Introduction to Topology

Fülszöveg

^ Mathfematidal Loflc
;Yii. ERSHOV, CbrKVMem. UR Acad. Sc?-anij Yu. PALYUTIN, Cand. Sc (Math.)
This book presents in a systematic inanner a number of topics iq; modern mathematical logic and the theory of algorithms. It is i/rtended for uniyersrty and college students .majoring in mathematics, and can be used as both a textbook of mathematical logic and a text for specialist courses, It is based on a course in mathematical logic delivered by the first of the authors,in the Mathematics Department of Nqvosibirsk State Llii|iversity for many-^y^rs. The presentation oVthe propositional calpulus and the calculus of predicates is not traditional, beginning with a * study of sequentiar variants of the calculi of nsiHtral deduction (although the traditional, Hilbertian, calculi also appear here). It gives a good insight into all the-cyles of inference, makes it possible to acquire ,A>iTiore rapidly a h-^bit of nflaking formal proofs, affords a practical ^.sprpqrtunity of making all... Tovább

Fülszöveg

^ Mathfematidal Loflc
;Yii. ERSHOV, CbrKVMem. UR Acad. Sc?-anij Yu. PALYUTIN, Cand. Sc (Math.)
This book presents in a systematic inanner a number of topics iq; modern mathematical logic and the theory of algorithms. It is i/rtended for uniyersrty and college students .majoring in mathematics, and can be used as both a textbook of mathematical logic and a text for specialist courses, It is based on a course in mathematical logic delivered by the first of the authors,in the Mathematics Department of Nqvosibirsk State Llii|iversity for many-^y^rs. The presentation oVthe propositional calpulus and the calculus of predicates is not traditional, beginning with a * study of sequentiar variants of the calculi of nsiHtral deduction (although the traditional, Hilbertian, calculi also appear here). It gives a good insight into all the-cyles of inference, makes it possible to acquire ,A>iTiore rapidly a h-^bit of nflaking formal proofs, affords a practical ^.sprpqrtunity of making all necessary formaliproofs for such calculi. : There arVaTew'ex^^^ virtually after/e^ch section of the-book.
This textbook is a primary manual of topology. It contains the basic concepts and theorems of general topology and homotopy theory, the classification of two-dimensional surfaces, an outline of smooth manifold theory and mappings of smooth manifolds. The book also includes elements of Morse and homology theory with their applications to fixed points. Finally, the role of topology in mathematical analysis, geometry, mechanics and differential equations theory is demonstrated. Originally designed for university students, this textbook may as well be useful to the mathematics teachers and all those who intend to be introduced to the elements of topology. Vissza