Combinatorial homotopy and 4-dimensional complexes by Hans Joachim Baues

By Hans Joachim Baues

The objective of the sequence is to offer new and significant advancements in natural and utilized arithmetic. good verified in the neighborhood over twenty years, it bargains a wide library of arithmetic together with numerous vital classics.

The volumes provide thorough and exact expositions of the equipment and concepts necessary to the subjects in query. moreover, they impart their relationships to different components of arithmetic. The sequence is addressed to complex readers wishing to completely examine the topic.

Editorial Board

Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia college, big apple, USA
Markus J. Pflaum, collage of Colorado, Boulder, USA
Dierk Schleicher, Jacobs college, Bremen, Germany

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Sample text

The conditional connective p → q represents the following English constructs: • if p then q • q if p • p only if q • p implies q • q follows from p • q whenever p • p is a sufficient condition for q • q is a necessary condition for p. 2. The biconditional connective p ↔ q represents the following English constructs: • p if and only if q (often written p iff q) • p and q imply each other • p is a necessary and sufficient condition for q • p and q are equivalent. 3. In computer programming and circuit design, the following notation for logical operators is used: p AND q for p ∧ q, p OR q for p ∨ q, NOT p for ¬p, p XOR q for p ⊕ q, p NOR q for p ↓ q, p NAND q for p | q.

After World War II he returned to Princeton as professor of statistics, where he founded the Department of Statistics in 1966. His work in statistics included the areas of spectra of time series and analysis of variance. He invented (with J. W Cooley) the fast Fourier transform. He was awarded the National Medal of Science and served on the President’s Science Advisory Committee. He also coined the word “bit” for a binary digit. Alan Turing (1912–1954) studied mathematics at King’s College, Cambridge and in 1936 invented the concept of a Turing machine to answer the questions of what a computation is and whether a given computation can in fact be carried out.

C 2000 by CRC Press LLC Facts: 1. The conditional connective p → q represents the following English constructs: • if p then q • q if p • p only if q • p implies q • q follows from p • q whenever p • p is a sufficient condition for q • q is a necessary condition for p. 2. The biconditional connective p ↔ q represents the following English constructs: • p if and only if q (often written p iff q) • p and q imply each other • p is a necessary and sufficient condition for q • p and q are equivalent. 3. In computer programming and circuit design, the following notation for logical operators is used: p AND q for p ∧ q, p OR q for p ∨ q, NOT p for ¬p, p XOR q for p ⊕ q, p NOR q for p ↓ q, p NAND q for p | q.

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