Historically, nonclassical physics developed in three stages. First
came a collection of "ad hoc" assumptions and then a cookbook of
equations known as "quantum mechanics." The equations and their
philosophical underpinnings were then collected into a model based
on the mathematics of Hilbert space. From the Hilbert space model
came the abstaction of "quantum logics." This book explores all
three stages, but not in historical order. Instead, in an effort to
illustrate how physics and abstract mathematics influence each
other we hop back and forth between a purely mathematical
development of Hilbert space, and a physically motivated definition
of a logic, partially linking the two throughout, and then bringing
them together at the deepest level in the last two chapters. This
book should be accessible to undergraduate and beginning graduate
students in both mathematics and physics. The only strict
prerequisites are calculus and linear algebra, but the level of
mathematical sophistication assumes at least one or two
intermediate courses, for example in mathematical analysis or
advanced calculus. No background in physics is assumed.
General
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