### 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