This textbook gives a detailed and comprehensive presentation of linear algebra based on an axiomatic treatment of linear spaces. For this fourth edition some new material has been added to the text, for instance, the intrinsic treatment of the classical adjoint of a linear transformation in Chapter IV, as well as the discussion of quaternions and the classifica- tion of associative division algebras in Chapter VII. Chapters XII and XIII have been substantially rewritten for the sake of clarity, but the contents remain basically the same as before. Finally, a number of problems covering new...

Stereochemistry is the part of chemistry that relates observable prop- erties of chemical compounds to the structure of their molecules, i. e. the relative spatial arrangement of their constituent atoms. In classical stereochemistry, the spatial arrangements relevant for interpreting and predicting a given chemical property are customarily described by geometric features/ symmetries in some suitably chosen rigid model of the molecule The solution of stereochemical problems involving single molecular species is the danain of the geometry based approaches, such as the methods of classical...

The first volume of Lecture Notes in Quantum Chemistry (Lecture Notes in Chemistry 58, Springer Verlag, Berlin 1992) contained a compilation of selected lectures given at the two first European Summer Schools in Quantum Chemistry (ESQC), held in southern Sweden in August 1989 and 1991, respectively. The notes were written by the teachers at the school and covered a large range of topics in ab initio quantum chemistry. After the third summer school (held in 1993) it was decided to put together a second volume with additional material. Important lecture material was excluded in the first volume...

Classical circuit theory is a mathematical theory of linear, passive circuits, namely, circuits composed of resistors, capacitors and inductors. Like many a thing classical, it is old and enduring, structured and precise, simple and elegant. It is simple in that everything in it can be deduced from ?rst principles based on a few physical laws. It is enduring in that the things we can say about linear, passive circuits are universally true, unchanging. No matter how complex a circuit may be, as long as it consists of these three kinds of elements, its behavior must be as prescribed by the...

Computers are playing a fundamental role in enhancing exploratory learning techniques in education. This volume in the NATO Special Programme on Advanced Educational Technology covers the state of the art in the design and use of computer systems for exploratory learning. Contributed chapters treat principles, theory, practice, and examples of some of the best contemporary computer-based learning environments: Logo, Boxer, Microworlds, Cabri-Geometre, Star Logo, Table Top, Geomland, spreadsheets, Function Machines, and others. Emphasis is on mathematics and science education. Synthetic...

Until recently quantum chemical ab initio calculations were re- stricted to atoms and very small molecules. As late as in 1960 Allen l and Karo stated: "Almost all of our ab initio experience derives from diatomic LCAO calculations --- N and we have found in the litera- ture "approximately eighty calculations, three-fourths of which are for diatomic molecules --- There are approximately twenty ab initio calculations for molecules with more than two atoms, but there is a decided dividing line between the existing diatomic and polyatomic wave functions. Confidence in the satisfactory evaluation...

This volume features invited lectures presented in the workshop-cum-symposium on aspects of many-body effects in molecules and extended systems, Calcutta, February 1 - 10, 1988. The organizers invited leading experts to present recent developments of many-body methods as applied to molecules and condensed systems. The panorama portrayed is quite broad, but by no means exhaustive. The emphasis is undoubtedly on a "molecular point of view."

We live in a molecular world, almost closed shell in nature, and for this reason Chemistry has been a science dealing with closed shell mol- ecules. However, the high degree of experimental sophistication reached in the past decade has made more apparent the role of open shell structures in chemical research. A parallel phenomenon can be observed in the development of SCF theory, where closed shell molecular calculations at any level of complexity compose the main body of references which can be obtained in Quantum Chemistry today. Besides the linkage between experimental and theoretical...

Molecules in liquid and solid media are exposed to strong inter- action forces from the surrounding medium. The formulation of a comprehensive theory of chemical processes in condensed media is consequently an elaborate task involving concepts from several areas of the natural sciences. Within the las two and a half decades very notable results towards the formulation of a 'unified' quantum mechanical theory of such processes have in fact been achieved, and by the variety of physical, chemical, and biological processes which can be suitably covered by this framework, the new theory represents...

"The second step is to determine constitution, Le. which atoms are bonded to which and by what types of bond. The result is ex- pressed by a planar graph (or the corresponding connectivity mat- rix) ---- In constitutional formulae, the atoms are represented by letters and the bonds by lines. They describe the topology of the molecule." VLADIMIR PRELOG, Nobel Lecture, December l2;h 1975. In the present notes we describe the topological approach to the che- mistry of conjugated molecules using graph-theoretical concepts. Con- jugatedstructures may be conveniently studied using planar and...