Scot Gould

Scot Gould

697 Reputation

14 Badges

11 years, 82 days
Claremont McKenna, Pitzer, Scripps College
Professor of Physics
Upland, California, United States
Dr. Scot Gould is a professor of physics in the W.M. Keck Science Department of Claremont McKenna, Pitzer, and Scripps Colleges - members of The Claremont Colleges in California. He was involved in the early development of the atomic force microscope. His research has included numerous studies and experiments using scanning probe microscopes, particularly those involving natural fibers such as spider silk. More recently, he was involved in developing and sustaining AISS. This full-year multi-unit, non-traditional, interdisciplinary undergraduate science education course integrated topics from biology, chemistry, physics, mathematics, and computer science. His current interest is integrating computational topics into the physics curriculum. He teaches the use of Maple's computer algebraic and numerical systems to assist students in modeling and visualizing physical and biological systems. His Dirac-notation-based quantum mechanics course is taught solely through Maple.

MaplePrimes Activity


These are replies submitted by Scot Gould

Interesting. I don't use this format for comments. I enter comments in the text blocks. Regardless, comments do appear to fail to copy only when one uses the "2D-Input" style. It does copy properly under "Maple Input". 

 

@taro 

While I love elegance and simplicity in the solution, I think they want to identify the extreme points of the expression, not the first derivative. 

A delightful post. I can immediately apply the 3rd, 4th and 5th techniques to some important simulation problems. Thumbs up.

@nm 

L:=[[1,2,3], [4, 5, 6]];
a:=array(1..nops(L));
seq(point(a[i], L[i]), i=1..nops(L));

then the labels are elements of an array: a[1], a[2] and not individual entities: a__||1, a__||2.

My apologies to this improperly constructed question. I correctly stated my goal, but in my haste to write the post, I created an obviously "nonsense" example. A more typical example I tend to solve is: x^2 – a = 0 where all constants are positive.

By my definition, slickest = fewest number of characters required, hence I like Tom Leslie’s answer the best.

So, while I probably didn’t deserve any “love” from this group, I do appreciate the fact that people thought critically, ignored the example, and provided solutions to the question. At this point, I am reminded of the famous quote by former U.S. Vice President and convicted felon Spiro T. Agnew, “Don’t judge us by what we say, judge us by what we do.”  

@Axel Vogt of using the evalf(Int()) process, it takes my verion of Maple (2016.1) 28 minutes to calculate. But, before I peformed the evalf() command, I did separate out the convert() function.

f(x) := exp(-(1/2)*x^2)/sqrt(2*Pi);
g := convert((f(x)*f(y)*x*x)*abs(x+y), piecewise, x);
gInt := Int(Int(g, x = -infinity .. infinity), y = -infinity .. infinity);
evalf(gInt);

However, if I ask it to determine the value(gInt), the calculation is within a second, as you pointed out. Hence I learned something about the difference between a numeric and an algebraic integration in Maple. 

(On a separate note: I'll bet the problem in the int() function is related to the bug someone found in the erf() function involving int() :  http://www.mapleprimes.com/posts/207471-Bug-In-Integrate.)

 

Did you find that using the first method required nearly a half hour of calculation while the second method, though producing an incorrect answer, was performed within a second as they did for me?

@Ian Thompson 

Traditional index: In working with a couple other books for which I am more interested in process and not data, it is my experience that the Table of Contents is more useful. I applaud your idea of not including the index, even if it was for other reasons.  This will allow me to emphasize ideas from a holistic perspective, instead of the cheat-sheet perspective.  

Statistics: No, I don’t believe a section of statistics would be beneficial to most readers. In the US, most undergraduate students use Excel for statistics in the introductory sciences; Maple is considered a step up. I use Maple because it does a far better job than Excel with traditional comparative tests such as the chi-square goodness of fit test. (My colleagues in the Stats department feel that Excel should be banned from the university.)  In upper division bio courses, students move to R. (Minitab, wow, does that bring back memories. Maybe Minitab is still used in the UK, but only my oldest biology colleagues can remember using it here in the US.)

Topics I will need to include for our students: For our upper division physics courses, we are more likely to use numerical techniques for both sets of linked differential equations (initial value problems) as well as boundary value problems. However, while I believe Maple does do well in solving boundary value problems symbolically when compared to some other math packages, for the type of problems we face in physics and engineering, it tends to be less effective. But, if you start adding text for these types of problems, your book will begin to balloon.

Ditto operator: you may be correct that its use is contextual and relatively harmless for short examples. I’m not completely convinced since I repeatedly found that in helping students, the lack of assigning an answer lead to more difficulty in reading the answer and for them in obtaining an answer. Since I’ll be emphasizing the longer examples, I’m not terribly concerned.

Arrays and Tables: It is my experience that leaving these structures to the later chapters makes sense. A large body of problems can be solved without them. The distinction between sequences, lists and sets is far more important. In attempting to reduce the amount of Maple content in the introductory courses, I actually don’t even mention sets.   

Finally, I stand by my comments regarding the occurrence of taking a limit in undergraduate physics- they are pretty rare. I agree that limits do show up in theoretical physics, but not extensively until graduate school. I just happen to choose limits as one of the very few sections I might not assign.

Again, let me say your text shows that your experience extends beyond being highly knowledge about Maple – it includes a great deal of “being in the trenches with the students.”  Nicely done.

Instead of grading, I have spent far too much time reading “Understanding Maple”.  Overall, I like it quite a bit, so much I plan to assign it in some of my courses. There are many features of it that will serve the science, technology, engineering and mathematics instructor well.

So why the positive perspective? Firstly, it is brief which is very important. This is book that is for a course where computational techniques enhance the concepts, but do not drive them. Many students simply ignore books > 200 pages simply because the activation barrier to find something useful is overwhelming. Though this leads to an interesting pedagogical question. The text lacks a traditional index though it does possess an index by “Maple Notation”. Instead, the Table of Contents probably best serves as an index for asking that question, “How do I solve the following type of problem?” I’ll be interested in feedback by the students when I use it next year on this question.

Next, the text is laid out where I could easy assign a chapter weekly or biweekly and students wouldn’t feel their physics course has turned into a course on Maple. In describing what they liked least about my courses, “Too much Maple” comes up about 10-20% of the time.  Much of this complaint feel is unwarranted, but that is for another discussion.

Chapter 2 on “Getting Started”, which really is the first chapter of content, is packed with…content. In the past, I’ve highly recommended Doug Meade’s book “Getting Started with Maple”, especially for the students in the first-year course because of it brevity. However, if anything, “Understanding Maple” is terser. Just the facts, mam. Indeed, chapters on solving equations, differential calculus and linear algebra cover the essentials. For me that is enough and should serve as a refresher to students who may have looked at Doug’s book or have worked with me during the introductory course. In the chapter on graphics, I particularly like his use of the modern command dataplot .  This ties in nicely with the  Maplesoft Webinar on the topic.  

However, where this book really shines, and why I’ll be requiring the students to pony up $20 for the text, is in the last quarter where he discusses programming. I have agonized, attempted, and not have always succeeded sufficiently well enough the covering  of the basic programming properties such as conditional statements, looping, procedures, etc. Most of my students possess no formal programming experience. Yes, they get it, but having it in black and white works better. Now I will simply point to those sections of the text and say, “read.”  By the second year, while some of our students will have started Python, enough will not have seen the concept of a procedure. Designing a worksheet with multiple procedures is essential in solving problems the students face in introductory quantum mechanical. Indeed, by the second year, no longer do I say, “Here is an equation of 4 unknowns, I give you three of the unknowns and you solve for the other one.”

One might quibble about the choice of topics or a particular solution. For example, while assumptions are very important in science, we rarely care about limits. L’Hospital’s rule shows up so infrequently for undergradate texts, it usually used as the punch line to a joke.  And while I’m not going to discuss “tables”, I will need to add an entire section of statistics. I do like the fact that Ian tends to lean toward the philosophy of greater readability over the clever solution and Maple shortcuts. For example, while it is true we can learn the definition fi, the phrase end if is so much easier to understand the first time. 

However, if there is one pedagogical disagreement I have with this text is the extensive use of the “ditto operator”, %. Since the vast majority of the students I teach have completed, or will complete, a programming class, I strongly emphasis the use of assigning all outcomes to a variable, even if it is the same variable such as zelda := simplify(zelda) assuming positive.   It is my experience that if you are requiring to approach problems from a programming perspective, then these problems require numerous lines of code and one can’t simply ditto one’s way through the worksheet.

I might also suggest a visible graph or two. While including plots it would increase the thickness of the book, I feel seeing the examples would provide the reader a target to shoot for.

It is clearly apparent that Ian has taught this material numerous times. I particular like the “starred” paragraphs pointing out infamous pit falls such as ‘e’ does not mean exp(1). Several of the gotchas made me laugh. As I read, I would reminise about the experiences of having to show numerous students where their code had failed for exactly those reasons he describes. More than once I bet we both said to a student, “Sorry, Maple simply isn’t sophisticated enough to read your mind.” In my view, his prose is also very easy to read; it is sophisticated without requiring a Ph.D. in English.

In short, this book is targeted to new Maple users who don’t require knowing everything, but just enough to solve 80-90% of the problems the user is going to face.  

(This text was edited for, hopefully, improved clearity. The original post we written in an American pub while enjoying a pint or two.)

 

@Christopher2222 

I can understand your comments. I must deal with this issue every semester. However, from my view, the distinction between ‘e’ and exp() is important. The letter ‘e’ is well established in the natural sciences as the letter for the fundamental charge (or elementary charge.) It represents the charge of all protons, and the negative value of it is the charge of all electrons; that is, as far as we know. For those in the natural sciences, the key word here is “fundamental”.

I see the difference between the italicized ‘e’, i.e., the symbol ‘e’, and the regular ‘e’, as a representation for exp(), as an important teaching moment.

Approximately 10 years ago, Robert visited my campus. I spent a delightful afternoon talking about pedagogy, the use of Maple in the classroom and techniques to solve problems that I and the students face in both introductory and upper division physics. While Robert may not have been trained as a physicist, I remember thinking to myself as he was gently (and I mean gently) suggesting a different path to solve a problem, “Wow, Robert really is sharp! He could teach my courses. I wonder if he is interested in a position here?” But in looking at these photos of his “redirect energy/retirement” party, I discovered Robert appeared to have found a fountain of youth at Maplesoft! Robert hasn’t aged in 10 years!  We didn’t have a chance wooing him to our campus.

Robert, I’m hoping you will continue to visit (haunt?) Maple Primes.  It is obvious your understanding of how humans learn is elegant and extensive.  Your richly deserve the accolades you have received.

Now, I have to tell one story related to Robert. At the beginning of this semester, I tried to, gently, introduce Maple into a course as an alternative to the TI-89 calculators.  One of the students told me she had later watched many videos on Maple including a few from the “Clickable Calculus” series so that she could get up to speed.

Later I worked through a number of the “vector field” examples in class with the students following along and reproducing my commands. After class I asked the video watching student if she found the class useful. “Yes, but I found the guy who did those calculus videos more helpful.” 

So, Robert, are you interested in another job?

@Axel Vogt Regarding your PS. Does SW = software? As far as I can tell, all three manuals are free as electronic text. They want money for the hard copies which I don't consider unreasonable. If there is one area Maplesoft has improved upon considerable is help, either within the program or online. However, I still find Doug Meade's book, "Getting Started", more informative and efficient in helping most people getting started.

I'm very much looking forward to reading this text. I have been searching for an update to what I felt has been the most useful of Maple introductory texts, "Getting Started with Maple". While "Getting Started" is in its 4th edition, it was last updated in 2008. And while students tend to try to accomplish all tasks after only watching some videos and the simple excercises I cover in class, they do appreciate a richer introduction once they realize using computers is not simply a passing fad,  I have tried to promote the programable approach in using Maple to solve problems rather than what I see in other courses which is the "glorified calculator" / Wolfram Alpha approach. The reality is that the single line command and response techinque possesses the lowest activation barrier. Hopefully I can actually require this text for my classes. At 21 USD for the paperback version, or 11 USD for the Kindle version, students are less likely to avoid purchasing it based on cost. (At this point, "Getting Started" is about 62 USD.)

You are missing a multiplication between the end of the sine function and the term that is squared.


When I teach Maple, I make sure that students learn to explicitly include the "*" symbol at all times. For example:

int(sin(n*Pi*x/L)*((x/L)^2)^2, x=0..L)

So you are not alone in making this error. Sometimes it is simply the need for another pair of eyes.

@Christopher2222  You are not alone. My only post ended up listed as a question. Hence I'm not sure what the "post" button does.

First 17 18 19 20 21 Page 19 of 21