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Stillwell is the author of many textbooks and other books on mathematics including: Classical Topology and Combinatorial Group Theory, 1980, ISBN 0-387-97970-0. 2012 pbk reprint of 1993 2nd edition ISBN 978-0-387-97970-0. Mathematics and Its History, 1989, pbk reprint of 2nd edition 2002; 3rd edition 2010, ISBN 0-387-95336-1 [7]
Reverse Mathematics: Proofs from the Inside Out. First edition. Reverse Mathematics: Proofs from the Inside Out is a book by John Stillwell on reverse mathematics, the process of examining proofs in mathematics to determine which axioms are required by the proof. It was published in 2018 by the Princeton University Press. [1][2][3][4][5][6]
"Analysis Situs" is a seminal mathematics paper that Henri Poincaré published in 1895. [1] Poincaré published five supplements to the paper between 1899 and 1904. [2]These papers provided the first systematic treatment of topology and revolutionized the subject by using algebraic structures to distinguish between non-homeomorphic topological spaces, founding the field of algebraic topology. [3]
Recognition problem. The recognition problem is a sub-problem of the homeomorphism problem, in which one simplicial complex is given as a fixed parameter. Given another simplicial complex as an input, the problem is to decide whether it is homeomorphic to the given fixed complex. The recognition problem is decidable for the 3-dimensional sphere.
e. In the mathematical field of geometric topology, the Poincaré conjecture (UK: / ˈpwæ̃kæreɪ /, [2] US: / ˌpwæ̃kɑːˈreɪ /, [3][4] French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured by Henri Poincaré in ...
The algebra of throws was described as "projective arithmetic" by John Stillwell (2005). [9] In a section called "Projective arithmetic", he says The real difficulty is that the construction of a + b, for example, is different from the construction of b + a, so it is a "coincidence" if a + b = b + a.
In the mathematical field of topology, a topological space is usually defined by declaring its open sets. [1] However, this is not necessary, as there are many equivalent axiomatic foundations, each leading to exactly the same concept. For instance, a topological space determines a class of closed sets, of closure and interior operators, and of ...
In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up to continuous (in the compact-open topology) deformation. It is of fundamental importance for the study of 3-manifolds via their embedded ...