B689  Topics in Graphics and Human Computer Interaction
Mathematical Modeling:
Concepts, Programming, and Visualization
Andrew J. Hanson
Spring 2012
Section Section 26466  3 credit hours
Meets TUESDAYS at 4:00pm.
We will meet 4pm on Thursday the second two weeks and the last
two weeks of the term)
Instructor: Andrew
J. Hanson
hansona at indiana.edu
Class Meeting: Tuesdays, 4:00pm6:00pm in LH008;
special laboratory meetings on Thursdays in LH008 at 4:00pm
the second two weeks and the last two weeks of the term.
Office Hours: Friday 10:30am12:00noon,
or by appointment, in Lindley 401D
First Meeting: 4:00pm Tuesday 10 January 2012 in LH008.
Last W: 4:00pm Wednesday 7 March 2012.
Project Proposals: Due week of 1923 March 2012.
Project 20minute Oral Presentations begin Tuesday
17 April 2012, Thu 19 April 2012, Tue 24 April 2012, Thu 26 April 2012
Final Project Written Reports Due: by 11:59pm
Wednesday 2 May 2012.
B689 Contents

Outline of First Lectures

First Three+ Weeks of Course (at least 4 classes):
We will learn Mathematica from scratch in the first two/three
weeks or so, and smoothly transition from basics to applications after that.
Course lecture notes. (Intro Mathematica tutorial lectures a, b, c.)
The world is full of books based on Mathematica.
One example of a very nice reference, with part of it excerpted online
at Google Books is The Mathematica
Cookbook. in the O'Reilly series.
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 9 January 2012