Titlebook: Symmetry Theory in Molecular Physics with Mathematica; A new kind of tutori William McClain Textbook 2008 Springer-Verlag New York 2008 Gro

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The meaning of symmetry,., and . are terms invoked in dictionaries to explain the meaning of the word .. But the formal study of symmetry must begin with a much simpler, more precise definition.

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Axioms of group theory,In this book, we will be concerned almost exclusively with . of symmetry transforms. But the “group” is one of the most general concepts in mathematics, and we must begin with the axioms of group theory, stated in a form that applies to all kinds of groups.

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The fundamental theorem,This Chapter puts together the definition of . given in Chapter 4, and the definition of . given in Chapter 5.

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Molecules,Our . molecules are written and maintained by a simple form of object-oriented programming, which insures that errors are caught at the time of molecule entry, rather than during their use.

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Product groups,Multiplication to closure is not the only way to construct groups. In this chapter we show how one can sometimes combine two groups already known to make a new, larger group. We begin with an example. Look at the tabulated Cartesian matrices that represent groups C. and C.

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Tabulated representations of groups,In this chapter we discuss the package operator CartesianRepresentationTable, or CartRep for short, . back in Chapter 8 ( MultiplicationTables). All the group names returned by GroupCatalog have a CartRep kept in the Symmetry package

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Visualizing groups,In Chapter 15 (MakeGroup) we developed tools for generating every possible point group, and in Chapter 18 (CartesianRepresentations) we actually did it (well, not all of them).