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Classical Topology and Combinatorial Group Theory: v. 72 by John Stillwell PDF

By John Stillwell

lately, many scholars were brought to topology in highschool arithmetic. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formulation, and knots, the coed is resulted in anticipate that those picturesque principles will come to complete flower in college topology classes. What a unhappiness "undergraduate topology" proves to be! In so much associations it truly is both a carrier path for analysts, on summary areas, in any other case an creation to homological algebra within which the single geometric task is the of completion of commutative diagrams. images are saved to a minimal, and on the finish the scholar nonetheless does nr~ comprehend the best topological proof, resembling the rcason why knots exist. for my part, a well-balanced creation to topology should still rigidity its intuitive geometric element, whereas admitting the valid curiosity that analysts and algebraists have within the topic. At any price, this is often the purpose of the current booklet. In help of this view, i've got the historic improvement the place manageable, because it in actual fact exhibits the effect of geometric notion in any respect phases. this isn't to assert that topology got its major impetus from geometric recreations just like the seven bridges; fairly, it resulted from the l'isualization of difficulties from different elements of mathematics-complex research (Riemann), mechanics (Poincare), and staff thought (Dehn). it truly is those connec­ tions to different components of arithmetic which make topology a major in addition to a gorgeous subject.

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Classical Topology and Combinatorial Group Theory: v. 72 (Graduate Texts in Mathematics) by John Stillwell

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