After a few initial chapters on the basics of

*Mathematica*, the logic of this book is controlled by group theory.

The book has three major parts. Part I begins with the most elementary symmetry concepts, showing how to express them in terms of matrices and permutations, before moving on to the construction of mathematical groups. In Part II, mathematical group theory is presented with motivating questions and experiments first, and theorems that answer those questions second. In Part III, the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems, which are now seen to fall within a unified intellectual framework.

Intended for students of chemistry and molecular physics, the book may be read either independently or on a computer screen with

*Mathematica* running behind it. The included CD-ROM presents the entire content of the book plus interactive examples using

*Mathematica* notebooks for problem-solving and learning.

Introduction | A Tutorial on Notebooks | A Basic

*Mathematica* Tutorial | The Meaning of Symmetry | Axioms of Group Theory | Several Kinds of Groups | The Fundamental Theorem | The Multiplication Table | Molecules | The Point Groups | Euler Rotation Matrices | Lie's Axis-Angle Rotations | Recognizing Matrices | Introduction to the Character Table | The Operator

`MakeGroup` | Product Groups | Naming the Point Groups | Tabulated Representations of Groups | Visualizing Groups | Subgroups | Lagrange's Theorem | Classes | Symmetry and Quantum Mechanics | Transformation of Functions | Matrix Representations of Groups | Similar Representations | The

`MakeRep` Operators | Reducible Representations | The

`MakeUnity` Operator | Schur's Reduction | Schur's First Lemma | Schur's Second Lemma | The Great Orthogonality | Character Orthogonalities | Reducible Rep Analysis | The Regular Representation | Projection Operators | Tabulated Bases for Representations | Quantum Matrix Elements | Constructing SALCs | Hybrid Orbitals | Vibration Analysis | Multiple Symmetries | One-Photon Selection Rules | Two-Photon Tensor Projections | Three-Photon Tensor Projections | Class Sums and Their Products | Make a Character Table | Appendices

Physics,

Tutorial and Reference