fwchapman

Dr. Frederick W. Chapman

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13 years, 177 days
F.W. Chapman Solutions
Technical Consultant, Research Scientist, and Business Owner
Bethlehem, Pennsylvania, United States

Social Networks and Content at Maplesoft.com


 

Frederick W. Chapman, PhD

I am a research mathematician and an expert on mathematical software. I completed my PhD in Applied Mathematics with a specialization in computer algebra and symbolic computation in 2003 at the University of Waterloo. My PhD supervisor was Prof. Keith O. Geddes, co-inventor of the Maple computer algebra system. In my PhD thesis, I invented an infinite parameterized family of bilinear series expansions for multivariate functions, which I named Geddes series expansions in honor of my thesis supervisor.

Geddes series are more general than both Taylor series and Fourier series since the terms of a Geddes series can contain arbitrary functions. The Geddes series family is more versatile than traditional series expansions because the parameters of the Geddes series family are not numbers, or even functions, but rather linear functionals on function spaces. Geddes series have dozens of computational applications ranging from the fast and accurate approximation of high-dimensional multiple integrals to the automatic derivation and proof of multivariate identities for elementary and special functions.

To secure independent funding for my research program and provide the resources needed to develop Geddes series to their full potential, I founded F.W. Chapman Solutions, an interdisciplinary consulting firm which blends information technology with visual arts and mathematical sciences.

What can my company do for you?

My firm's Professional Services Division has the expertise and equipment to provide complete solutions which seamlessly blend four strategic areas:

1. Mathematical Software

• Consulting
• Onsite/Online Training
• Coding, Testing, Debugging

2. e-Learning

• Computer-Based Training
• Automated Quizzes/Tests
• Online Courses

3. Web Design & Database Applications

• Websites, Blogs, Photo Galleries
• e-Commerce, User Accounts
• Databases, Online Forms
• Online Marketing, Social Media
• Web Analytics, SEO

4. Digital Photography & Post Production

• Advanced Digital Imaging Lab, Online Photo Library
• Retouching/Compositing, Captioning/Keywording
• Online Searching/Browsing/Proofing/Ordering
• Mobile Photo Studio, On-Location Photo Shoots
• Business Portraits, Product Shots
• Architectural Interiors/Exteriors, Cultural/Social Events

My Commercial Products Division develops targeted information products to sell online and sells photos as digital downloads and prints. My Scientific Research Division does original research in mathematics and computing and uses the results to develop more powerful mathematical software and better digital image processing algorithms.

Why should you hire my company?

I am a university professor turned entrepreneur — a scientist, technologist, and artist with decades of experience solving complex problems in a wide range of disciplines. My company uses industry-leading tools to provide innovative, cost-effective, reliable solutions for businesses, professionals, artists, performers, educators, researchers, and other clients.

When you need proven solutions from an experienced professional problem solver, you need F.W. Chapman Solutions. I thank you for your business!

 


 

F.W. Chapman Solutions

F.W. Chapman Solutions is a vibrant synthesis of information technology, visual arts, and mathematical sciences. Founded by professor-turned-entrepreneur Frederick W. Chapman, PhD, the company provides an integrated suite of professional services on a freelance basis, develops its own line of targeted information products to sell online, and conducts independent scientific research for scholarly publication and future commercialization. Here is a brief overview of the company's areas of expertise.

Professional Services

• Mathematical Software Consulting
• e-Learning & Computer-Based Training
• Web Design & Database Applications
• Digital Photography & Post Production

Commercial Products

• e-Books, e-Courses, e-Manuals
• Photo Downloads & Prints

Scientific Research

• Computational Functional Analysis
• Multivariate Interpolation/Approximation
• Multilinear Algebra, Matrix Analysis
• Computer Algebra, Symbolic Computation
• Symbolic-Numeric Methods, Parallel Algorithms

For more information about F.W. Chapman Solutions, please visit the company website, blog, and photo library:

www.fwchapman.com

blog.fwchapman.com

photos.fwchapman.com

 


MaplePrimes Activity


These are replies submitted by fwchapman

Darin,

Thanks for the news on the new parallelism features in Maple 14.  Am I correct in assuming that these features can be used on a single machine with a multi-core processor?  I'm building a new machine with an Intel Core i7 Quad-Core processor, 8 GB of RAM, and 64-bit Windows 7.  Are there any special issues with parallelism in Maple 14 on this computing platform?

I just noticed that you've written a whole series of articles on parallelism in Maple.  I've bookmarked your blog and look forward to studying your articles!

Thanks again,

Fred

__________________________________________________________

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Technical Consultant and Research Scientist at F.W. Chapman Solutions
www.fwchapman.com  |  blog.fwchapman.com  |  photos.fwchapman.com

@Will Thanks for passing my suggestion on to the appropriate person.

As for Question vs. Post, I originally started to create a Post, but then I read, "If you have a question, consider asking a question instead."  Since my suggestion was in the form of a question, I posted a Question.  :)  I was puzzled that in the Question screen there was no check box for MaplePrimes -- only for Maplesoft products.  So I guess I should have created a Post, since there is a check box for MaplePrimes there.

My reason for telling you this rambling story is to point out that it wasn't quite clear where MaplePrimes suggestions should go.  Do you want to put something at the top of the Questions screen to steer people to the Post screen if they have a MaplePrimes suggestion?

Fred

Will, thanks for fixing the title/profile issue!  To celebrate, I've created a new subdomain of my main domain name:

mapleprimes.fwchapman.com

__________________________________________________________

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Technical Consultant and Research Scientist at F.W. Chapman Solutions
www.fwchapman.com  |  blog.fwchapman.com  |  photos.fwchapman.com

Will,

I entered a Title under the Company/Institution Details in my profile and checked the box to make it public, but my title does not show up underneath my Company/Institution when I view my profile.

Thanks,

Fred

___________________________________________________________________

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Technical Consultant and Research Scientist at F.W. Chapman Solutions
www.fwchapman.com  |  blog.fwchapman.com  |  photos.fwchapman.com

@Alec Mihailovs Thanks for all the info, Alec!  I recently learned of NumPy as part of SciPy, and I think I would lean in that direction myself if I were going the free open-source route.

Fred

@Alec Mihailovs I can't find any information about the MATLAB home edition.  Can you please post a link where I can find out more?

There are some free open-source projects which people often use alternatives to MATLAB.  One is Scilab, and the other is Octave/Gnuplot.  I'm not aware of a home edition for MATLAB, though.

Thanks,

Fred

Ian, thanks for asking this question.

Bryan, thanks for providing the answer.

The existence of the Maple Personal Edition came as a total surprise to me, but it is priced even lower than the the home edition of that "other" leading computer algebra system!  That's going to be wonderful news to a lot of people.

Fred

____________________________________________________________________

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Freelance Consultant & Scientific Researcher at  F.W. Chapman Solutions

@Will The "Using Maple Since" field in the user profile is not saved.  I set it to "Before 1995" and click on Submit, but when I come back later to edit my profile, the setting has been forgotten.  I've tried it several times in the past few days, always with the same results.

Fred

Will,

Thanks for your speedy reply!  I'm now able to update my profile -- no more error message.

For some reason, it doesn't remember the Using Maple Since field.

Where do the Technical Interests/Fields and Other Interests or Hobbies show up on the site?  I didn't see them in my profile view -- only on the profile update screen.

Thanks again,

Fred

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Freelance Consultant & Scientific Researcher at  F.W. Chapman Solutions

Hello Will,

Congratulations to you and Maplesoft on getting the new MaplePrimes site up and running.  I absolutely LOVE the new design!  It looks fabulous.

If I remember correctly, the old site was implemented using Drupal.  What platform are you using for the new site?

By the way, I ran into a small problem after I migrated my MaplePrimes account.  I'm not able to update my profile.  When I try to submit my changes, I get an unspecified error message.  Other than that, so far so good!

Best wishes,

Fred

 

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Freelance Consultant & Scientific Researcher at  F.W. Chapman Solutions

Alec, thanks for your comments.  I have some questions and comments in reply.

1. Is there a specific reason you don't want to join LinkedIn?  The basic services are totally free.  I only use the free services, and I find LinkedIn to be a great way to reconnect with old colleagues and meet interesting new ones.  LinkedIn is a powerful professional networking and career development tool and thus has value in its own right.  A lot of Maplesoft employees are already LinkedIn members, as are some very high-profile experts in computational mathematics, such as Jon Borwein and David Bailey.

2. The Maple Global Network is independent of Maplesoft.  Though I believe Maplesoft to be a force for considerable good in our field, I think it is beneficial to also have independent Maple groups like the ones we're discussing.

3. You can add a link to the Maple Wiki on MaplePrimes yourself in Books > Great Maple Links > Great Maple tools and resources.  That's where I added a permanent link to the Maple Global Network group on LinkedIn.

4. Finally, I'd like to add that I am considering expanding the resources of the Maple Global Network beyond LinkedIn.  We're currently discussing a proposal on LinkedIn to use Google Apps to offer a suite of online communication and collaboration tools to all group members.  This would include wiki-style websites for all group members and group projects.  The advantage of Google Apps over a typical wiki is that we can control exactly who can see each web page and who can change it, in essence moderating selected portions of the site.

Now how do you feel about joining the Maple Global Network?  Am I wearing you down or just wearing you out?  :-)

Fred

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Research Mathematician / Mathematical Software Specialist / Maple Expert
Full Credentials & Freelance Consulting Services:  linkedin.fwchapman.info

Alec, thanks for your comments.  I have some questions and comments in reply.

1. Is there a specific reason you don't want to join LinkedIn?  The basic services are totally free.  I only use the free services, and I find LinkedIn to be a great way to reconnect with old colleagues and meet interesting new ones.  LinkedIn is a powerful professional networking and career development tool and thus has value in its own right.  A lot of Maplesoft employees are already LinkedIn members, as are some very high-profile experts in computational mathematics, such as Jon Borwein and David Bailey.

2. The Maple Global Network is independent of Maplesoft.  Though I believe Maplesoft to be a force for considerable good in our field, I think it is beneficial to also have independent Maple groups like the ones we're discussing.

3. You can add a link to the Maple Wiki on MaplePrimes yourself in Books > Great Maple Links > Great Maple tools and resources.  That's where I added a permanent link to the Maple Global Network group on LinkedIn.

4. Finally, I'd like to add that I am considering expanding the resources of the Maple Global Network beyond LinkedIn.  We're currently discussing a proposal on LinkedIn to use Google Apps to offer a suite of online communication and collaboration tools to all group members.  This would include wiki-style websites for all group members and group projects.  The advantage of Google Apps over a typical wiki is that we can control exactly who can see each web page and who can change it, in essence moderating selected portions of the site.

Now how do you feel about joining the Maple Global Network?  Am I wearing you down or just wearing you out?  :-)

Fred

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Research Mathematician / Mathematical Software Specialist / Maple Expert
Full Credentials & Freelance Consulting Services:  linkedin.fwchapman.info

Momiji,

I'm writing in reply to your comment that LinkedIn is very similar to Facebook and offers no compelling reason to join the Maple Global Network.  There are significant differences between LinkedIn and Facebook.  LinkedIn is a serious professional networking and career development tool used by CEOs and VPs as well as world-famous mathematicians and computer scientists.  I know this because some of them are in my LinkedIn network.  Facebook is a social networking tool used by high school and college students.  Their features may be similar, but their audiences are worlds apart.

If all that LinkedIn offers isn't enough to compel you to join the Maple Global Network, how about the power of Google Apps?  We are now reviewing a proposal to expand the services of the Maple Global Network by adopting the Google Apps online communication and collaboration tools.  This would provide personalized email addresses, free member websites, collaborative online documents, and more.  These tools would give us the resources to effectively manage group projects like reporting and tracking Maple bugs online and working together to developing a Maple IDE.

If these new features interest you, I invite you to join the Maple Global Network on LinkedIn and participate in the ongoing discussion!

With best wishes,

Fred Chapman (Group Owner)

Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Research Mathematician / Mathematical Software Specialist / Maple Expert
Full Credentials & Freelance Consulting Services:  linkedin.fwchapman.info

Hello Jimmy and Axel—how nice to meet you both again here on MaplePrimes! As I wrote to Jimmy in a private email, we plan to include Geddes-Newton multiple integration in a future release of Maple, but that won't happen very soon. Meanwhile, we can develop short ad hoc Maple codes to apply the technique to Jimmy's problem. Axel's change of variables is an important step in the right direction because it transforms the original integrand into a new integrand of the form f(x,y)*u(x)*v(y), where f(x,y) is a symmetric function; i.e., f(x,y) = f(y,x). The region of integration is transformed from one rectangle into another rectangle. Now you want to expand the symmetric part f(x,y) of the new integrand in a Geddes-Newton series on the smallest square which contains the new region of integration—the region of approximation needs to be symmetric since the function is symmetric, and it clearly needs to include the region of integration. For this particular function, you can choose all of the splitting points on the diagonal of the square. This will generate a finite sum of terms of the form g[i](x)*h[i](y). Next, multiply each term of the Geddes-Newton series by the weight function u(x)*v(y) to obtain terms of the form g[i](x)*u(x)*h[i](y)*v(y). Now integrate termwise and separate the variables; i.e., integrate g[i](x)*u(x) with respect to x, then integrate h[i](y)*v(y) with respect to y, and multiply the results. Note that this reduces the 2-D integral of each term to a product of unnested 1-D integrals—that's the key idea! This separation-of-variables method based on symmetric Geddes-Newton series expansions should easily accommodate high-precision integration for Jimmy's problem. I look forward to hearing about your results! With best wishes, Fred Frederick W. Chapman, Postdoctoral Fellow, University of Waterloo
www.fwchapman.infowww.geddes-series.info
Hello Jimmy and Axel—how nice to meet you both again here on MaplePrimes! As I wrote to Jimmy in a private email, we plan to include Geddes-Newton multiple integration in a future release of Maple, but that won't happen very soon. Meanwhile, we can develop short ad hoc Maple codes to apply the technique to Jimmy's problem. Axel's change of variables is an important step in the right direction because it transforms the original integrand into a new integrand of the form f(x,y)*u(x)*v(y), where f(x,y) is a symmetric function; i.e., f(x,y) = f(y,x). The region of integration is transformed from one rectangle into another rectangle. Now you want to expand the symmetric part f(x,y) of the new integrand in a Geddes-Newton series on the smallest square which contains the new region of integration—the region of approximation needs to be symmetric since the function is symmetric, and it clearly needs to include the region of integration. For this particular function, you can choose all of the splitting points on the diagonal of the square. This will generate a finite sum of terms of the form g[i](x)*h[i](y). Next, multiply each term of the Geddes-Newton series by the weight function u(x)*v(y) to obtain terms of the form g[i](x)*u(x)*h[i](y)*v(y). Now integrate termwise and separate the variables; i.e., integrate g[i](x)*u(x) with respect to x, then integrate h[i](y)*v(y) with respect to y, and multiply the results. Note that this reduces the 2-D integral of each term to a product of unnested 1-D integrals—that's the key idea! This separation-of-variables method based on symmetric Geddes-Newton series expansions should easily accommodate high-precision integration for Jimmy's problem. I look forward to hearing about your results! With best wishes, Fred Frederick W. Chapman, Postdoctoral Fellow, University of Waterloo
www.fwchapman.infowww.geddes-series.info
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