Mathematical techniques in crystallography and materials science

1 Matrices: Definition and Fundamental Operations.- 2 Symmetry of Finite Objects.- 3 Symmetry of Infinitely Repeated Patterns.- 4 Vectors.- 5 Tensors.- 6 Data Fitting.- 7 Estimation of Uncertainty.- 8 Significance and Accuracy.- 9 Constrained Crystal Structure Refinement.- Appendix A Eigenvalues and Eigenvectors of 3 × 3 Symmetric Matrices.- Appendix B Stereographic Projection.- Appendix C Sublattices and Superlattices.- Appendix D The Probability Integral, the Gamma Function, and Related Topics.- Appendix E The Harmonic Oscillator in Quantum Mechanics: Bloch's Theorem.- Appendix F Symmetry Restrictions on Second-, Third-, and Fourth-Rank Tensors.- Appendix G Some Useful Computer Programs.