fun getting in shape (?) for December!
Thursday, September 16, 2010
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.
Tuesday, September 14, 2010
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.
- 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.
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...!
Early December again brings the
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.
Thursday, July 15, 2010
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.
Friday, May 28, 2010
From the pages of the Magazine that carried his articles for more than 25 years: Scientific American.
Friday, May 21, 2010
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:
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!
Thursday, May 13, 2010
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).
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....
Thursday, May 6, 2010
- Adam Saltz
- Xinlu Huang
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. ;-)
Friday, April 30, 2010
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.
Thursday, April 22, 2010
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?
Thursday, March 25, 2010
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?
Wednesday, January 27, 2010
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.
Friday, January 15, 2010
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!
Wednesday, January 13, 2010
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?
Tuesday, January 12, 2010
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,
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:
"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.
See what Hopkins Math can offer you? Something to teach even a Supreme Court Justice.
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.