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Author: Marco Manetti Publisher: Springer ISBN: 3319169580 Category : Mathematics Languages : en Pages : 315
Book Description
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.
Author: Marco Manetti Publisher: Springer ISBN: 3319169580 Category : Mathematics Languages : en Pages : 315
Book Description
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.
Author: Nicola Fusco Publisher: Springer Nature ISBN: 3031041518 Category : Mathematics Languages : en Pages : 678
Book Description
This work is a textbook on Mathematical Analysis written by expert lecturers in the field. This textbook, other than the classical differentiation and integration tools for functions of several real variables, metric spaces, ordinary differential equations, implicit function and so on, also provides opportunities to go deeper into certain topics: among them, the Ascoli-Arzelà theorem, the regularity of convex functions in R^n, L^p spaces and absolutely continuous functions, all topics that are paramount in modern Mathematical Analysis. Other instances include the Weierstrass theorem on polynomial approximation of continuous functions or Peano's existence theorem (typically only existence, without uniqueness) for nonlinear ODEs and systems under general assumptions. The content is discussed in an elementary way and, at a successive stage, some topics are examined from several, more penetrating, angles. The agile organization of the subject matter helps instructors to effortlessly determine which parts to present during lectures and where to stop. The authors believe that any textbook can contribute to the success of a lecture course only to a point, and the choices made by lecturers are decisive in this respect. The book is addressed to graduate or undergraduate honors students in Mathematics, Physics, Astronomy, Computer Science, Statistics and Probability, attending Mathematical Analysis courses at the Faculties of Science, Engineering, Economics and Architecture.
Author: Lorenzo Peccati Publisher: Springer ISBN: 3030023362 Category : Mathematics Languages : en Pages : 347
Book Description
This book is aimed at students in social sciences programs that include some course in quantitative methods. Stats for social sciences is frequently the subject of textbooks, while maths for social sciences is often neglected: monographs on specific themes (like, for instance, social choice systems or game theory applications) are available, but they do not adequately cover the topic in general. This textbook stems from the Bocconi University’s new "Bachelor in Government", which was launched in 2015, and is intended for undergraduate students who do not exclude maths from their toolbox. It discusses various concrete applications in political economics, political science, sociology, and demography and explores topics like Grexit, Macron’s success, immigration effects and the Arab Spring.
Author: H. Kennedy Publisher: Springer Science & Business Media ISBN: 9400989849 Category : History Languages : en Pages : 238
Book Description
All students of mathematics know of Peano's postulates for the natural numbers and his famous space-filling curve, yet their knowledge often stops there. Part of the reason is that there has not until now been a full-scale study of his life and works. This must surely be surprising, when one realizes the length of his academic career (over 50 years) and the extent of his publica tions (over 200) in a wide variety of fields, many of which had immediate and long-term effects on the development of modern mathematics. A study of his life seems long overdue. It appeared to me that the most likely person to write a biography of Peano would be his devoted disciple Ugo Cassina, with whom I studied at the University of Milan in 1957-58. I wrote to Professor Cassina on 29 October, 1963, inquiring if he planned to write the biography, and I offered him my assistance, since I hoped to return to Italy for a year. He replied on 28 November, 1963, suggesting that we collaborate, meaning by this that I would write the biography, in English, using his material and advice. I gladly agreed to this suggestion, but work on the project had hardly begun when Professor Cassina died unexpectedly on 5 October, 1964. I then decided to continue the project on my own. I spent the academic year 1966-67 in Turin; completion of the book took ten years.
Author: Julian Lowell Coolidge Publisher: Courier Corporation ISBN: 0486158535 Category : Mathematics Languages : en Pages : 484
Book Description
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.
Author: Süleyman ŞENYURT Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 11
Book Description
In this article, we investigate special Smarandache curves with regard to Sabban frame of involute curve. We created Sabban frame belonging to spherical indicatrix of involute curve. It was explained Smarandache curves position vector is consisted by Sabban vectors belonging to spherical indicatrix. Then, we calculated geodesic curvatures of this Smarandache curves. The results found for each curve was given depend on evolute curve. The example related to the subject were given and their figures were drawn with Mapple program.
Author: Marco Manetti
Author: Marco Manetti
Author: Nicola Fusco
Author: Lorenzo Peccati
Author: H. Kennedy
Author: United States. Superintendent of Documents
Author: Alfred North Whitehead
Author: 
Author: CÁNDIDO JUARA ROPERO
Author: Julian Lowell Coolidge
Author: Süleyman ŞENYURT