PART Ⅰ FINITE GROUPS

Ⅰ．ABSTRACT FINITE GROUPS

1．2．The cyclic group of order

1．3．The dihedral groups

1．4．S-groups

1．5．Permutation groups

1．6．Basic definitions and theorems

Ⅱ．MATRIX ALGEBRA

2．2．Linear operators

2．3．Combinations of operators

2．4．Matrix algebra and group theory

2．5．Non-square matrices

2．6．The theory of vector spaces

2．7．Eigenvectors and eigenvalues

2．8．Functions of a diagonal operator

Ⅲ．COMPLEX AND HYPERCOMPLEX NUMBERS

3．2．Scalar products and vector duals

3．3．Related matrices:(i)the adjoint and reciprocal

3．4．Related matrices:(ii)the transpose and associate

3．5．Related matrices:(iii)orthogonal and unitary matrices

3．6．Eigenvalues of special matrices

3．7．Reciprocal vectors

3．8．Dyads and dyadics

3．9．Linear algebras

3．10．Nomenclature

Ⅳ．CONJUGATION AND EQUIVALENCE

4．2．Conjugation

4．3．Factor groups

4．4．The implications of equivalence

4．5．The algebra of classes

4．6．Oblique axis theory

4．7．Reduction of a matrix to diagonal form

4．8．Functions of an arbitrary operator

Ⅴ．REPRESENTATIONS--THE HEART OF THE MATTER

5．2．Reducibility

5．3．The fundamental theorems

5．4．Some simple corollaries

5．5．Group characters

5．6．Induced and Kronecker product representations

Ⅵ．REVIEW OP GROUPS TO ORDER 24

6．2．Cyclic groups

6．3．S-groups

6．4．Groups up to order 6

6．5．Groups of orders 7 and 8

6．6．Direct product and generalized dihedral groups

6．7．Groups of orders 9 to 24;symmetric groups

Ⅶ．MISCELLANEOUS ADDENDA AND NUMERICAL METHODS

7．2．Matrices not reducible to diagonal form

7．3．Numerical evaluation of determinants

7．4．The reciprocal of a matrix

7．5．Computation of eigenvalues and eigenvectors

7．6．The orthogonality relations

7．7．Operator space

7．8．Some miscellaneous proofs

PART Ⅱ APPLICATIONS OF FINITE GROUPS

Ⅷ．THE EXTERNAL FORMS OF CRYSTALS

8．2．Forms without multiple axes

8．3．Forms with one multiple axis

8．4．Forms with more than one multiple axis

8．5．Graphical representation of symmetry types

Ⅸ．THE INTERNAL STRUCTURE OF CRYSTALS

9．2．The lattice hypothesis

9．3．The three-dimensional point lattices:(i)from lattice to symmetry

9．4．The complete lattice group

9．5．The three-dimensional point lattices:(ii)from symmetry to lattice

9．6．The conventional axes and matrices

9．7．The space groups

9．8．The reciprocal lattice

Ⅹ．THE VIBRATIONS OF MOLECULES

10．2．Procedure for transformation of coordinates

10．3．The normal modes of symmetrical molecules

10．4．The structure of the ozone molecule(i)

10．5．Numerical determination of natural frequencies

Ⅺ．FACTOR ANALYSIS

11．2．The basic problem of factor analysis

11．3．A simple solution

11．4．Correlation and rank

11．5．Correlation and error

11．6．Transformations of the f-space

11．7．Rotation of axes and oblique factors

11．8．Application to the problem of aromatic activity

11．9．Spearman＇s approach

PAST Ⅲ CONTINUOUS GROUPS AND APPLICATIONS

Ⅻ．CONTINUOUS GROUPS:INTRODUCTION

12．2．Representations and characters in continuous groups

12．3．The groups u2 and r3

12．4．Representations of u2 and r3

12．5．The numerical groups

12．6．Infinitesimal operators and the group manifold

12．7．Differential operators and Hilbert space

12．8．Eigenvector theory in Hilbert space

12．9．Functions of two or more variables

ⅩⅢ．THE SYMMETRIC AND FULL LINEAR GROUPS

13．2．The simple symmetric functions

13．3．Relations between the symmetric functions

13．4．The Kronecker mth power

13．5．The simple characters of fn

13．6．The characters of the symmetric groups

13．7．Schur functions

13．8．Further development of Schur functions

13．9．Subgroups of the symmetric and full linear groups

13．10．The spinor group

ⅩⅣ．TENSORS

14．2．The metric tensor

14．3．General notions

14．4．The volume element and the Laplace operator

14．5．Tensor properties of matter:(i)symmetrical tensors

14．6．Tensor properties of matter:(ii)in crystals

14．7．The identification of tensor types

ⅩⅤ．RELATIVITY THEORY

15．2．The Galilean transformation

15．3．The Lorentz group

15．4．The representations of the Lorentz group

15．5．The four-dimensional principle

15．6．Curvature of space

15．7．The basic principles of general relativity

15．8．Relativistic and quantum-relativistic units

ⅩⅥ．QUANTUM THEORY

16．2．The basic postulates

16．3．Vector observables

16．4．The commutation rules and wave functions

16．5．The Schrodinger equations

16．6．The free particle and the simple harmonic oscillator

16．7．Central force fields and spherical harmonics

16．8．Perturbation theory

16．9．Symmetry considerations

16．10．n-Electron systems

ⅩⅦ．MOLECULAR STRUCTURE AND SPECTRA

17．2．Diatomic molecules

17．3．Methods of molecular analysis

17．4．Tetrahedral molecules

17．5．Covalency maxima and stereochemistry

17．6．Unsaturated compounds

17．7．Spectra and selection rules

17．8．The structure of ozone(ii)

17．9．Related problems in crystals

ⅩⅧ．EDDINGTON＇S QUANTUM RELATIVITY

18．2．The nature of measurement

18．3．Measures and measurables

18．4．The E-frame and sedenion algebra

18．5．Rotations and reality conditions

18．6．Anchoring the E-frame

18．7．The primary analysis

18．8．k-Factor theory

18．9．Strain vectors and quantum theory

18．10．The double frame and wave tensors

18．11．The cosmic number

18．12．Conclusions

BIBLIOGRAPHY

INDEX