The Chalkboard

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.........