A Calculus of Number Based on Spatial Forms - University of ...

PREFACE
This work attempts to clarify mathematics, to make complex ideas accessible
to those with less mathematical training. In this thesis, I have reduced number
and operator representation down to three forms, revealing a simplicity to
numbers. I hope this work may aid those who have struggled to understand
numbers and computation, as well as elementary algebra, for I surely consider
these topics in new light.
I am not a mathematician, so writing a thesis about mathematics has been
achallenge for me. For years, I have struggled to understand what research
in mathematics is all about that I might contribute to its continuing progress.
Alas, essential concepts continue to elude me and I remain uncertain about
what mathematicians are actually doing. Nonetheless, I believe mywork to
have some relevance to them and have tried to describe it in a manner that
would avail mathematical researchers to make use <strong>of</strong> it, though my audience
also includes the less mathematically inclined.
Ihave benetted from many discussions with friends and colleagues during
the development <strong>of</strong> this material. Most recognize some insight here, though I
am not certain whether they liked the material itself or just the idea <strong>of</strong> trying
to make mathematics easier to understand.
I thank William Bricken with my heart and soul. William introduced
me to boundary mathematics and has served as my mentor throughout this
research|his guidance and direction has made it all happen.
I thank the rest <strong>of</strong> my thesis committee: Judith Ramey, William Winn,
and Steven Tanimoto. Each <strong>of</strong> them played unique roles in the development
<strong>of</strong> this material. I was privileged to have had such excellent support for my
research.
I credit my zest for research toPenelope Sanderson, with whom I studied
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