Thursday, December 13, 2007

Summer Research Opportunities

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.

Thursday, November 1, 2007

Essential Calculus Environment

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

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.


Putnam Training Sessions, Fall 2007

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.


The German Abitur

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.

Wednesday, September 19, 2007

The Hunt!

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

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....

Tuesday, July 31, 2007

Math in the Media - First Do the Math

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....

Monday, July 30, 2007

We're Back...!

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.

Wednesday, May 9, 2007

Mathematics Study Tips - Notes

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

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.

Thursday, April 19, 2007

Awards 2007 - The Best of Us

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

Excellence in Teaching for Teaching Assistants

William Kelso Morrill Award for Excellence in the Teaching of Mathematics

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.

Friday, April 13, 2007

Virtual Mathematics - Online JHU Summer Courses

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:
  1. 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).

  2. 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....

Monday, April 9, 2007

Math in the Media - The Mozart of Mathematics

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....

Tuesday, April 3, 2007

Future Scholar Results announced....

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...!

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.

Monday, March 19, 2007

Math in the Media - E8!

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 :

Monday, March 5, 2007

Math Club News - Putnam Training

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.

Thursday, March 1, 2007

Putnam Training Sessions

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.

Wednesday, February 28, 2007

There is a rumor...

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

Definition - Dynamical Systems

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....

Monday, February 26, 2007

Teaching Awards

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 by March 9th. The winner will be announced in May on the Mathematics web page at

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

Friday, February 23, 2007

The Future Scholars Competition starts now.

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!

Wednesday, February 21, 2007

Math in the Media - Anxiety

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....

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.