Mathematical Modeling

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Multiwavelets for Quantitative Pattern Matching, Hawaiian International Conference on System Sciences (2009)
This was my presentation in Hawaii that accompanied my paper on pattern matching, published in...
 

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Wavelet Decompositions for Quantitative Pattern Matching, Proceedings of the 42nd Annual Hawaii International Conference on System Sciences (CD-ROM) (2009)
The purpose of this paper is to provide an introduction to the concepts of wavelets...
 

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At Least Four Distinct Circadian Regulatory Mechanisms Required for All Phases of Rhythms in mRNA Amount (with Sigrid Jacobshagen and Claire Rinehart), Journal of Biological Rhythms (2008)
Since the advent of techniques to investigate gene expression on a large scale, numerous circadian...
 

Mathematics Education

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Comic Books That Teach Mathematics, Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)

During the 2008--2009 academic year, the author embarked on an extremely non-standard curriculum path: developing...

 

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Comic Books That Teach Mathematics, 2009 Bridges Banff Conference (2009)
During the 2008--2009 academic year, the author embarked on an extremely non-standard curriculum path: developing...
 

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Using Works of Visual Art to Teach Matrix Transformations (with James Luke Akridge, Rachel Bowman, and Peter Hamburger), Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)
The authors present a modern technique for teaching matrix transformations on $\R^2$ that incorporates works...
 

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Operation Comics, Issue #3 (2009)
This is the third issue of Operation Comics, with my superhero Wonderguy and his able...
 

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Elementary-Level Mathematics Content in Comic Book Format (with Janet Tassell, Mary Evans, Cathy Willoughby, and Melissa Zimmer), Council on Postsecondary Education Scholarship of Teaching and Learning Conference (2009)
 

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Operation Comics, Issue #2 (with Alex O'Keefe and Missy Pitcock) (2009)
This is the second issue of Operation Comics, with my superhero Wonderguy and his able...
 

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Operation Comics, Issue #1 (with Annie Erskine) (2009)
This is the first of three comics that will be produced during the Spring 2009...
 

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My Trig Book, Mathematics Faculty Publications (2009)
This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton...
 

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A "Sound" Approach to Fourier Transforms: Using Music to Teach Trigonometry, 2007 Bridges Donostia Conference Proceedings (2007)
If a large number of educated people were asked, ``What was your most exciting class?'',...
 

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Math Matters: Why Do I Need to Know This? (Episode 10, Segment 1 - consumer mathematics), WKYU internal cable (2006)
This is the first segment of the tenth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 10, Segment 2 - circles and Pythagorean theorem), WKYU internal cable (2006)
This is the second segment of the tenth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 10, Segment 3 - exponential and logarithmic functions), WKYU internal cable (2006)
This is the third segment of the tenth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 11, Segment 1 - amortized loans), WKYU internal cable (2006)
This is the first segment of the eleventh episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 11, Segment 2 - least common multiple and greatest common divisor), WKYU internal cable (2006)
This is the first segment of the eighth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 11, Segment 3 - systems of two linear equations), WKYU internal cable (2006)
This is the third segment of the eleventh episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 12, Segment 1 - credit-card debt), WKYU internal cable (2006)
This is the first segment of the twelfth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 12, Segment 2 - matrix multiplication), WKYU internal cable (2006)
This is the second segment of the twelfth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 12, Segment 3 - population models), WKYU internal cable (2006)
This is the third segment of the twelfth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 13, Segment 1 - matrix multiplication), WKYU internal cable (2006)
This is the first segment of the thirteenth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 13, Segment 2 - matrix multiplication), WKYU internal cable (2006)
This is the second segment of the thirteenth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 13, Segment 3 - population models), WKYU internal cable (2006)
This is the third segment of the thirteenth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 14 - annuities and fair division), WKYU internal cable (2006)
This is the fourteenth episode of the program, where I discuss annuities and a method...
 

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Math Matters: Why Do I Need to Know This? (Episode 1 - Venn diagrams, exponent rules, compound interest, and the Rule of Seventy), WKYU-TV internal cable (2006)
This is the first episode of my TV program. Topics include Venn diagrams, exponent rules,...
 

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Math Matters: Why Do I Need to Know This? (Episode 2, Segment 1 - logic), WKYU-TV internal cable (2006)
This is the first segment of the second episode of the program, where I discuss...
 

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Math Matters: Why Do I Need To Know This? (Episode 2, Segment 2 - factoring), WKYU-TV internal cable (2006)
This is the second segment of the second episode of the program, where I discuss...
 

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Math Matters: Why Do I Need To Know This? (Episode 2, Segment 3 - rational expressions), WKYU-TV internal cable (2006)
This is the third segment of the second episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 3, Segment 1 - logical fallacies), WKYU-TV internal cable (2006)
This is the first segment of the third episode of the program, where I discuss...
 

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Math Matters: Why Do I Need To Know This? (Episode 3, Segment 2 - polygons), WKYU-TV internal cable (2006)
This is the second segment of the third episode of the program, where I discuss...
 

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Math Matters: Why Do I Need To Know This? (Episode 3, Segment 3 - tessellations), WKYU-TV internal cable (2006)
This is the third segment of the third episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 4, Segment 1 - counting techniques and probability), WKYU-TV internal cable (2006)
This is the first segment of the fourth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 4, Segment 2 - unit conversions), WKYU-TV internal cable (2006)
This is the second segment of the fourth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 4, Segment 3 - radical expressions), WKYU-TV internal cable (2006)
This is the third segment of the fourth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 5, Segment 1 - expected value), WKYU-TV internal cable (2006)
This is the first segment of the fifth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 5, Segment 2 - formula for a polynomial through a set of points), WKYU-TV internal cable (2006)
This is the second segment of the fifth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 5, Segment 3 - slope of a line), WKYU-TV internal cable (2006)
This is the third segment of the fifth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 6, Segment 1 - surface area), WKYU-TV internal cable (2006)
This is the first segment of the sixth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 6, Segment 2 - complex numbers), WKYU-TV internal cable (2006)
This is the second segment of the sixth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 6, Segment 3 - inequalities), WKYU-TV internal cable (2006)
This is the third segment of the sixth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 7, Segment 1 - graphs of data), WKYU-TV internal cable (2006)
This is the first segment of the seventh episode of the program, where I discuss...
 

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Math Matters: Why Do I Need To Know This? (Episode 7, Segment 2 - volume), WKYU-TV internal cable (2006)
This is the second segment of the seventh episode of the program, where I discuss...
 

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Math Matters: Why Do I Need To Know This? (Episode 7, Segment 3 - quadratic formula), WKYU-TV internal cable (2006)
This is the third segment of the seventh episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 8, Segment 1 - similar and congruent triangles), WKYU internal cable (2006)
This is the first segment of the eighth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need To Know This? (Episode 8, Segment 2 - different base numerals), WKYU internal cable (2006)
This is the first segment of the eighth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 9, Segment 1 - normal distributions), WKYU internal cable (2006)
This is the first segment of the ninth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 9, Segment 1 - normal distributions), WKYU internal cable (2006)
This is the first segment of the ninth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 9, Segment 2 - divisibility theorems), WKYU internal cable (2006)
This is the second segment of the ninth episode of the program, where I discuss...
 

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Math Matters: Why Do I Need to Know This? (Episode 9, Segment 3 - number of polynomial solutions and end behavior), WKYU internal cable (2006)
This is the third segment of the ninth episode of the program, where I discuss...
 

Wavelets

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Wavelet Decompositions for Quantitative Pattern Matching, Proceedings of the 42nd Annual Hawaii International Conference on System Sciences (CD-ROM) (2009)
The purpose of this paper is to provide an introduction to the concepts of wavelets...
 

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Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements on [0,1], Applied and Computational Harmonic Analysis (2007)
Geronimo, Hardin, et al have previously constructed orthogonal and biorthogonal scaling vectors by extending a...
 

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An Orthogonal Scaling Vector Generating a Space of $C^1$ Cubic Splines Using Macroelements, Journal of Concrete and Applicable Mathematics: Special Issue on Wavelets and Applications (2006)
The main result of this paper is the creation of an orthogonal scaling vector of...
 

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Balanced Scaling Vectors Using Linear Combinations of Existing Scaling Vectors, Approximation Theory XI: Gatlinburg 2004 (2005)
The majority of the research done into creating balanced multiwavelets has involved establishing a series...
 

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Orthogonal Macroelement Scaling Vectors and Wavelets in 1-D (with Douglas P. Hardin), The Arabian Journal for Science and Engineering: Special Issue on Fractals and Wavelets (2003)
We develop a {\em macroelement} based technique for constructing orthogonal univariate multiwavelets. We illustrate the...
 

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A Construction of Compactly-Supported Biorthogonal Scaling Vectors and Multiwavelets on $R^2$, Journal of Approximation Theory (2002)
In \cite{K}, a construction was given for a class of orthogonal compactly-supported scaling vectors on...
 
A Short-support Dual Mask to the Piecewise Linears on a Uniform Triangulation, Approximation Theory X: Wavelets, Splines, and Applications (2002)
Much work has been done in finding duals and wavelets for a single scaling function...
 
Constructions of Orthogonal and Biorthogonal Scaling Functions and Multiwavelets Using Fractal Interpolation Surfaces, Advances in Imaging And Electron Physics (2002)
This chapter is a survey of the work that has been done by Donovan, Geronimo,...
 

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A Construction of Orthogonal Compactly-Supported Multiwavelets on $\R^{2}$, Applied and Computational Harmonic Analysis (2000)
This paper will provide the general construction of the continuous, orthogonal, compactly-supported multiwavelets associated with...
 
A construction of two-dimensional multiwavelets on a triangulation (with George C. Donovan, Jeff S. Geronimo, and Douglas P. Hardin), Wavelet Application in Signal and Image Processing IV (1996)
A family of continuous, compactly supported, bivariate multi-scaling functions have recently been constructed by Donovan,...
 
Multiresolution analyses and fractal functions (with Douglas P. Hardin and Peter Massopust), Journal of Approximation Theory (1992)
 

No subject area

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Math Matters: Why Do I Need To Know This? (Episode 8, Segment 3 - piecewise functions), WKYU internal cable (2006)
This is the third segment of the eighth episode of the program, where I discuss...