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Topology

2015-06-19 Mathematics
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Release : 2015-06-19
Genre : Mathematics
Kind : eBook
Book Rating : 580/5 ( reviews)

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Book Synopsis Topology by : Marco Manetti

Download or read book Topology written by Marco Manetti. This book was released on 2015-06-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Maths for Social Sciences

2018-12-28 Mathematics
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Release : 2018-12-28
Genre : Mathematics
Kind : eBook
Book Rating : 362/5 ( reviews)

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Book Synopsis Maths for Social Sciences by : Lorenzo Peccati

Download or read book Maths for Social Sciences written by Lorenzo Peccati. This book was released on 2018-12-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Principia Mathematica

1910 Logic, Symbolic and mathematical
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Release : 1910
Genre : Logic, Symbolic and mathematical
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Principia Mathematica by : Alfred North Whitehead

Download or read book Principia Mathematica written by Alfred North Whitehead. This book was released on 1910. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Analysis

2023-01-01 Mathematics
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Release : 2023-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 518/5 ( reviews)

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Book Synopsis Mathematical Analysis by : Nicola Fusco

Download or read book Mathematical Analysis written by Nicola Fusco. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Peano

2012-12-06 History
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Release : 2012-12-06
Genre : History
Kind : eBook
Book Rating : 849/5 ( reviews)

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Book Synopsis Peano by : H. Kennedy

Download or read book Peano written by H. Kennedy. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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