B689/B490  Topics in Graphics and Human Computer Interaction
Mathematical Modeling:
Concepts, Programming, and Visualization
Andrew J. Hanson
Spring 2011
Section 28196/28193  3 credit hours
Meets TUESDAYS at 4:00pm
we will meet on Thursday the first two weeks and the last
two weeks of the term if possible)
Instructor: Andrew
J. Hanson
hansona at indiana.edu
Class Meeting: Tuesdays, 4:00pm6:00pm in LH115;
selected laboratory meetings on Thursdays in LH115 at 4:00pm
the first two weeks and the last two weeks of the term.
Office Hours: Wednesday 2:00pm3:00pm, or by appointment, in Lindley
401D
First Meeting: 4:00pm Tuesday 11 January 2011 in LH115.
Last W: 4:00pm Wednesday 9 March 2011.
tentative: Project Proposals: Due Monday March 22 2011.
tentative: Final Project Oral Presentations tentatively begin Tuesday
19 April 2011, Thu 21 April 2011, Tue 26 April 2011, Thu 28 April 2011
Final Project Written Reports Due: by Friday 6 May 2011.
B689 Contents

Weekly Lecture Plan IN DEVELOPMENT (to be revised
continuously!)

First Two Weeks of Course (Four classes):
We will learn Mathematica from scratch in the first two weeks.
Purpose and Motivation: Back
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Mathematical modeling methods are essential in every branch of modern
science, and are especially critical in any attempt to produce visual representations
supporting data visualization, problem domain analysis, and pedagogical
illustration. This course will introduce basic techniques of mathematical
modeling with applications to scientific visualization. The target
audience is any student
with an interest in applying innovative mathematical modeling methods,
particularly those with visual aspects, to their research. Among the areas
from which we would like to encourage participation are cognitive
science, chemistry, physics, astrophysics, mathematics, biology, and, of
course, computer science.
Mathematical modeling methods are essential in every branch of modern
science, and are especially critical for any attempt to produce visual
representations supporting data visualization and concept
illustration. This course will introduce the basic techniques of
mathematical modeling with applications to scientific visualization.
The target audience is mainly graduate students, and possibly a few
advanced undergraduates, in a variety of disciplines; the course
should be useful to those with an interest in learning mathematical
modeling methods, particularly those with visual aspects, and applying
them to their research. Among the areas from which we may draw domain
material are mathematics, physics, cognitive science, chemistry,
astrophysics, biology, and, of course, computer science and
informatics.
Examples of likely topics include the following, and topics
can be adapted to the interests of the class members:
 Fundamental principles of quaternion orientation selection and
orientation control. A taste of Clifford algebras. See instructor's
book "Visualizing Quaternions", MorganKauffman, 2006.
 Rapid prototyping of geometric shapes and data models.
 Design principles for graphic representations and interaction.
 Understanding the Fourth Dimension.
 Fundamental principles of geometry, data representation, and
modeling in N Dimensions
 Barycentric coordinates and applications
 Real and complex projective geometry, projective
invariants.
 Potential project domains include Mathematica Manipulate[] systems
that can be submitted to the Wolfram Demonstrations Project
 iPhone applications that can be submitted to the Apple Apps site
Back
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Andrew J. Hanson
Updated November 2010