1 Groups and Subgroups. - 1. 1 Definitions and Basics. - 1. 2 Group Table. - 1. 3 Rearrangement Theorem. - 1. 4 Building Groups. Subgroups. - Summary of Topics for Chapter 1. - Problems. - 2 Classes and Platonic Solids. - 2. 1 Conjugate Elements. - 2. 2 Classes. - 2. 3 Direct Product. - 2. 4 Cnv and Dn Groups. - 2. 5 Platonic Solids. T O and I Groups. - Summary of Topics for Chapter 2. - Problems. - 3 Matrices Irreps and the Great Orthogonality Theorem. - 3. 1 Matrix Representations of Operators. - 3. 2 Irreducible Representations. - 3. 3 Great Orthogonality Theorem (GOT). - 3. 4 Six Important Rules. - 3. 5 Character Tables. Bases. - 3. 6 Representations of Cyclic Groups. - Summary of Topics for Chapter 3. - Problems. - 4 Quantum Mechanics the Full Rotation Group and Young Diagrams. - 4. 1 Application to Quantum Mechanics. - 4. 2 Full Rotation Group O(3). - 4. 3 SU(2). - 4. 4 Irreps of O(3)+ and Coupled Angular Momentum States. - 4. 5 Symmetric Group; Cayley's Theorem. - 4. 6 Young Diagrams. - 4. 7 Degenerate Perturbation Theory. - Summary of Topics for Chapter 4. - Problems. - 5 Space Groups Brillouin Zone and the Group of k. - 5. 1 Cosets and Invariant Subgroups. The Factor Group. - 5. 2 Primitive Vectors. Braviais Lattice. Reciprocal Lattice Space. - 5. 3 Crystallographic Point Groups and Reciprocal Lattice Space. - 5. 4 Bloch Waves and Space Groups. - 5. 5 Application to Semiconductor Materials. - 5. 6 Time Reversal Space Inversion and Double Space Groups. - Summary of Topics for Chapter 5. - Problems. - 6 Atoms in Crystals and Correlation Diagrams. - 6. 1 Central-Field Approximation. - 6. 2 Atoms in Crystal Fields. - 6. 3 Correlation Diagrams. - 6. 4 Electric and Magnetic Material Properties. - 6. 5 Tensors in Group Theory. - Summary of Topics for Chapter 6. - Problems. - 7 Elements of Abstract Algebra and the Galois Group. - 7. 1 IntegralDomains Rings and Fields. - 7. 2 Numbers. - 7. 3 Irreducible Polynomials. - 7. 4 The Galois Group. - Symbols for Chapter 7. - Summary of Topics for Chapter 7. - Problems. - Appendix A: Character Tables for the Point Groups. - Bibliography of Works in Group Theory and Allied Topics. Language: English