Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. "...an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette. 1952 edition.

System on Chip (SOC) having both digital and analog circuits has become increasingly prevalent in integrated circuit manufacturing industry. Electronic tests are classified as digital, analog and mixed signal. Current methodologies for the testing of digital circuits are well developed. In contrast, methodologies for the testing of analog circuits remain relatively underdeveloped due to the complex nature of analog signals. Compared to digital testing, analog testing lags far behind in methodologies and tools and therefore demands substantial research and development effort.

This book covers all the latest advances, as well as more established methods, in the application of statistical and optimisation methods within modern industry. These include applications from a range of industries that include micro-electronics, chemical, automotive, engineering, food, component assembly, household goods and plastics. Methods range from basic graphical approaches to generalised modelling, from designed experiments to process control. Solutions cover produce and process design, through manufacture to packaging and delivery, from single responses to multivariate problems.

After a classical presentation of quadratic mappings and Clifford algebras over arbitrary rings (commutative, associative, with unit), other topics involve more original methods: interior multiplications allow an effective treatment of deformations of Clifford algebras; the relations between automorphisms of quadratic forms and Clifford algebras are based on the concept of the Lipschitz monoid, from which several groups are derived; and the Cartan-Chevalley theory of hyperbolic spaces becomes much more general, precise and effective.

A straightforward explanation of the abstract principles common to science and mathematics, this helpful volume enables scientists and mathematicians to read and appreciate papers in fields different from their own. Topics include Euclid's algorithm; congruences; polynomials; complex numbers and algebraic fields; algebraic integers, ideals, and p-adic numbers and more. 1960 edition.